From e6322472f421aab775c4ae3c5d99775dccab3618 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 28 Oct 2023 11:42:57 +0200 Subject: [PATCH 01/48] Added quantum Bayesian inference --- .../algorithms/inference/__init__.py | 0 .../algorithms/inference/qbayesian.py | 159 ++++++++++++++++++ test/algorithms/inference/__init__.py | 11 ++ test/algorithms/inference/test_qbayesian.py | 95 +++++++++++ 4 files changed, 265 insertions(+) create mode 100644 qiskit_machine_learning/algorithms/inference/__init__.py create mode 100644 qiskit_machine_learning/algorithms/inference/qbayesian.py create mode 100644 test/algorithms/inference/__init__.py create mode 100644 test/algorithms/inference/test_qbayesian.py diff --git a/qiskit_machine_learning/algorithms/inference/__init__.py b/qiskit_machine_learning/algorithms/inference/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py new file mode 100644 index 000000000..10db151b5 --- /dev/null +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -0,0 +1,159 @@ +# This code is part of a Qiskit project. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + + +from qiskit import Aer, QuantumCircuit, transpile +from qiskit.visualization import plot_histogram +from qiskit.circuit import QuantumRegister +from qiskit.circuit.library import GroverOperator + +class QBayesian: + + # Discrete quantum Bayesian network + def __init__(self, circuit: QuantumCircuit = None): + """ + Run the provided quantum circuit on the Aer simulator backend. + + Parameters: + - circuit: The quantum circuit to be executed. + Every r.v. should be assigned exactly one register of one distinct qubit. + The qubits in the circuit should be enumerated by + + """ + # TODO: test if every register contains only one unique qubit + + if circuit is None: + raise ValueError("Quantum circuit must be provided") + + self.circ = circuit + # Label of register mapped to its qubit + self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} + # Label of register mapped to its qubit index + self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} + self.samples = {} + + + def getSe(self, ctrls): + """ + Creates Se for Grover + + ctrls: control qubits represent the evidence var + """ + # Create circuit with registers from given quantum circuit + opSe = QuantumCircuit(*self.circ.qregs) + # Q=X\E + query_var = {self.label2qubit[reg.name] for reg in self.circ.qregs} - set(ctrls) + # Generate Se + for q in query_var: + # multi control z gate + opSe.h(q) + opSe.mcx(ctrls, q) + opSe.h(q) + # x gate + opSe.x(q) + # multi control z gate + opSe.h(q) + opSe.mcx(ctrls, q) + opSe.h(q) + # x gate + opSe.x(q) + return opSe + + def rejectionSampling(self, evidence): + def run_circuit(circuit, shots=10_000): + """ + Run the provided quantum circuit on the Aer simulator backend. + + Parameters: + - circuit: The quantum circuit to be executed. + - shots (default=10,000): The number of times the circuit is executed. + + Returns: + - counts: A dictionary with the counts of each quantum state result. + """ + + # Get the Aer simulator backend + simulator_backend = Aer.get_backend('aer_simulator') + + # Transpile the circuit for the given backend + transpiled_circuit = transpile(circuit, simulator_backend) + + # Run the transpiled circuit on the simulator + job = simulator_backend.run(transpiled_circuit, shots=shots) + result = job.result() + + # Get the counts of quantum state results + counts = result.get_counts(transpiled_circuit) + + return counts + + # Get Se + e_reg = [self.label2qubit[qrg.name] for qrg in self.circ.qregs if qrg.name in evidence] + opSe = self.getSe(e_reg) + # Grover + opG = GroverOperator(opSe, self.circ) + # Amplitude amplification circuit + qregs = self.circ.qregs + qc = QuantumCircuit(*qregs) + qc.append(self.circ, qregs) + qc.append(opG, qregs) + # Measure + qc.measure_all() + # Run circuit + counts = run_circuit(qc) + # Retrieve valid samples + self.samples = {} + # Assume key is bin and e_key is the qubits number + for key, val in counts.items(): + accept = True + for e_key, e_val in evidence.items(): + if int(key[self.label2qidx[e_key]]) != e_val: + accept = False + break + if accept: + self.samples[key] = val + return self.samples + + + def inference(self, query, evidence: dict=None): + """ + - query: The query variables. If Q is a real subset of X\E the rest will be filled + - evidence: Provide evidence if rejection sampling should be executed. If you want to indicate no evidence + insert an empty list. If you want to indicate no new evidence keep this variable empty. + """ + if evidence is not None: + self.rejectionSampling(query, evidence) + else: + if not self.samples: + raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") + + q_count = 0 + tValidS = 0 + for sample_key, sample_val in self.samples.items(): + add = True + for q_key, q_val in query.items(): + if int(sample_key[self.label2qidx[q_key]]) != q_val: + add = False + break + if add: + q_count += sample_val + tValidS += sample_val + return q_count/tValidS + + + def visualize(self): + """Visualizes valid samples""" + return plot_histogram(self.samples) + + + + diff --git a/test/algorithms/inference/__init__.py b/test/algorithms/inference/__init__.py new file mode 100644 index 000000000..def83287c --- /dev/null +++ b/test/algorithms/inference/__init__.py @@ -0,0 +1,11 @@ +# This code is part of a Qiskit project. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py new file mode 100644 index 000000000..18b49682e --- /dev/null +++ b/test/algorithms/inference/test_qbayesian.py @@ -0,0 +1,95 @@ +# This code is part of a Qiskit project. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +import numpy as np +from qiskit_machine_learning.algorithms.inference.qbayesian import QBayesian +from qiskit import Aer, QuantumCircuit, transpile +from qiskit.circuit import QuantumRegister + +def test_ciruit(): + theta_A = 2 * np.arcsin(np.sqrt(0.25)) + theta_B_nA = 2 * np.arcsin(np.sqrt(0.6)) + theta_B_A = 2 * np.arcsin(np.sqrt(0.7)) + theta_C_nBnA = 2 * np.arcsin(np.sqrt(0.1)) + theta_C_nBA = 2 * np.arcsin(np.sqrt(0.55)) + theta_C_BnA = 2 * np.arcsin(np.sqrt(0.7)) + theta_C_BA = 2 * np.arcsin(np.sqrt(0.9)) + + qrA = QuantumRegister(1, name='A') + qrB = QuantumRegister(1, name='B') + qrC = QuantumRegister(1, name='C') + + # Define a 3-qubit quantum circuit + qcA = QuantumCircuit(qrA, qrB, qrC, name="Bayes net") + + # P(A) + qcA.ry(theta_A, 0) + + # P(B|-A) + qcA.x(0) + qcA.cry(theta_B_nA, qrA, qrB) + qcA.x(0) + + # P(B|A) + qcA.cry(theta_B_A, qrA, qrB) + + # P(C|-B,-A) + qcA.x(0) + qcA.x(1) + qcA.mcry(theta_C_nBnA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(0) + qcA.x(1) + + # P(C|-B,A) + qcA.x(1) + qcA.mcry(theta_C_nBA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(1) + + # P(C|B,-A) + qcA.x(0) + qcA.mcry(theta_C_BnA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(0) + + # P(C|B,A) + qcA.mcry(theta_C_BA, [qrA[0], qrB[0]], qrC[0]) + + qcA.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1).show() + # In the order the qubits were added + qubits = qcA.qubits + #print(qubits) + #print(qcA.num_qubits) + #print(qcA.qregs) + qbayesian = QBayesian(qcA) + evidence = {'A': 0, 'C': 0} + #a = qcA.qregs + #print('a: ',a) + #b = [qcA.qregs[0],qcA.qregs[2]] + #print('b: ', b) + #c = list(set(a)-set(b)) + #print(c) + #ctrls = [qrg for qrg in qcA.qregs if qrg.name in evidence] + #print(ctrls) + #for q in c: + # print(q) + # qcA.mcx(ctrls, q) + #print(qcA.qregs[0]) + #qcA.h(qcA.qregs[0]) + #qcA.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1).show() + #qc = QuantumCircuit(*qcA.qregs) + #test_cases = [format(i, '03b') for i in range(8)] + samples = qbayesian.rejectionSampling(evidence=evidence) + + query = {'B': 1} + print(qbayesian.inference(query)) + print(samples) + +test_ciruit() From d1ccc0ec2d7a4a7abfb2969d916d639e4292c71f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 28 Oct 2023 13:29:56 +0200 Subject: [PATCH 02/48] Allowed inference with no evidence --- .../algorithms/inference/qbayesian.py | 47 +++--- test/algorithms/inference/test_qbayesian.py | 141 +++++++++--------- 2 files changed, 91 insertions(+), 97 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 10db151b5..86cf3f28f 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -13,27 +13,20 @@ from qiskit import Aer, QuantumCircuit, transpile from qiskit.visualization import plot_histogram -from qiskit.circuit import QuantumRegister from qiskit.circuit.library import GroverOperator class QBayesian: # Discrete quantum Bayesian network - def __init__(self, circuit: QuantumCircuit = None): + def __init__(self, circuit: QuantumCircuit): """ Run the provided quantum circuit on the Aer simulator backend. Parameters: - circuit: The quantum circuit to be executed. Every r.v. should be assigned exactly one register of one distinct qubit. - The qubits in the circuit should be enumerated by """ - # TODO: test if every register contains only one unique qubit - - if circuit is None: - raise ValueError("Quantum circuit must be provided") - self.circ = circuit # Label of register mapped to its qubit self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} @@ -68,8 +61,8 @@ def getSe(self, ctrls): opSe.x(q) return opSe - def rejectionSampling(self, evidence): - def run_circuit(circuit, shots=10_000): + def rejectionSampling(self, evidence, shots: int=None): + def run_circuit(circuit, shots=100_000): """ Run the provided quantum circuit on the Aer simulator backend. @@ -80,7 +73,7 @@ def run_circuit(circuit, shots=10_000): Returns: - counts: A dictionary with the counts of each quantum state result. """ - + print(shots) # Get the Aer simulator backend simulator_backend = Aer.get_backend('aer_simulator') @@ -96,22 +89,27 @@ def run_circuit(circuit, shots=10_000): return counts - # Get Se + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) + # Amplitude amplification circuit if evidence not empty e_reg = [self.label2qubit[qrg.name] for qrg in self.circ.qregs if qrg.name in evidence] - opSe = self.getSe(e_reg) - # Grover - opG = GroverOperator(opSe, self.circ) - # Amplitude amplification circuit - qregs = self.circ.qregs - qc = QuantumCircuit(*qregs) - qc.append(self.circ, qregs) - qc.append(opG, qregs) + if len(e_reg) != 0: + # Get Se + opSe = self.getSe(e_reg) + # Grover + opG = GroverOperator(opSe, self.circ) + qc.append(opG, self.circ.qregs) # Measure qc.measure_all() # Run circuit - counts = run_circuit(qc) + if shots is None: + counts = run_circuit(qc) + else: + counts = run_circuit(qc, shots) # Retrieve valid samples self.samples = {} + re=0 # Assume key is bin and e_key is the qubits number for key, val in counts.items(): accept = True @@ -121,17 +119,20 @@ def run_circuit(circuit, shots=10_000): break if accept: self.samples[key] = val + else: + re+=val + print(re) return self.samples - def inference(self, query, evidence: dict=None): + def inference(self, query, evidence: dict=None, shots: int=None): """ - query: The query variables. If Q is a real subset of X\E the rest will be filled - evidence: Provide evidence if rejection sampling should be executed. If you want to indicate no evidence insert an empty list. If you want to indicate no new evidence keep this variable empty. """ if evidence is not None: - self.rejectionSampling(query, evidence) + self.rejectionSampling(query, evidence, shots) else: if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 18b49682e..c7d153447 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -11,85 +11,78 @@ # that they have been altered from the originals. import numpy as np +import unittest +from test import QiskitMachineLearningTestCase +from qiskit_algorithms.utils import algorithm_globals from qiskit_machine_learning.algorithms.inference.qbayesian import QBayesian -from qiskit import Aer, QuantumCircuit, transpile +from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister -def test_ciruit(): - theta_A = 2 * np.arcsin(np.sqrt(0.25)) - theta_B_nA = 2 * np.arcsin(np.sqrt(0.6)) - theta_B_A = 2 * np.arcsin(np.sqrt(0.7)) - theta_C_nBnA = 2 * np.arcsin(np.sqrt(0.1)) - theta_C_nBA = 2 * np.arcsin(np.sqrt(0.55)) - theta_C_BnA = 2 * np.arcsin(np.sqrt(0.7)) - theta_C_BA = 2 * np.arcsin(np.sqrt(0.9)) +class TestQBayesianInference(QiskitMachineLearningTestCase): + """Test QBayesianInference Algorithm""" + def setUp(self): + super().setUp() + algorithm_globals.random_seed = 10598 + # Probabilities + theta_A = 2 * np.arcsin(np.sqrt(0.25)) + theta_B_nA = 2 * np.arcsin(np.sqrt(0.6)) + theta_B_A = 2 * np.arcsin(np.sqrt(0.7)) + theta_C_nBnA = 2 * np.arcsin(np.sqrt(0.1)) + theta_C_nBA = 2 * np.arcsin(np.sqrt(0.55)) + theta_C_BnA = 2 * np.arcsin(np.sqrt(0.7)) + theta_C_BA = 2 * np.arcsin(np.sqrt(0.9)) + # Random variables + qrA = QuantumRegister(1, name='A') + qrB = QuantumRegister(1, name='B') + qrC = QuantumRegister(1, name='C') + # Define a 3-qubit quantum circuit + qcA = QuantumCircuit(qrA, qrB, qrC, name="Bayes net") + # P(A) + qcA.ry(theta_A, 0) + # P(B|-A) + qcA.x(0) + qcA.cry(theta_B_nA, qrA, qrB) + qcA.x(0) + # P(B|A) + qcA.cry(theta_B_A, qrA, qrB) + # P(C|-B,-A) + qcA.x(0) + qcA.x(1) + qcA.mcry(theta_C_nBnA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(0) + qcA.x(1) + # P(C|-B,A) + qcA.x(1) + qcA.mcry(theta_C_nBA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(1) + # P(C|B,-A) + qcA.x(0) + qcA.mcry(theta_C_BnA, [qrA[0], qrB[0]], qrC[0]) + qcA.x(0) + # P(C|B,A) + qcA.mcry(theta_C_BA, [qrA[0], qrB[0]], qrC[0]) + # Quantum Bayesian inference + self.qbayesian = QBayesian(qcA) - qrA = QuantumRegister(1, name='A') - qrB = QuantumRegister(1, name='B') - qrC = QuantumRegister(1, name='C') - # Define a 3-qubit quantum circuit - qcA = QuantumCircuit(qrA, qrB, qrC, name="Bayes net") + def test_rejection_sampling(self): + """Test rejection sampling with different amount of evidence""" + test_cases = [{'A': 0, 'B': 0}, {'A': 0}, {}] + true_res = [ + {'000': 2700, '001': 300}, + {'011': 1763, '001': 3504, '010': 13483, '000': 26948}, + {'100': 3042, '110': 31606, '001': 3341, '011': 1731, '111': 15653, '010': 13511, '000': 27109, '101': 4007} + ] + for e in test_cases: + samples = self.qbayesian.rejectionSampling(evidence=e) - # P(A) - qcA.ry(theta_A, 0) + print(samples) + #self.assertTrue(np.all(samples>0)) + def test_inference(self): + ... - # P(B|-A) - qcA.x(0) - qcA.cry(theta_B_nA, qrA, qrB) - qcA.x(0) + def test_parameter(self): + ... - # P(B|A) - qcA.cry(theta_B_A, qrA, qrB) - - # P(C|-B,-A) - qcA.x(0) - qcA.x(1) - qcA.mcry(theta_C_nBnA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(0) - qcA.x(1) - - # P(C|-B,A) - qcA.x(1) - qcA.mcry(theta_C_nBA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(1) - - # P(C|B,-A) - qcA.x(0) - qcA.mcry(theta_C_BnA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(0) - - # P(C|B,A) - qcA.mcry(theta_C_BA, [qrA[0], qrB[0]], qrC[0]) - - qcA.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1).show() - # In the order the qubits were added - qubits = qcA.qubits - #print(qubits) - #print(qcA.num_qubits) - #print(qcA.qregs) - qbayesian = QBayesian(qcA) - evidence = {'A': 0, 'C': 0} - #a = qcA.qregs - #print('a: ',a) - #b = [qcA.qregs[0],qcA.qregs[2]] - #print('b: ', b) - #c = list(set(a)-set(b)) - #print(c) - #ctrls = [qrg for qrg in qcA.qregs if qrg.name in evidence] - #print(ctrls) - #for q in c: - # print(q) - # qcA.mcx(ctrls, q) - #print(qcA.qregs[0]) - #qcA.h(qcA.qregs[0]) - #qcA.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1).show() - #qc = QuantumCircuit(*qcA.qregs) - #test_cases = [format(i, '03b') for i in range(8)] - samples = qbayesian.rejectionSampling(evidence=evidence) - - query = {'B': 1} - print(qbayesian.inference(query)) - print(samples) - -test_ciruit() +if __name__ == "__main__": + unittest.main() From e3c12876c9e280f9a788964c35f3f2b480ca4d5e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 28 Oct 2023 21:51:39 +0200 Subject: [PATCH 03/48] Passed inference test --- .../algorithms/inference/qbayesian.py | 4 +++- test/algorithms/inference/test_qbayesian.py | 17 ++++++++++++++++- 2 files changed, 19 insertions(+), 2 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 86cf3f28f..29b989df6 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -106,6 +106,7 @@ def run_circuit(circuit, shots=100_000): if shots is None: counts = run_circuit(qc) else: + print("here") counts = run_circuit(qc, shots) # Retrieve valid samples self.samples = {} @@ -121,6 +122,7 @@ def run_circuit(circuit, shots=100_000): self.samples[key] = val else: re+=val + print(counts) print(re) return self.samples @@ -132,7 +134,7 @@ def inference(self, query, evidence: dict=None, shots: int=None): insert an empty list. If you want to indicate no new evidence keep this variable empty. """ if evidence is not None: - self.rejectionSampling(query, evidence, shots) + self.rejectionSampling(evidence, shots) else: if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index c7d153447..cefc847c9 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -11,6 +11,7 @@ # that they have been altered from the originals. import numpy as np +import math import unittest from test import QiskitMachineLearningTestCase from qiskit_algorithms.utils import algorithm_globals @@ -79,7 +80,21 @@ def test_rejection_sampling(self): print(samples) #self.assertTrue(np.all(samples>0)) def test_inference(self): - ... + test_q_1, test_e_1 = ({'B': 1}, {'A': 1, 'C': 1}) + test_q_2 = {'B': 0} + true_res = [0.79, 0.21] + res = [] + samples = [] + # 1. Query + res.append(self.qbayesian.inference(query=test_q_1, evidence=test_e_1)) + samples.append(self.qbayesian.samples) + # 2. Query + res.append(self.qbayesian.inference(query=test_q_2)) + samples.append(self.qbayesian.samples) + # Correct inference + self.assertTrue(np.all(np.isclose(true_res, res, rtol=0.05))) + # No change in samples + self.assertTrue(samples[0] == samples[1]) def test_parameter(self): ... From 143ef3a9dbd83dc9e7dc9d69b825561de6b05896 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Wed, 1 Nov 2023 20:23:03 +0100 Subject: [PATCH 04/48] Passed inference test --- .../algorithms/inference/qbayesian.py | 88 ++++++++----------- 1 file changed, 39 insertions(+), 49 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 29b989df6..7ecd71664 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -9,11 +9,14 @@ # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. - - +import numpy as np from qiskit import Aer, QuantumCircuit, transpile from qiskit.visualization import plot_histogram -from qiskit.circuit.library import GroverOperator +from qiskit.quantum_info import Statevector +from qiskit.algorithms import AmplificationProblem +from qiskit.primitives import Sampler +from qiskit_algorithms import Grover +from qiskit.primitives import Sampler class QBayesian: @@ -35,33 +38,27 @@ def __init__(self, circuit: QuantumCircuit): self.samples = {} - def getSe(self, ctrls): + def getAmplifyPrb(self, evidence): """ - Creates Se for Grover + Creates Amplification Problem - ctrls: control qubits represent the evidence var + evidence: ... """ - # Create circuit with registers from given quantum circuit - opSe = QuantumCircuit(*self.circ.qregs) - # Q=X\E - query_var = {self.label2qubit[reg.name] for reg in self.circ.qregs} - set(ctrls) - # Generate Se - for q in query_var: - # multi control z gate - opSe.h(q) - opSe.mcx(ctrls, q) - opSe.h(q) - # x gate - opSe.x(q) - # multi control z gate - opSe.h(q) - opSe.mcx(ctrls, q) - opSe.h(q) - # x gate - opSe.x(q) - return opSe - - def rejectionSampling(self, evidence, shots: int=None): + # Evidence to qubit index + e_idx = [self.label2qidx[e] for e in evidence].sort() + # Binary format of good states + bin_str = [format(i, f'0{(self.circ.num_qubits-len(e_idx))}b') for i in range(2**(self.circ.num_qubits-len(e_idx)))] + # Get good states + good_states = [] + for b in bin_str: + for e in e_idx: + good_states.append(b[:e]+evidence[e]+b[:e]) + # Get statevector by transform good states like 010 regarding its idx (2+1=3) of statevector to 1 and o/w to 0 + oracle = Statevector([(format(i, f'0{self.circ.num_qubits}b') in good_states) for i in range(2**self.circ.num_qubits)]) + return AmplificationProblem(oracle, state_preparation=self.circ, is_good_state=good_states) + + + def rejectionSampling(self, evidence, shots: int=None, grover_iter=None, backend=None): def run_circuit(circuit, shots=100_000): """ Run the provided quantum circuit on the Aer simulator backend. @@ -89,28 +86,25 @@ def run_circuit(circuit, shots=100_000): return counts - # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) + # If evidence is empty + if len(evidence) == 0: + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) + # Measure + qc.measure_all() + # Run circuit + samples = run_circuit(qc, shots) + return samples + # Amplitude amplification circuit if evidence not empty - e_reg = [self.label2qubit[qrg.name] for qrg in self.circ.qregs if qrg.name in evidence] - if len(e_reg) != 0: - # Get Se - opSe = self.getSe(e_reg) - # Grover - opG = GroverOperator(opSe, self.circ) - qc.append(opG, self.circ.qregs) - # Measure - qc.measure_all() + ampPrb = self.getAmplifyPrb(evidence) + # Grover with default number of iterations given by good states from amplitude amplification problem + grover = Grover(Sampler(shots)) # Run circuit - if shots is None: - counts = run_circuit(qc) - else: - print("here") - counts = run_circuit(qc, shots) + counts = grover.amplify(ampPrb) # Retrieve valid samples self.samples = {} - re=0 # Assume key is bin and e_key is the qubits number for key, val in counts.items(): accept = True @@ -120,10 +114,6 @@ def run_circuit(circuit, shots=100_000): break if accept: self.samples[key] = val - else: - re+=val - print(counts) - print(re) return self.samples From 42eb77a5aac556e3baef8a014dd4e6a38813584a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 3 Nov 2023 19:03:47 +0100 Subject: [PATCH 05/48] Works with AmplitudeProblem algorithm --- .../algorithms/inference/qbayesian.py | 41 +++++++++++++------ test/algorithms/inference/test_qbayesian.py | 1 - 2 files changed, 29 insertions(+), 13 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 7ecd71664..3974a85fc 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -14,7 +14,6 @@ from qiskit.visualization import plot_histogram from qiskit.quantum_info import Statevector from qiskit.algorithms import AmplificationProblem -from qiskit.primitives import Sampler from qiskit_algorithms import Grover from qiskit.primitives import Sampler @@ -44,22 +43,33 @@ def getAmplifyPrb(self, evidence): evidence: ... """ - # Evidence to qubit index - e_idx = [self.label2qidx[e] for e in evidence].sort() + # Evidence to reversed qubit index sorted by index + num_qubits = self.circ.num_qubits + e2idx = sorted( + [(num_qubits-self.label2qidx[e_key]-1, e_val) for e_key, e_val in evidence.items()], key=lambda x: x[0] + ) # Binary format of good states - bin_str = [format(i, f'0{(self.circ.num_qubits-len(e_idx))}b') for i in range(2**(self.circ.num_qubits-len(e_idx)))] + num_evd = len(e2idx) + bin_str = [format(i, f'0{(num_qubits-num_evd)}b') for i in range(2**(num_qubits-num_evd))] # Get good states good_states = [] + print(bin_str) for b in bin_str: - for e in e_idx: - good_states.append(b[:e]+evidence[e]+b[:e]) + for e_idx, e_val in e2idx: + b = b[:e_idx]+str(e_val)+b[e_idx:] + good_states.append(b) + print(evidence) + print("GOOD states") + print(good_states) # Get statevector by transform good states like 010 regarding its idx (2+1=3) of statevector to 1 and o/w to 0 - oracle = Statevector([(format(i, f'0{self.circ.num_qubits}b') in good_states) for i in range(2**self.circ.num_qubits)]) + print([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) + oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) return AmplificationProblem(oracle, state_preparation=self.circ, is_good_state=good_states) def rejectionSampling(self, evidence, shots: int=None, grover_iter=None, backend=None): def run_circuit(circuit, shots=100_000): + # TODO: needed?? """ Run the provided quantum circuit on the Aer simulator backend. @@ -70,7 +80,6 @@ def run_circuit(circuit, shots=100_000): Returns: - counts: A dictionary with the counts of each quantum state result. """ - print(shots) # Get the Aer simulator backend simulator_backend = Aer.get_backend('aer_simulator') @@ -100,16 +109,24 @@ def run_circuit(circuit, shots=100_000): # Amplitude amplification circuit if evidence not empty ampPrb = self.getAmplifyPrb(evidence) # Grover with default number of iterations given by good states from amplitude amplification problem - grover = Grover(Sampler(shots)) + grover = Grover(sampler=Sampler()) # Run circuit - counts = grover.amplify(ampPrb) + a=grover.amplify(ampPrb) + print(a.circuit_results) + print(a.circuit_results[0]) + #TODO why multiple results here + #print(grover.amplify(ampPrb).iterations) + #print(grover.amplify(ampPrb).max_probability) + counts = grover.amplify(ampPrb).circuit_results[-1] + print("Result is ") + print(counts) # Retrieve valid samples self.samples = {} - # Assume key is bin and e_key is the qubits number for key, val in counts.items(): accept = True for e_key, e_val in evidence.items(): - if int(key[self.label2qidx[e_key]]) != e_val: + # Check if evidence fits with sample + if int(key[self.circ.num_qubits-self.label2qidx[e_key]-1]) != e_val: accept = False break if accept: diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index cefc847c9..4b9cd9fa6 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -76,7 +76,6 @@ def test_rejection_sampling(self): ] for e in test_cases: samples = self.qbayesian.rejectionSampling(evidence=e) - print(samples) #self.assertTrue(np.all(samples>0)) def test_inference(self): From cd976ba25e3dc71205c38b7ba68238c1e91d1716 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 4 Nov 2023 13:57:12 +0100 Subject: [PATCH 06/48] Run GroverOperator until it matches all evidence --- .../algorithms/inference/qbayesian.py | 69 +++++++++++++------ 1 file changed, 49 insertions(+), 20 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 3974a85fc..29c1cbe49 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -10,12 +10,10 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. import numpy as np -from qiskit import Aer, QuantumCircuit, transpile +from qiskit import Aer, QuantumCircuit, transpile, QuantumRegister, ClassicalRegister from qiskit.visualization import plot_histogram from qiskit.quantum_info import Statevector -from qiskit.algorithms import AmplificationProblem -from qiskit_algorithms import Grover -from qiskit.primitives import Sampler +from qiskit.circuit.library import GroverOperator class QBayesian: @@ -36,8 +34,7 @@ def __init__(self, circuit: QuantumCircuit): self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} self.samples = {} - - def getAmplifyPrb(self, evidence): + def getGroverOp(self, evidence): """ Creates Amplification Problem @@ -64,7 +61,7 @@ def getAmplifyPrb(self, evidence): # Get statevector by transform good states like 010 regarding its idx (2+1=3) of statevector to 1 and o/w to 0 print([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) - return AmplificationProblem(oracle, state_preparation=self.circ, is_good_state=good_states) + return GroverOperator(oracle, state_preparation=self.circ) def rejectionSampling(self, evidence, shots: int=None, grover_iter=None, backend=None): @@ -95,29 +92,61 @@ def run_circuit(circuit, shots=100_000): return counts + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) # If evidence is empty if len(evidence) == 0: - # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) # Measure qc.measure_all() # Run circuit samples = run_circuit(qc, shots) return samples + else: + # Get grover operator if evidence not empty + groverOp = self.getGroverOp(evidence) + # Amplitude amplification + e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} + E = {} + k=-1 + # If the measurement of the evidence qubits matches the evidence stop + while e!=E: + # Increment power + k += 1 + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) + # Apply grover operator 2^k times + qcGrover = QuantumCircuit(*self.circ.qregs) + qcGrover.append(groverOp, self.circ.qregs) + qcGrover = qcGrover.power(2**k) + qc.append(qcGrover, self.circ.qregs) + # Create a classical register with the size of the evidence + measurement_cr = ClassicalRegister(len(evidence)) + qc.add_register(measurement_cr) + # Map the evidence qubits to the classical bits and measure them + evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] + qc.measure([q for q in evidence_qubits], measurement_cr) + # Run the circuit with the Grover operator and measurements + e_samples = run_circuit(qc, shots=1024) + E_count = {self.label2qubit[e]: 0 for e in evidence} + for e_sample_key, e_sample_val in e_samples.items(): + # Go through reverse binary that matches order of qubits + for i, char in enumerate(e_sample_key[::-1]): + if int(char) == 1: + E_count[evidence_qubits[i]] += e_sample_val + else: + E_count[evidence_qubits[i]] += -e_sample_val + # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 + E = {e_count_key: int(e_count_val >= 0) for e_count_key, e_count_val in E_count.items()} + + + # TODO: measure query variables and return their count - # Amplitude amplification circuit if evidence not empty - ampPrb = self.getAmplifyPrb(evidence) # Grover with default number of iterations given by good states from amplitude amplification problem - grover = Grover(sampler=Sampler()) + counts = {} # Run circuit - a=grover.amplify(ampPrb) - print(a.circuit_results) - print(a.circuit_results[0]) - #TODO why multiple results here - #print(grover.amplify(ampPrb).iterations) - #print(grover.amplify(ampPrb).max_probability) - counts = grover.amplify(ampPrb).circuit_results[-1] + print("Result is ") print(counts) # Retrieve valid samples From 0922e90053aae51742b18b12a12077d2d4eea1e9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 4 Nov 2023 18:20:39 +0100 Subject: [PATCH 07/48] Quantum rejection sampling with GroverOperator --- .../algorithms/inference/qbayesian.py | 61 ++++++++++++------- 1 file changed, 38 insertions(+), 23 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 29c1cbe49..fb6a07715 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -10,7 +10,7 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. import numpy as np -from qiskit import Aer, QuantumCircuit, transpile, QuantumRegister, ClassicalRegister +from qiskit import Aer, QuantumCircuit, transpile, ClassicalRegister from qiskit.visualization import plot_histogram from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator @@ -110,7 +110,7 @@ def run_circuit(circuit, shots=100_000): E = {} k=-1 # If the measurement of the evidence qubits matches the evidence stop - while e!=E: + while (e != E) or (k > 10): # Increment power k += 1 # Create circuit @@ -121,14 +121,17 @@ def run_circuit(circuit, shots=100_000): qcGrover.append(groverOp, self.circ.qregs) qcGrover = qcGrover.power(2**k) qc.append(qcGrover, self.circ.qregs) + # Add quantum circuit for measuring + qc_measure = QuantumCircuit(*self.circ.qregs) + qc_measure.append(qc, self.circ.qregs) # Create a classical register with the size of the evidence - measurement_cr = ClassicalRegister(len(evidence)) - qc.add_register(measurement_cr) + measurement_ecr = ClassicalRegister(len(evidence)) + qc_measure.add_register(measurement_ecr) # Map the evidence qubits to the classical bits and measure them evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] - qc.measure([q for q in evidence_qubits], measurement_cr) + qc_measure.measure([q for q in evidence_qubits], measurement_ecr) # Run the circuit with the Grover operator and measurements - e_samples = run_circuit(qc, shots=1024) + e_samples = run_circuit(qc_measure, shots=1024) E_count = {self.label2qubit[e]: 0 for e in evidence} for e_sample_key, e_sample_val in e_samples.items(): # Go through reverse binary that matches order of qubits @@ -138,28 +141,40 @@ def run_circuit(circuit, shots=100_000): else: E_count[evidence_qubits[i]] += -e_sample_val # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 - E = {e_count_key: int(e_count_val >= 0) for e_count_key, e_count_val in E_count.items()} - - - # TODO: measure query variables and return their count - - # Grover with default number of iterations given by good states from amplitude amplification problem - counts = {} + E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} + + print(k) + + # Create a classical register with the size of the evidence + measurement_qcr = ClassicalRegister(self.circ.num_qubits-len(evidence)) + qc.add_register(measurement_qcr) + # Map the query qubits to the classical bits and measure them + query_qubits = [(label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if label not in evidence] + query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1]) + # Measure query variables and return their count + qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit - - print("Result is ") + counts = run_circuit(qc, shots=100000) + print("Counts") print(counts) + # Build default string with evidence + query_string = '' + varIdxSorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] + for var in varIdxSorted: + if var in evidence: + query_string += str(evidence[var]) + else: + query_string += 'q' # Retrieve valid samples self.samples = {} + # Replace placeholder q with query variables from samples for key, val in counts.items(): - accept = True - for e_key, e_val in evidence.items(): - # Check if evidence fits with sample - if int(key[self.circ.num_qubits-self.label2qidx[e_key]-1]) != e_val: - accept = False - break - if accept: - self.samples[key] = val + query = query_string + for char in key: + query=query.replace('q', char, 1) + self.samples[query] = val + print('samples') + print(self.samples) return self.samples From 72d2294056ba6be86302264972a68168f1afd87f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 5 Nov 2023 17:30:56 +0100 Subject: [PATCH 08/48] Quantum Bayesian inference --- .../algorithms/inference/qbayesian.py | 105 +++++++++++------- test/algorithms/inference/test_qbayesian.py | 37 ++++-- 2 files changed, 91 insertions(+), 51 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index fb6a07715..b6439c960 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -10,12 +10,43 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. import numpy as np -from qiskit import Aer, QuantumCircuit, transpile, ClassicalRegister -from qiskit.visualization import plot_histogram +from qiskit import QuantumCircuit, transpile, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator +from qiskit_aer import AerSimulator + +"""Quantum Bayesian Inference""" class QBayesian: + r""" + Implements Quantum Bayesian Inference algorithm. The algorithm has been developed in [1] + and includes methods ``getGroverOp``, ``rejectionSampling`` and ``inference``. + + **References** + [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. + "Quantum inference on Bayesian networks." Physical Review A 89.6 (2014): 062315. + + + Usage: + ------ + To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. + You can then use the `inference` method to estimate probabilities given evidence, optionally using + rejection sampling and Grover's algorithm for amplification. + + Example: + -------- + + # Define a quantum circuit + qc = QuantumCircuit(...) + + # Initialize the QBayesian class with the circuit + qb = QBayesian(qc) + + # Perform inference + result = qb.inference(query={...}, evidence={...}) + + print("Probability of query given evidence:", result) + """ # Discrete quantum Bayesian network def __init__(self, circuit: QuantumCircuit): @@ -27,6 +58,11 @@ def __init__(self, circuit: QuantumCircuit): Every r.v. should be assigned exactly one register of one distinct qubit. """ + # Test valid input + for qrg in circuit.qregs: + if qrg.size>1: + raise ValueError("Every register needs to be mapped to exactly one unique qubit") + # Initialize QBayesian self.circ = circuit # Label of register mapped to its qubit self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} @@ -34,7 +70,7 @@ def __init__(self, circuit: QuantumCircuit): self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} self.samples = {} - def getGroverOp(self, evidence): + def getGroverOp(self, evidence: dict): """ Creates Amplification Problem @@ -50,23 +86,19 @@ def getGroverOp(self, evidence): bin_str = [format(i, f'0{(num_qubits-num_evd)}b') for i in range(2**(num_qubits-num_evd))] # Get good states good_states = [] - print(bin_str) for b in bin_str: for e_idx, e_val in e2idx: b = b[:e_idx]+str(e_val)+b[e_idx:] good_states.append(b) - print(evidence) - print("GOOD states") - print(good_states) # Get statevector by transform good states like 010 regarding its idx (2+1=3) of statevector to 1 and o/w to 0 - print([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) return GroverOperator(oracle, state_preparation=self.circ) - def rejectionSampling(self, evidence, shots: int=None, grover_iter=None, backend=None): + def rejectionSampling(self, evidence: dict, + shots: int=None, + grover_iter=None): def run_circuit(circuit, shots=100_000): - # TODO: needed?? """ Run the provided quantum circuit on the Aer simulator backend. @@ -78,29 +110,27 @@ def run_circuit(circuit, shots=100_000): - counts: A dictionary with the counts of each quantum state result. """ # Get the Aer simulator backend - simulator_backend = Aer.get_backend('aer_simulator') - + simulator_backend = AerSimulator() # Transpile the circuit for the given backend transpiled_circuit = transpile(circuit, simulator_backend) - # Run the transpiled circuit on the simulator job = simulator_backend.run(transpiled_circuit, shots=shots) result = job.result() - # Get the counts of quantum state results counts = result.get_counts(transpiled_circuit) + # Convert counts to relative counts (probabilities) + relative_counts = {state: count / shots for state, count in counts.items()} + return relative_counts - return counts - - # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) # If evidence is empty if len(evidence) == 0: + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) # Measure qc.measure_all() # Run circuit - samples = run_circuit(qc, shots) + samples = run_circuit(qc, shots=100000) return samples else: # Get grover operator if evidence not empty @@ -110,7 +140,7 @@ def run_circuit(circuit, shots=100_000): E = {} k=-1 # If the measurement of the evidence qubits matches the evidence stop - while (e != E) or (k > 10): + while (e != E) and (k < 10): # Increment power k += 1 # Create circuit @@ -140,11 +170,10 @@ def run_circuit(circuit, shots=100_000): E_count[evidence_qubits[i]] += e_sample_val else: E_count[evidence_qubits[i]] += -e_sample_val + # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} - print(k) - # Create a classical register with the size of the evidence measurement_qcr = ClassicalRegister(self.circ.num_qubits-len(evidence)) qc.add_register(measurement_qcr) @@ -155,8 +184,6 @@ def run_circuit(circuit, shots=100_000): qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit counts = run_circuit(qc, shots=100000) - print("Counts") - print(counts) # Build default string with evidence query_string = '' varIdxSorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] @@ -171,16 +198,14 @@ def run_circuit(circuit, shots=100_000): for key, val in counts.items(): query = query_string for char in key: - query=query.replace('q', char, 1) + query = query.replace('q', char, 1) self.samples[query] = val - print('samples') - print(self.samples) return self.samples - def inference(self, query, evidence: dict=None, shots: int=None): + def inference(self, query: dict, evidence: dict=None, shots: int=None): """ - - query: The query variables. If Q is a real subset of X\E the rest will be filled + - query: The query variables. If Q is a real subset of X\E, it will be marginalized. - evidence: Provide evidence if rejection sampling should be executed. If you want to indicate no evidence insert an empty list. If you want to indicate no new evidence keep this variable empty. """ @@ -190,23 +215,23 @@ def inference(self, query, evidence: dict=None, shots: int=None): if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") - q_count = 0 - tValidS = 0 + + # Get probability of query + query_indices = [(self.label2qidx[q_key], q_val) for q_key, q_val in query.items()] + query_indices_sorted = sorted(query_indices, key=lambda x: x[0], reverse=True) + # Get probability of query + res = 0 for sample_key, sample_val in self.samples.items(): add = True - for q_key, q_val in query.items(): - if int(sample_key[self.label2qidx[q_key]]) != q_val: + for q_idx, q_val in query_indices_sorted: + if int(sample_key[q_idx]) != q_val: add = False break if add: - q_count += sample_val - tValidS += sample_val - return q_count/tValidS + res += sample_val + return res - def visualize(self): - """Visualizes valid samples""" - return plot_histogram(self.samples) diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 4b9cd9fa6..460ba60f7 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -70,33 +70,48 @@ def test_rejection_sampling(self): """Test rejection sampling with different amount of evidence""" test_cases = [{'A': 0, 'B': 0}, {'A': 0}, {}] true_res = [ - {'000': 2700, '001': 300}, - {'011': 1763, '001': 3504, '010': 13483, '000': 26948}, - {'100': 3042, '110': 31606, '001': 3341, '011': 1731, '111': 15653, '010': 13511, '000': 27109, '101': 4007} + {'000': 0.9, '100': 0.1}, + {'000': 0.36, '100': 0.04, '010': 0.18, '110': 0.42}, + {'000': 0.27, '001': 0.03375, '010': 0.135, '011': 0.0175, + '100': 0.03, '101': 0.04125, '110': 0.315, '111': 0.1575} ] - for e in test_cases: - samples = self.qbayesian.rejectionSampling(evidence=e) - print(samples) - #self.assertTrue(np.all(samples>0)) + for e, res in zip(test_cases, true_res): + samples = self.qbayesian.rejectionSampling(evidence=e, shots=100000) + self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.1) + for sample_key, sample_val in samples.items()])) + def test_inference(self): test_q_1, test_e_1 = ({'B': 1}, {'A': 1, 'C': 1}) test_q_2 = {'B': 0} - true_res = [0.79, 0.21] + test_q_3 = {} + test_q_4, test_e_4 = ({'B': 1}, {'A': 0}) + true_res = [0.79, 0.21, 1, 0.6] res = [] samples = [] - # 1. Query + # 1. Query basic inference res.append(self.qbayesian.inference(query=test_q_1, evidence=test_e_1)) samples.append(self.qbayesian.samples) - # 2. Query + # 2. Query basic inference res.append(self.qbayesian.inference(query=test_q_2)) samples.append(self.qbayesian.samples) + # 3. Query marginalized inference + res.append(self.qbayesian.inference(query=test_q_3)) + samples.append(self.qbayesian.samples) + # 4. Query marginalized inference + res.append(self.qbayesian.inference(query=test_q_4, evidence=test_e_4)) # Correct inference self.assertTrue(np.all(np.isclose(true_res, res, rtol=0.05))) # No change in samples self.assertTrue(samples[0] == samples[1]) def test_parameter(self): - ... + """Tests properties of QBayesian""" + # Create a quantum circuit with a register that has more than one qubit + with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): + QBayesian(QuantumCircuit(QuantumRegister(2, 'qr'))) + # Test + with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): + QBayesian(QuantumCircuit(QuantumRegister(1, 'qr'))).inference({'A': 0}) if __name__ == "__main__": unittest.main() From adf90c0e770320eda8e53ac167f3e903f349535b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 5 Nov 2023 19:01:53 +0100 Subject: [PATCH 09/48] Started QBayesian tutorial --- .../13_quantum_bayesian_inference.ipynb | 59 ++++++++ .../algorithms/inference/qbayesian.py | 133 +++++++++--------- test/algorithms/inference/test_qbayesian.py | 2 + 3 files changed, 124 insertions(+), 70 deletions(-) create mode 100644 docs/tutorials/13_quantum_bayesian_inference.ipynb diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb new file mode 100644 index 000000000..2f13d4b59 --- /dev/null +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -0,0 +1,59 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Quantum Bayesian Inference with Qiskit\n", + "\n", + "##### Quantum Bayesian inference allows us to use quantum computing to perform inference on Bayesian networks, potentially leveraging quantum parallelism for more efficient computation. This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks." + ], + "metadata": { + "collapsed": false + }, + "id": "64eb0ac8be046640" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 1: Creating a Quantum Circuit for Bayesian Network\n", + "\n", + "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." + ], + "metadata": { + "collapsed": false + }, + "id": "cafd433bf5016f60" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "initial_id", + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index b6439c960..387d82918 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -19,8 +19,7 @@ class QBayesian: r""" - Implements Quantum Bayesian Inference algorithm. The algorithm has been developed in [1] - and includes methods ``getGroverOp``, ``rejectionSampling`` and ``inference``. + Implements Quantum Bayesian Inference algorithm. The algorithm has been developed in [1]. **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. @@ -70,11 +69,10 @@ def __init__(self, circuit: QuantumCircuit): self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} self.samples = {} - def getGroverOp(self, evidence: dict): + def getGroverOp(self, evidence: dict) -> GroverOperator: """ - Creates Amplification Problem - - evidence: ... + Constructs a Grover operator based on the provided evidence. The evidence is used to determine + the "good states" that the returned Grover operator can amplify. """ # Evidence to reversed qubit index sorted by index num_qubits = self.circ.num_qubits @@ -94,33 +92,58 @@ def getGroverOp(self, evidence: dict): oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) return GroverOperator(oracle, state_preparation=self.circ) - - def rejectionSampling(self, evidence: dict, - shots: int=None, - grover_iter=None): - def run_circuit(circuit, shots=100_000): - """ - Run the provided quantum circuit on the Aer simulator backend. - - Parameters: - - circuit: The quantum circuit to be executed. - - shots (default=10,000): The number of times the circuit is executed. - - Returns: - - counts: A dictionary with the counts of each quantum state result. - """ - # Get the Aer simulator backend - simulator_backend = AerSimulator() - # Transpile the circuit for the given backend - transpiled_circuit = transpile(circuit, simulator_backend) - # Run the transpiled circuit on the simulator - job = simulator_backend.run(transpiled_circuit, shots=shots) - result = job.result() - # Get the counts of quantum state results - counts = result.get_counts(transpiled_circuit) - # Convert counts to relative counts (probabilities) - relative_counts = {state: count / shots for state, count in counts.items()} - return relative_counts + def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: + """ Run the provided quantum circuit for the number of shots on the Aer simulator backend. """ + # Get the Aer simulator backend + simulator_backend = AerSimulator() + # Transpile the circuit for the given backend + transpiled_circuit = transpile(circuit, simulator_backend) + # Run the transpiled circuit on the simulator + job = simulator_backend.run(transpiled_circuit, shots=shots) + result = job.result() + # Get the counts of quantum state results + counts = result.get_counts(transpiled_circuit) + # Convert counts to relative counts (probabilities) + relative_counts = {state: count / shots for state, count in counts.items()} + return relative_counts + + def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (GroverOperator, set): + """ + Applies the Grover operator to the quantum circuit 2^k times. It measures the evidence qubits and returns a + tuple containing the updated quantum circuit and a set of the measured evidence qubits. + """ + # Create circuit + qc = QuantumCircuit(*self.circ.qregs) + qc.append(self.circ, self.circ.qregs) + # Apply grover operator 2^k times + qcGrover = QuantumCircuit(*self.circ.qregs) + qcGrover.append(groverOp, self.circ.qregs) + qcGrover = qcGrover.power(2 ** k) + qc.append(qcGrover, self.circ.qregs) + # Add quantum circuit for measuring + qc_measure = QuantumCircuit(*self.circ.qregs) + qc_measure.append(qc, self.circ.qregs) + # Create a classical register with the size of the evidence + measurement_ecr = ClassicalRegister(len(evidence)) + qc_measure.add_register(measurement_ecr) + # Map the evidence qubits to the classical bits and measure them + evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] + qc_measure.measure([q for q in evidence_qubits], measurement_ecr) + # Run the circuit with the Grover operator and measurements + e_samples = self.run_circuit(qc_measure, shots = 1024) + E_count = {self.label2qubit[e]: 0 for e in evidence} + for e_sample_key, e_sample_val in e_samples.items(): + # Go through reverse binary that matches order of qubits + for i, char in enumerate(e_sample_key[::-1]): + if int(char) == 1: + E_count[evidence_qubits[i]] += e_sample_val + else: + E_count[evidence_qubits[i]] += -e_sample_val + # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 + E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} + return qc, E + + def rejectionSampling(self, evidence: dict, shots: int = 100000) -> dict: # If evidence is empty if len(evidence) == 0: @@ -130,7 +153,7 @@ def run_circuit(circuit, shots=100_000): # Measure qc.measure_all() # Run circuit - samples = run_circuit(qc, shots=100000) + samples = self.run_circuit(qc, shots=shots) return samples else: # Get grover operator if evidence not empty @@ -138,41 +161,13 @@ def run_circuit(circuit, shots=100_000): # Amplitude amplification e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} E = {} - k=-1 + k = -1 # If the measurement of the evidence qubits matches the evidence stop while (e != E) and (k < 10): # Increment power k += 1 - # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) - # Apply grover operator 2^k times - qcGrover = QuantumCircuit(*self.circ.qregs) - qcGrover.append(groverOp, self.circ.qregs) - qcGrover = qcGrover.power(2**k) - qc.append(qcGrover, self.circ.qregs) - # Add quantum circuit for measuring - qc_measure = QuantumCircuit(*self.circ.qregs) - qc_measure.append(qc, self.circ.qregs) - # Create a classical register with the size of the evidence - measurement_ecr = ClassicalRegister(len(evidence)) - qc_measure.add_register(measurement_ecr) - # Map the evidence qubits to the classical bits and measure them - evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] - qc_measure.measure([q for q in evidence_qubits], measurement_ecr) - # Run the circuit with the Grover operator and measurements - e_samples = run_circuit(qc_measure, shots=1024) - E_count = {self.label2qubit[e]: 0 for e in evidence} - for e_sample_key, e_sample_val in e_samples.items(): - # Go through reverse binary that matches order of qubits - for i, char in enumerate(e_sample_key[::-1]): - if int(char) == 1: - E_count[evidence_qubits[i]] += e_sample_val - else: - E_count[evidence_qubits[i]] += -e_sample_val - - # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 - E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} + # Create circuit with 2^k times grover operator + qc, E = self.powerGrover(groverOp=groverOp, evidence=evidence, k=k) # Create a classical register with the size of the evidence measurement_qcr = ClassicalRegister(self.circ.num_qubits-len(evidence)) @@ -183,7 +178,7 @@ def run_circuit(circuit, shots=100_000): # Measure query variables and return their count qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit - counts = run_circuit(qc, shots=100000) + counts = self.run_circuit(qc, shots=shots) # Build default string with evidence query_string = '' varIdxSorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] @@ -203,7 +198,7 @@ def run_circuit(circuit, shots=100_000): return self.samples - def inference(self, query: dict, evidence: dict=None, shots: int=None): + def inference(self, query: dict, evidence: dict=None, shots: int=100000) -> float: """ - query: The query variables. If Q is a real subset of X\E, it will be marginalized. - evidence: Provide evidence if rejection sampling should be executed. If you want to indicate no evidence @@ -214,9 +209,7 @@ def inference(self, query: dict, evidence: dict=None, shots: int=None): else: if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") - - - # Get probability of query + # Get sorted indices of query qubits query_indices = [(self.label2qidx[q_key], q_val) for q_key, q_val in query.items()] query_indices_sorted = sorted(query_indices, key=lambda x: x[0], reverse=True) # Get probability of query diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 460ba60f7..7232143f5 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -106,6 +106,8 @@ def test_inference(self): def test_parameter(self): """Tests properties of QBayesian""" + # Test + self.qbayesian.inference(query={'B': 1}, evidence={'A': 0, 'C': 0}, shots=10) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(2, 'qr'))) From b157f6cd2c5a6e04f23d9d4895ad474ca32f71f7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 6 Nov 2023 22:59:51 +0100 Subject: [PATCH 10/48] QBayesian tutorial + debugging order in inference() --- .../13_quantum_bayesian_inference.ipynb | 230 +++++++++++++++++- .../algorithms/inference/__init__.py | 18 ++ .../algorithms/inference/qbayesian.py | 7 +- test/algorithms/inference/test_qbayesian.py | 22 +- 4 files changed, 268 insertions(+), 9 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 2f13d4b59..4840b8e6b 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -15,9 +15,9 @@ { "cell_type": "markdown", "source": [ - "# Step 1: Creating a Quantum Circuit for Bayesian Network\n", + "# Step 1: Creating Rotations for Bayesian Network\n", "\n", - "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." + "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies. In this example we consider a simple Bayesian network that is only based on a chain of nodes." ], "metadata": { "collapsed": false @@ -26,13 +26,233 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "initial_id", "metadata": { - "collapsed": true + "collapsed": true, + "ExecuteTime": { + "end_time": "2023-11-06T21:57:29.810306Z", + "start_time": "2023-11-06T21:57:29.799011Z" + } }, "outputs": [], - "source": [] + "source": [ + "# Include libraries\n", + "import numpy as np\n", + "\n", + "# Define rotation angles\n", + "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", + "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_B_nA = 2 * np.arcsin(np.sqrt(0.3))" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Step 2: Create a Quantum Circuit for Bayesian Network" + ], + "metadata": { + "collapsed": false + }, + "id": "5cd1787e381e1030" + }, + { + "cell_type": "code", + "execution_count": 13, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import QuantumRegister\n", + "from qiskit import QuantumCircuit\n", + "# Define quantum registers \n", + "qrA = QuantumRegister(1, name='A')\n", + "qrB = QuantumRegister(1, name='B')\n", + "\n", + "# Define a 2-qubit quantum circuit\n", + "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", + "#Apply the R_Y_theta rotation gate on the first qubit\n", + "qc.ry(theta_A, 0)\n", + "# Apply the controlled-R_Y_theta rotation gate\n", + "qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB)\n", + "# Apply the X gate on the first qubit\n", + "qc.x(0)\n", + "# Apply the controlled-R_Y_theta rotation gate\n", + "qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB)\n", + "# Apply another X gate on the first qubit\n", + "qc.x(0)\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-06T21:57:29.883674Z", + "start_time": "2023-11-06T21:57:29.808175Z" + } + }, + "id": "c4984e988c8ededd" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 3: Perform Inference" + ], + "metadata": { + "collapsed": false + }, + "id": "644fd909109b2e64" + }, + { + "cell_type": "code", + "execution_count": 14, + "outputs": [ + { + "data": { + "text/plain": "0.11883" + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit_machine_learning.algorithms .inference import QBayesian\n", + "\n", + "query = {'B': 0}\n", + "evidence = {'A': 1}\n", + "# Initialize quantum bayesian\n", + "qbayesian = QBayesian(circuit=qc)\n", + "# Inference\n", + "qbayesian.inference(query=query, evidence=evidence)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-06T21:57:30.066237Z", + "start_time": "2023-11-06T21:57:29.889944Z" + } + }, + "id": "8d7a132268680e61" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 4: Generalize the approach for n nodes" + ], + "metadata": { + "collapsed": false + }, + "id": "fb1ef1a3c7e0ac9f" + }, + { + "cell_type": "code", + "execution_count": 15, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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+ }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Choose the number of nodes\n", + "n = 10 \n", + "# Generate probabilities\n", + "prob = np.random.random_sample(2*(n-1)+1)\n", + "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", + "# Define quantum registers \n", + "qr = [QuantumRegister(1, name=str(i)) for i in range(n)]\n", + "# Generate circuit\n", + "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", + "#Apply the R_Y_theta rotation gate on the first qubit\n", + "qc.ry(theta[0], 0)\n", + "# Apply the controlled-R_Y_theta rotations\n", + "for i in range(1, n, 1):\n", + " qc.cry(theta_B_A, control_qubit=i-1, target_qubit=i)\n", + " qc.x(i-1)\n", + " qc.cry(theta_B_nA, control_qubit=i-1, target_qubit=i)\n", + " qc.x(i-1)\n", + "# Draw circuit\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-06T21:57:30.383786Z", + "start_time": "2023-11-06T21:57:30.066801Z" + } + }, + "id": "9021e193f69b0392" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 5: Inference" + ], + "metadata": { + "collapsed": false + }, + "id": "6180fa5c5fae8d" + }, + { + "cell_type": "code", + "execution_count": 17, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "evidence = {str(i): 0 for i in range(n-1)}\n", + "# Initialize quantum bayesian\n", + "qbayesian = QBayesian(circuit=qc)\n", + "# Inference\n", + "samples = qbayesian.rejectionSampling(evidence=evidence)\n", + "\n", + "plot_histogram(samples)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-06T21:58:27.926140Z", + "start_time": "2023-11-06T21:58:26.067519Z" + } + }, + "id": "352129ef4f8f6cff" + }, + { + "cell_type": "code", + "execution_count": 16, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-06T21:57:32.318408Z", + "start_time": "2023-11-06T21:57:32.315907Z" + } + }, + "id": "bbeb5794115cb625" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/inference/__init__.py b/qiskit_machine_learning/algorithms/inference/__init__.py index e69de29bb..5003e7b22 100644 --- a/qiskit_machine_learning/algorithms/inference/__init__.py +++ b/qiskit_machine_learning/algorithms/inference/__init__.py @@ -0,0 +1,18 @@ +# This code is part of a Qiskit project. +# +# (C) Copyright IBM 2020, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" Inference Package """ + + +from .qbayesian import QBayesian + +__all__ = ["QBayesian"] diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 387d82918..c07156d36 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -210,13 +210,14 @@ def inference(self, query: dict, evidence: dict=None, shots: int=100000) -> floa if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") # Get sorted indices of query qubits - query_indices = [(self.label2qidx[q_key], q_val) for q_key, q_val in query.items()] - query_indices_sorted = sorted(query_indices, key=lambda x: x[0], reverse=True) + query_indices_rev = [ + (self.circ.num_qubits-self.label2qidx[q_key]-1, q_val) for q_key, q_val in query.items() + ] # Get probability of query res = 0 for sample_key, sample_val in self.samples.items(): add = True - for q_idx, q_val in query_indices_sorted: + for q_idx, q_val in query_indices_rev: if int(sample_key[q_idx]) != q_val: add = False break diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 7232143f5..605b7f49e 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -11,7 +11,6 @@ # that they have been altered from the originals. import numpy as np -import math import unittest from test import QiskitMachineLearningTestCase from qiskit_algorithms.utils import algorithm_globals @@ -115,5 +114,26 @@ def test_parameter(self): with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(1, 'qr'))).inference({'A': 0}) + def test_trivial_circuit(self): + # Define rotation angles + theta_A = 2 * np.arcsin(np.sqrt(0.2)) + theta_B_A = 2 * np.arcsin(np.sqrt(0.9)) + theta_B_nA = 2 * np.arcsin(np.sqrt(0.3)) + # Define quantum registers + qrA = QuantumRegister(1, name='A') + qrB = QuantumRegister(1, name='B') + # Define a 2-qubit quantum circuit + qc = QuantumCircuit(qrA, qrB, name="Bayes net small") + qc.ry(theta_A, 0) + qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB) + qc.x(0) + qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB) + qc.x(0) + qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1) + # Initialize quantum bayesian + qb = QBayesian(circuit=qc) + # Inference + self.assertTrue(np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.05))) + if __name__ == "__main__": unittest.main() From 60f683d20e51e0f0172fdf6430b5c544b0f6d748 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Tue, 7 Nov 2023 22:36:32 +0100 Subject: [PATCH 11/48] Add best_qc and docs --- .../13_quantum_bayesian_inference.ipynb | 150 +++++++++++++----- .../algorithms/inference/qbayesian.py | 103 ++++++++---- test/algorithms/inference/test_qbayesian.py | 14 +- 3 files changed, 197 insertions(+), 70 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 4840b8e6b..9867c39a3 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -5,7 +5,10 @@ "source": [ "# Quantum Bayesian Inference with Qiskit\n", "\n", - "##### Quantum Bayesian inference allows us to use quantum computing to perform inference on Bayesian networks, potentially leveraging quantum parallelism for more efficient computation. This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks." + "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions. \n", + "\n", + "##### This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", + "\n" ], "metadata": { "collapsed": false @@ -17,7 +20,7 @@ "source": [ "# Step 1: Creating Rotations for Bayesian Network\n", "\n", - "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies. In this example we consider a simple Bayesian network that is only based on a chain of nodes." + "In the first example we consider a simple Bayesian network that is only based on two nodes." ], "metadata": { "collapsed": false @@ -26,20 +29,71 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 25, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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+ }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "# Create a directed graph\n", + "G = nx.DiGraph()\n", + "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", + "G.add_node('A', pos=(0, 0))\n", + "G.add_node('B', pos=(1, 0))\n", + "# Add a directed edge from A to B\n", + "G.add_edge('A', 'B')\n", + "# Get the positions of each node\n", + "pos = nx.get_node_attributes(G, 'pos')\n", + "# Draw the graph\n", + "nx.draw(G, pos, with_labels=True, node_size=2000, node_color='skyblue', arrowstyle='->', arrowsize=20)\n", + "# Show the plot\n", + "plt.show()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-07T21:09:43.425590Z", + "start_time": "2023-11-07T21:09:43.346977Z" + } + }, + "id": "925af2a5fe37bf8c" + }, + { + "cell_type": "markdown", + "source": [ + "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", + "$$P(A)=0.2$$\n", + "$$P(B|A)=0.9$$\n", + "$$P(B|-A)=0.3$$" + ], + "metadata": { + "collapsed": false + }, + "id": "c2fedc900c1152d3" + }, + { + "cell_type": "code", + "execution_count": 26, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-06T21:57:29.810306Z", - "start_time": "2023-11-06T21:57:29.799011Z" + "end_time": "2023-11-07T21:09:43.433405Z", + "start_time": "2023-11-07T21:09:43.429410Z" } }, "outputs": [], "source": [ "# Include libraries\n", "import numpy as np\n", - "\n", "# Define rotation angles\n", "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", @@ -49,7 +103,9 @@ { "cell_type": "markdown", "source": [ - "# Step 2: Create a Quantum Circuit for Bayesian Network" + "# Step 2: Create a Quantum Circuit for Bayesian Network\n", + "\n", + "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." ], "metadata": { "collapsed": false @@ -58,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 27, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, - "execution_count": 13, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -76,7 +132,6 @@ "# Define quantum registers \n", "qrA = QuantumRegister(1, name='A')\n", "qrB = QuantumRegister(1, name='B')\n", - "\n", "# Define a 2-qubit quantum circuit\n", "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", "#Apply the R_Y_theta rotation gate on the first qubit\n", @@ -94,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-06T21:57:29.883674Z", - "start_time": "2023-11-06T21:57:29.808175Z" + "end_time": "2023-11-07T21:09:43.513653Z", + "start_time": "2023-11-07T21:09:43.438798Z" } }, "id": "c4984e988c8ededd" @@ -103,7 +158,9 @@ { "cell_type": "markdown", "source": [ - "# Step 3: Perform Inference" + "# Step 3: Perform Inference\n", + "\n", + "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the `inference` method to estimate probabilities given evidence." ], "metadata": { "collapsed": false @@ -112,13 +169,13 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 28, "outputs": [ { "data": { - "text/plain": "0.11883" + "text/plain": "0.1198" }, - "execution_count": 14, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -128,7 +185,7 @@ "\n", "query = {'B': 0}\n", "evidence = {'A': 1}\n", - "# Initialize quantum bayesian\n", + "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", "qbayesian.inference(query=query, evidence=evidence)" @@ -136,8 +193,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-06T21:57:30.066237Z", - "start_time": "2023-11-06T21:57:29.889944Z" + "end_time": "2023-11-07T21:09:43.609079Z", + "start_time": "2023-11-07T21:09:43.511357Z" } }, "id": "8d7a132268680e61" @@ -145,7 +202,9 @@ { "cell_type": "markdown", "source": [ - "# Step 4: Generalize the approach for n nodes" + "# Step 4: Generalize the approach for n nodes\n", + "\n", + "Now we generalize the approach for n nodes in a chain with random probabilities." ], "metadata": { "collapsed": false @@ -154,14 +213,14 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 29, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 15, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -190,8 +249,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-06T21:57:30.383786Z", - "start_time": "2023-11-06T21:57:30.066801Z" + "end_time": "2023-11-07T21:09:43.864198Z", + "start_time": "2023-11-07T21:09:43.636377Z" } }, "id": "9021e193f69b0392" @@ -199,7 +258,7 @@ { "cell_type": "markdown", "source": [ - "# Step 5: Inference" + "We could also do inference with this model, but the chosen probabilities are random, as is the result." ], "metadata": { "collapsed": false @@ -208,14 +267,21 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 31, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'0000000000': 0.42099, '1000000000': 0.57901}\n" + ] + }, { "data": { "text/plain": "
", - "image/png": 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" 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}, - "execution_count": 17, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -228,31 +294,43 @@ "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", "samples = qbayesian.rejectionSampling(evidence=evidence)\n", - "\n", + "print(samples)\n", "plot_histogram(samples)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-06T21:58:27.926140Z", - "start_time": "2023-11-06T21:58:26.067519Z" + "end_time": "2023-11-07T21:10:04.221991Z", + "start_time": "2023-11-07T21:10:03.259818Z" } }, "id": "352129ef4f8f6cff" }, + { + "cell_type": "markdown", + "source": [ + "# Step 5: Pachinko \n", + "\n", + "Now let us consider the Pachinko game, where each node " + ], + "metadata": { + "collapsed": false + }, + "id": "438ad95c79da22d9" + }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "outputs": [], "source": [], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-06T21:57:32.318408Z", - "start_time": "2023-11-06T21:57:32.315907Z" + "end_time": "2023-11-07T21:09:44.709280Z", + "start_time": "2023-11-07T21:09:44.708151Z" } }, - "id": "bbeb5794115cb625" + "id": "7000db4359eed86a" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index c07156d36..fdf681a89 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -9,6 +9,8 @@ # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. +import copy + import numpy as np from qiskit import QuantumCircuit, transpile, ClassicalRegister from qiskit.quantum_info import Statevector @@ -23,7 +25,7 @@ class QBayesian: **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. - "Quantum inference on Bayesian networks." Physical Review A 89.6 (2014): 062315. + "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. Usage: @@ -50,11 +52,15 @@ class QBayesian: # Discrete quantum Bayesian network def __init__(self, circuit: QuantumCircuit): """ - Run the provided quantum circuit on the Aer simulator backend. + Run the provided quantum circuit on the Aer simulator backend. For other simulator overwrite the method + run_circuit(). + + Args: + circuit (QuantumCircuit): The quantum circuit representing the Bayesian network. Each random variable + should be assigned to exactly one register of one qubit. - Parameters: - - circuit: The quantum circuit to be executed. - Every r.v. should be assigned exactly one register of one distinct qubit. + Raises: + ValueError: If any register in the circuit is not mapped to exactly one qubit. """ # Test valid input @@ -67,12 +73,20 @@ def __init__(self, circuit: QuantumCircuit): self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} # Label of register mapped to its qubit index self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} + # Samples from rejection sampling self.samples = {} + # True if rejection sampling converged after limit + self.converged = bool def getGroverOp(self, evidence: dict) -> GroverOperator: """ Constructs a Grover operator based on the provided evidence. The evidence is used to determine - the "good states" that the returned Grover operator can amplify. + the "good states" that the Grover operator will amplify. + Args: + evidence (dict): A dictionary representing the evidence with keys as variable labels and + values as states. + Returns: + GroverOperator: The constructed Grover operator. """ # Evidence to reversed qubit index sorted by index num_qubits = self.circ.num_qubits @@ -109,8 +123,14 @@ def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (GroverOperator, set): """ - Applies the Grover operator to the quantum circuit 2^k times. It measures the evidence qubits and returns a - tuple containing the updated quantum circuit and a set of the measured evidence qubits. + Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns + a tuple containing the updated quantum circuit and a set of the measured evidence qubits. + Args: + groverOp (GroverOperator): The Grover operator to be applied. + evidence (dict): A dictionary representing the evidence. + k (int): The power to which the Grover operator is raised. + Returns: + tuple: A tuple containing the updated quantum circuit and a set of the measured evidence qubits. """ # Create circuit qc = QuantumCircuit(*self.circ.qregs) @@ -143,8 +163,18 @@ def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (Grov E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} return qc, E - def rejectionSampling(self, evidence: dict, shots: int = 100000) -> dict: - + def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10) -> dict: + """ + Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures + all qubits. If evidence is provided, it uses the Grover operator for amplitude amplification and iterates + until the evidence matches or a limit is reached. + Args: + evidence (dict): A dictionary representing the evidence. + shots (int): The number of times the circuit will be executed. + limit (int): The maximum number of iterations for the Grover operator. + Returns: + dict: A dictionary containing the samples as a dictionary + """ # If evidence is empty if len(evidence) == 0: # Create circuit @@ -155,30 +185,35 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000) -> dict: # Run circuit samples = self.run_circuit(qc, shots=shots) return samples - else: - # Get grover operator if evidence not empty - groverOp = self.getGroverOp(evidence) - # Amplitude amplification - e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} - E = {} - k = -1 - # If the measurement of the evidence qubits matches the evidence stop - while (e != E) and (k < 10): - # Increment power - k += 1 - # Create circuit with 2^k times grover operator - qc, E = self.powerGrover(groverOp=groverOp, evidence=evidence, k=k) + # Get grover operator if evidence not empty + groverOp = self.getGroverOp(evidence) + # Amplitude amplification + e, E = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} + best_QC, best_inter = QuantumCircuit(), 0 + self.converged = False + k = -1 + # If the measurement of the evidence qubits matches the evidence stop + while (e != E) and (k < limit): + # Increment power + k += 1 + # Create circuit with 2^k times grover operator + qc, E = self.powerGrover(groverOp=groverOp, evidence=evidence, k=k) + # Test number of + if len(e.intersection(E)) > best_inter: + best_qc = qc + if e == E: + self.converged = True # Create a classical register with the size of the evidence measurement_qcr = ClassicalRegister(self.circ.num_qubits-len(evidence)) - qc.add_register(measurement_qcr) + best_qc.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them query_qubits = [(label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if label not in evidence] query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1]) # Measure query variables and return their count - qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) + best_qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit - counts = self.run_circuit(qc, shots=shots) + counts = self.run_circuit(best_qc, shots=shots) # Build default string with evidence query_string = '' varIdxSorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] @@ -200,9 +235,19 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000) -> dict: def inference(self, query: dict, evidence: dict=None, shots: int=100000) -> float: """ - - query: The query variables. If Q is a real subset of X\E, it will be marginalized. - - evidence: Provide evidence if rejection sampling should be executed. If you want to indicate no evidence - insert an empty list. If you want to indicate no new evidence keep this variable empty. + Performs inference on the query variables given the evidence. It uses rejection sampling if evidence + is provided and calculates the probability of the query. + Args: + query (dict): The query variables with keys as variable labels and values as states. If Q is a real subset + of X\E, it will be marginalized. + evidence (dict, optional): The evidence variables. If provided, rejection sampling is executed. If you want + to indicate no evidence + insert an empty list. + shots (int): The number of times the circuit will be executed. + Returns: + float: The probability of the query given the evidence. + Raises: + ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: self.rejectionSampling(evidence, shots) diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 605b7f49e..27a6ee59b 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -75,11 +75,12 @@ def test_rejection_sampling(self): '100': 0.03, '101': 0.04125, '110': 0.315, '111': 0.1575} ] for e, res in zip(test_cases, true_res): - samples = self.qbayesian.rejectionSampling(evidence=e, shots=100000) + samples = self.qbayesian.rejectionSampling(evidence=e) self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.1) for sample_key, sample_val in samples.items()])) def test_inference(self): + """Test inference with different amount of evidence""" test_q_1, test_e_1 = ({'B': 1}, {'A': 1, 'C': 1}) test_q_2 = {'B': 0} test_q_3 = {} @@ -104,17 +105,20 @@ def test_inference(self): self.assertTrue(samples[0] == samples[1]) def test_parameter(self): - """Tests properties of QBayesian""" - # Test + """Tests parameter of QBayesian methods""" + # Test set limit + self.qbayesian.rejectionSampling(evidence={'B': 1}, limit=1) + # Test set shots self.qbayesian.inference(query={'B': 1}, evidence={'A': 0, 'C': 0}, shots=10) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(2, 'qr'))) - # Test - with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): + # Test invalid inference without evidence or generated samples + with self.assertRaises(ValueError, msg="QBayesian inference did not raise ValueError with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(1, 'qr'))).inference({'A': 0}) def test_trivial_circuit(self): + """Tests trivial quantum circuit""" # Define rotation angles theta_A = 2 * np.arcsin(np.sqrt(0.2)) theta_B_A = 2 * np.arcsin(np.sqrt(0.9)) From ec6c18c085b4ae0887bf21d833ef56637e6a82b7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Thu, 9 Nov 2023 01:00:18 +0100 Subject: [PATCH 12/48] Added Pachinko in Tut as Bayesian network --- .../13_quantum_bayesian_inference.ipynb | 261 +++++++++++++++--- .../algorithms/inference/qbayesian.py | 6 +- 2 files changed, 234 insertions(+), 33 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 9867c39a3..200eb3f93 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -29,7 +29,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 1, "outputs": [ { "data": { @@ -60,8 +60,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:09:43.425590Z", - "start_time": "2023-11-07T21:09:43.346977Z" + "end_time": "2023-11-08T23:55:45.204595Z", + "start_time": "2023-11-08T23:55:44.587163Z" } }, "id": "925af2a5fe37bf8c" @@ -81,13 +81,13 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 2, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-07T21:09:43.433405Z", - "start_time": "2023-11-07T21:09:43.429410Z" + "end_time": "2023-11-08T23:55:45.211204Z", + "start_time": "2023-11-08T23:55:45.203684Z" } }, "outputs": [], @@ -114,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 3, "outputs": [ { "data": { "text/plain": "
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" }, - "execution_count": 27, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:09:43.513653Z", - "start_time": "2023-11-07T21:09:43.438798Z" + "end_time": "2023-11-08T23:55:45.723868Z", + "start_time": "2023-11-08T23:55:45.213325Z" } }, "id": "c4984e988c8ededd" @@ -169,13 +169,21 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 4, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{Qubit(QuantumRegister(1, 'A'), 0): 0.931640625}\n", + "k: 0\n" + ] + }, { "data": { - "text/plain": "0.1198" + "text/plain": "0.12168" }, - "execution_count": 28, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -193,8 +201,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:09:43.609079Z", - "start_time": "2023-11-07T21:09:43.511357Z" + "end_time": "2023-11-08T23:55:46.525097Z", + "start_time": "2023-11-08T23:55:45.721959Z" } }, "id": "8d7a132268680e61" @@ -213,14 +221,14 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 5, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 29, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -232,7 +240,7 @@ "prob = np.random.random_sample(2*(n-1)+1)\n", "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", "# Define quantum registers \n", - "qr = [QuantumRegister(1, name=str(i)) for i in range(n)]\n", + "qr = [QuantumRegister(1, name=i) for i in range(n)]\n", "# Generate circuit\n", "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", "#Apply the R_Y_theta rotation gate on the first qubit\n", @@ -249,8 +257,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:09:43.864198Z", - "start_time": "2023-11-07T21:09:43.636377Z" + "end_time": "2023-11-08T23:55:46.923287Z", + "start_time": "2023-11-08T23:55:46.527817Z" } }, "id": "9021e193f69b0392" @@ -267,21 +275,27 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 6, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'0000000000': 0.42099, '1000000000': 0.57901}\n" + "{Qubit(QuantumRegister(1, '0'), 0): 0.62109375, Qubit(QuantumRegister(1, '1'), 0): 0.541015625, Qubit(QuantumRegister(1, '2'), 0): 0.47265625, Qubit(QuantumRegister(1, '3'), 0): 0.4453125, Qubit(QuantumRegister(1, '4'), 0): 0.4453125, Qubit(QuantumRegister(1, '5'), 0): 0.447265625, Qubit(QuantumRegister(1, '6'), 0): 0.40625, Qubit(QuantumRegister(1, '7'), 0): 0.376953125, Qubit(QuantumRegister(1, '8'), 0): 0.384765625}\n", + "k: 0\n", + "{Qubit(QuantumRegister(1, '0'), 0): 0.4609375, Qubit(QuantumRegister(1, '1'), 0): 0.380859375, Qubit(QuantumRegister(1, '2'), 0): 0.34765625, Qubit(QuantumRegister(1, '3'), 0): 0.298828125, Qubit(QuantumRegister(1, '4'), 0): 0.27734375, Qubit(QuantumRegister(1, '5'), 0): 0.23046875, Qubit(QuantumRegister(1, '6'), 0): 0.263671875, Qubit(QuantumRegister(1, '7'), 0): 0.244140625, Qubit(QuantumRegister(1, '8'), 0): 0.27734375}\n", + "k: 1\n", + "{Qubit(QuantumRegister(1, '0'), 0): -0.1015625, Qubit(QuantumRegister(1, '1'), 0): -0.14453125, Qubit(QuantumRegister(1, '2'), 0): -0.166015625, Qubit(QuantumRegister(1, '3'), 0): -0.1796875, Qubit(QuantumRegister(1, '4'), 0): -0.208984375, Qubit(QuantumRegister(1, '5'), 0): -0.21484375, Qubit(QuantumRegister(1, '6'), 0): -0.1875, Qubit(QuantumRegister(1, '7'), 0): -0.19140625, Qubit(QuantumRegister(1, '8'), 0): -0.20703125}\n", + "k: 2\n", + "{'1000000000': 0.53215, '0000000000': 0.46785}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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" + "image/png": 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" }, - "execution_count": 31, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -300,8 +314,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:10:04.221991Z", - "start_time": "2023-11-07T21:10:03.259818Z" + "end_time": "2023-11-08T23:55:50.448531Z", + "start_time": "2023-11-08T23:55:46.923961Z" } }, "id": "352129ef4f8f6cff" @@ -311,13 +325,198 @@ "source": [ "# Step 5: Pachinko \n", "\n", - "Now let us consider the Pachinko game, where each node " + "Pachinko is a popular Japanese game that combines elements of pinball and slot machines. Players purchase steel balls, launch them into a playfield filled with pins, and aim to land them in specific pockets. Let us now consider a pachinko game for 15 pins, in which a ball goes to the left or right of the pin with a probability of 0.5 in each case. You can use the following code to plot the Pachinko game." ], "metadata": { "collapsed": false }, "id": "438ad95c79da22d9" }, + { + "cell_type": "code", + "execution_count": 7, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "\n", + "# Create a new graph\n", + "G = nx.DiGraph()\n", + "\n", + "# Add nodes with their positions\n", + "positions = {'A': (2, -1), 'B': (1, -2.5), 'C': (3, -2.5),\n", + " 'D': (0, -4), 'E': (2, -4), 'F': (4, -4),\n", + " 'G': (-1, -5.5), 'H': (1, -5.5), 'I': (3, -5.5), 'J': (5, -5.5),\n", + " 'K': (-2, -7), 'L': (0, -7), 'M': (2, -7), 'N': (4, -7), 'O': (6, -7)}\n", + "\n", + "for node, pos in positions.items():\n", + " G.add_node(node, pos=pos)\n", + "\n", + "# Add edges with labels\n", + "edges = [('A', 'B', '1/2'), ('A', 'C', '1/2'),\n", + " ('B', 'D', '1/2'), ('B', 'E', '1/2'), \n", + " ('C', 'E', '1/2'), ('C', 'F', '1/2'),\n", + " ('D', 'G', '1/2'), ('D', 'H', '1/2'),\n", + " ('E', 'H', '1/2'), ('E', 'I', '1/2'),\n", + " ('F', 'I', '1/2'), ('F', 'J', '1/2'),\n", + " ('G', 'K', '1/2'), ('G', 'L', '1/2'),\n", + " ('H', 'L', '1/2'), ('H', 'M', '1/2'),\n", + " ('I', 'M', '1/2'), ('I', 'N', '1/2'),\n", + " ('J', 'N', '1/2'), ('J', 'O', '1/2')]\n", + "\n", + "for u, v, weight in edges:\n", + " G.add_edge(u, v, weight=weight)\n", + "\n", + "# Draw the graph\n", + "plt.figure(figsize=(10, 8))\n", + "nx.draw(G, pos=positions, with_labels=True, node_color='skyblue', node_size=2000, edge_color='gray')\n", + "nx.draw_networkx_edge_labels(G, pos=positions, edge_labels={(u, v): d['weight'] for u, v, d in G.edges(data=True)})\n", + "\n", + "plt.title(\"Pachinko\")\n", + "plt.show()\n" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-08T23:55:50.612524Z", + "start_time": "2023-11-08T23:55:50.456357Z" + } + }, + "id": "44baa6f9eaf8b320" + }, + { + "cell_type": "markdown", + "source": [ + "To convert the Pachinko game into a quantum circuit, no negation of the variables is required, since: $P(X)=0.5=1-P(X)=P(-X)$." + ], + "metadata": { + "collapsed": false + }, + "id": "5a4f56e71f082e28" + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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NGDAgDz30UKvmKnjbwerVq1v87fKtceCBB77ly6SGDh1atG/Bf7U4LRdNTU3t8p9JudmwYUM2bNhQ6hgl458LAAAAoNwoeNvBgAEDWjynqamprErTurq6stnB29TUlC5duqSurq7UcYpie3bw7rjjjtlpp53aOFH7e+6559LY2NjieZ35nwsAAACg42pNf/gqBW87aM326oaGhtTW1hYhTXE89dRTqampKXWMt1VfX58VK1akrq4uy5cvL3Wcojn88MNzxx13tHjeLbfcko9+9KNFSNS+rr322owfP77F8z772c/mhz/8YRESAQAAABSHgpfMnz+/1BFoY6ecckqLC95hw4blgAMOKFKi9nX00UdnwIABLT77evLkyUVKBAAAAFAcHf976oEWGz16dN7//ve3aM7Xv/71VFVVFSlR++rRo0e+8pWvtGjOIYcckv32269IiQAAAACKQ8H7vxYsWJB+/fo1/7j44ouTJD/72c+2ur5gwYISJ4W317Vr19x888155zvfuU3jzzvvvBx33HFFTtW+/uVf/iVf+MIXtmnssGHDcu211xY5EQAAAEDbU/D+r02bNuWvf/1r848XX3wxSfLSSy9tdX3Tpk0lTgrb5h3veEd++9vf5qijjnrTnbl1dXW54oor8s1vfrOd0xVfVVVVrrjiilx44YXp06fPG47p1q1bjj/++Nx3331vOgYAAACgI6sqFAqFUofg9V77krUNGzZ0yBeYlUPG/+vVl6wNHDiwU79k7f/6wx/+kB/84AeZNm1aNm7cmB122CFXXXVVxo0bl+7du5c6XtG9+OKLue6663LzzTdn7ty5eemll7LjjjvmiSeeSF1dXanjAQAAALSagreDKofytBwy/l+VWvC+qtLXn3gGAAAAQOfiiIYKM2fOnEyaNCkbN27MuHHjMmTIkOy999459NBDs3Tp0lLHAwAAAABaQMFbYW644YaMGzcuSXLSSSfliSeeyCOPPJKxY8dm4sSJpQ0HAAAAALSIgreTWb9+ferr69O3b9/ss88+GTp0aHr27JmJEydm06ZNWbBgQQ4++OD06tUro0ePbn751ogRI/LMM8+UNjwAAAAA0CIK3k6md+/eOf7443Paaadl8eLFueSSSzJixIjMmjUr8+bNy8iRI9/wpVqXXnppxo4dW4LEAAAAAEBrKXg7ocWLF2ffffdNkjz88MPNv77xxhtz9NFHv278BRdckKVLl+bCCy9s15wAAAAAwPZR8HZCb1TwFgqF3HHHHRk1atRWY6dOnZrrr78+t912W6qrq0sRFwAAAABoJQVvJ7NixYpUVVVl4MCBSZJHH300w4YNy4MPPpihQ4emtra2eezFF1+c2bNn56677krv3r1LlBgAAAAAaK1upQ5A21q0aFHz7t3klTN5p0+fnn79+mXcuHHN15cvX54zzjgjgwYNykEHHZQk6dmzZx544IH2jgwAAAAAtJKCt5MZM2ZMxowZ0/z7hQsXJkn22muvzJs3r/l6fX19CoVCu+cDAAAAANqOgrdCPP7446WOAAAAAAC0MQVvGWhoaCh1hDfUUXMBAAAAQKVQ8JaB/v37lzoCAAAAANABdSl1AAAAAAAAWscO3g6quro6GzZsKHWMbVZdXV3qCAAAAABQcRS8HVRVVVVqampKHQMAAAAA6MAc0QAAAAAAUKYUvAAAAAAAZUrBCwAAAABQphS8AAAAAABlSsELAAAAAFCmFLwAAAAAAGVKwQsAAAAAUKYUvAAAAAAAZUrBCwAAAABQphS8AAAAAABlSsELAAAAAFCmFLwAAAAAAGVKwQsAAAAAUKYUvAAAAAAAZUrBCwAAAABQphS8AAAAAABlSsELAAAAAFCmFLwAAAAAAGWqW6kDwBspFAppbGxs8/s2NTU1/9zQ0NCm966urk5VVVWb3hMAAAAA3oqClw6psbExtbW1Rbv/qlWr2vz+GzZsSE1NTZveEwAAAADeiiMaAAAAAADKlB28dHhr1qzpsDtjGxoa0r9//1LHAAAAAKBCKXjp8GpqajpswQsAAAAApeSIBgAAAACAMqXgBQAAAAAoUwpeAAAAAIAypeAFAAAAAChTCl46lfnz56eqqmqrH7W1tRk+fHimTZuWzZs3lzoiAAAAALSZbqUOAMVw3HHHZfTo0SkUClm9enWuvvrqnH766VmyZElmzpxZ6ngAAAAA0CYUvHRKw4cPz4QJE5p/P3ny5Oy5556ZNWtWzj///Oy6664lTAcAAAAAbcMRDVSEmpqajBgxIoVCIcuWLSt1HAAAAABoEwreJIVCIQsWLMhXv/rVjBw5Mn369En37t3Tv3//jBkzJr/4xS9KHZE28Gqx26dPnxInAQAAAIC24YiGJL/85S9zyCGHJEmqqqrynve8J4MGDcrSpUtzyy235JZbbsnnP//5zJo1K1VVVSVOy7ZobGzM2rVrm8/gnTFjRhYtWpT9998/Q4YMKXU8AAAAAGgTCt68soN30KBB+Zd/+ZeMHz8+/fr1S5Js2bIl3/ve93L66afnhz/8YT7wgQ9k8uTJJU7LtpgyZUqmTJmy1bVjjjkml19+eYkSQWlt2LAh119/ff70pz+lUCikvr4+n/zkJ7PTTjuVOlq7KBQKuffee/PAAw+ksbExO++8cw477LDstddepY4GAAAA20XBm2T//ffP//zP/6R79+5bXe/atWtOO+20/M///E+uuOKKzJw5U8FbJk466aR86lOfyqZNm/LYY4/loosuyvLly9OrV6/mMePHj09TU1Ouu+665mvr1q3LXnvtlalTp+aEE04oRXRoU3/5y1/yrW99K1dddVVeeOGFrT770pe+lBNPPDHnnntudt999xIlLK5CoZAf/vCHmTZtWh5//PHXff6xj30sX//61/OJT3yiBOkAAABg+zmDN8lOO+30unL3tV79g/8TTzzRXpHYToMHD84hhxySUaNG5ayzzsrcuXOzcOHCnHzyyc1jpk+fngULFmT27NnN10455ZQccMAByl06hT/84Q/58Ic/nMsuu+x15W6SNDQ0ZMaMGRkxYkSn/PdbU1NTTjrppEycOPENy90k+dWvfpVRo0blsssua+d0AAAA0DYUvNtg48aNSZLq6uoSJ6G1Ro4cmRNPPDHXXntt7r///iSvvGztyiuvzKmnnpqVK1dmzpw5mT9/fmbMmFHitLD9nn/++Rx++OF5+umn33bsn//85xx++OFZu3ZtOyRrP+ecc05mzZr1tuMKhUK+9KUvbbWbHwAAAMqFgncbXHvttUmSj370oyVOwvY499xz07Vr15x33nnN1w4//PAce+yxmTBhQiZPnpxZs2alb9++JUwJbePKK6/Mk08+uc3jn3nmmXz/+98vYqL2tWbNmkydOrVFc77+9a+nqampSIkAAACgOBS8b+PWW2/NTTfdlCQ566yzSpyG7bHHHntk/Pjxueeee3Lfffc1X586dWqWLl2aUaNG5YgjjihhQmgbTU1NrSprr7jiimzevLkIidrfrFmzsmnTphbNefrpp3PnnXcWKREAAAAUh4L3LSxbtiwnnnhikuTLX/5yRo4cWeJEbK+zzz47Xbp02WoXb01NTQYNGpRhw4aVMBm0ncWLF2fp0qUtnrdixYrmI0zKXWuPW3j1OzYAAACgXFQVCoVCqUN0RKtXr85HP/rRLF26NIcddlhuvvnmt3wR21vZb7/9snr16jZO2Lk1NTVl1apVSZINGzakpqamqF/vwAMPzJgxY3LmmWe2aF5DQ0Nqa2uTJHV1denSpWP/ncmqVavS1NSULl26pK6urtRxSqISnsHGjRvz17/+tVVz+/Tpkx122KGNE7W/V/9zbqlevXo5pgUAAIB2N2DAgDz00EOtmtutjbN0CuvWrcthhx2WpUuX5iMf+UhuuOGGVpe7yStl8YoVK9owIR3Rq4V0OWhqaqr4fyY9gze2bt26UkcoqY0bN/rnAgAAgLKi4P0//va3v+Xwww/PY489luHDh+eWW25JdXX1dt1zwIABbZSucrx2B2+5sIO3PFTCM9iyZUurv2tgt912266/0Ooo1q5dm5deeqnF82pra7PzzjsXIREAAAC8ue3pDx3R8BqNjY05/PDDc99992Xo0KG59957069fv1LHqkivPfqgPY5oaK1yyfmq+vr6rFixIgMHDszy5ctLHackKuUZHHnkkbn55ptbNOeggw7KL3/5yyIlal/XX399PvnJT7ZoTlVVVZYuXZpBgwYVKRUAAAC0vY693bAdvfzyyzn66KNz33335T3veU/uvvtu5S5Qtk455ZR2mdNRHXXUUamvr2/RnFGjRil3AQAAKDsK3rzy7czHH3987rzzztTX1+fuu+/O7rvvXupYAK32iU98okWF7ec+97kcc8wxRUzUvrp165af/exn6dmz5zaNHzhwYGbMmFHkVAAAAND2nMGb5Lrrrst//dd/JUl69OiRCRMmvOnYOXPmOFMX6PCqqqry//7f/0uPHj0ybdq0txx78skn53vf+16qqqraKV37+MhHPpLbb789Rx99dNavX/+m4wYPHpzbbrst73jHO9ovHAAAALQRBW+y1Yt4nn766Tz99NNvOnbjxo3tEQlgu3Xp0iUXX3xxPvvZz+b73/9+fvKTn6ShoSHJKwXw5z//+UyaNCkf+MAHSpy0eA488MA8/fTTueqqqzJ9+vQ89dRTzZ+NHDkykydPzj/8wz9s805fAAAA6Gi8ZI0OqVxeXlYuOV9VKS8YeyuV/AxefvnlvPOd78zq1auz++67Z8WKFaWO1K4KhUIGDhyYVatWpa6uLitXrix1JAAAANhuzuCl4syZMyeTJk3Kxo0bM27cuAwZMiR77713Dj300CxdurTU8aBoevToka5duyZJpzuOYVtUVVWlS5dX/mfv1Z8BAACg3PkTLhXnhhtuyLhx45IkJ510Up544ok88sgjGTt2bCZOnFjacAAAAADQAgpeOp3169envr4+ffv2zT777JOhQ4emZ8+emThxYjZt2pQFCxbk4IMPTq9evTJ69OjmnYwjRozIM888U9rwAAAAANACCl46nd69e+f444/PaaedlsWLF+eSSy7JiBEjMmvWrMybNy8jR45M9+7dXzfv0ksvzdixY0uQGAAAAABaR8FLp7R48eLsu+++SZKHH364+dc33nhjjj766NeNv+CCC7J06dJceOGF7ZoTAAAAALaHgpdO6Y0K3kKhkDvuuCOjRo3aauzUqVNz/fXX57bbbkt1dXUp4gIAAABAqyh46XRWrFiRqqqqDBw4MEny6KOPZtiwYXnwwQczdOjQ1NbWNo+9+OKLM3v27Nx1113p3bt3iRIDAAAAQOt0K3UAaGuLFi1q3r2bvHIm7/Tp09OvX7+MGzeu+fry5ctzxhlnZNCgQTnooIOSJD179swDDzzQ3pEBAAAAoFUUvHQ6Y8aMyZgxY5p/v3DhwiTJXnvtlXnz5jVfr6+vT6FQaPd8AAAAANBWFLxUjMcff7zUEQAAAACgTTmDFwAAAACgTNnBS4fX0NBQ6ghvqiNnAwAAAKDzU/DS4fXv37/UEQAAAACgQ3JEAwAAAABAmbKDlw6puro6GzZsKHWMFqmuri51BAAAAAAqjIKXDqmqqio1NTWljgEAAAAAHZojGgAAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMqUghcAAAAAoEwpeAEAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMqUghcAAAAAoEwpeAEAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMpUt1IHAF6vUCiksbGxze/b1NTU/HNDQ0Ob3ru6ujpVVVVtek8AAAAA3pqCFzqgxsbG1NbWFu3+q1atavP7b9iwITU1NW16TwAAAADemiMaAAAAAADKlB280MGtWbOmw+6MbWhoSP/+/UsdAwAAAKBiKXihg6upqemwBS8AAAAApeWIBgAAAACAMqXgBQAAAAAoUwpeAAAAAIAypeAFAAAAAChTCl7oRObPn5+qqqqtftTW1mb48OGZNm1aNm/eXOqIAAAAALShbqUOALS94447LqNHj06hUMjq1atz9dVX5/TTT8+SJUsyc+bMUscDAAAAoI0oeKETGj58eCZMmND8+8mTJ2fPPffMrFmzcv7552fXXXctYToAAAAA2oojGqAC1NTUZMSIESkUClm2bFmp4wAAAADQRhS8SX7xi19k0qRJ2X///TNw4MD07NkzO+64Y/bZZ5984xvfyNq1a0sdEbbbq8Vunz59SpwEAAAAgLbiiIYkF198cX71q1+lR48e2X333fP+978/f/nLX/Loo4/mkUceyaxZs3LnnXdmn332KXVU2CaNjY1Zu3Zt8xm8M2bMyKJFi7L//vtnyJAhpY4HAAAAQBuxgzfJ5z//+dxzzz154YUX8oc//CELFy7MH//4xzzyyCP5+7//+zz77LM5/vjjSx0TttmUKVOy6667Zrfddsv73//+TJ8+Pcccc0xuuummUkcDSmjDhg3505/+lDVr1mTz5s2ljtPuNm3alNWrV+fPf/5zGhoaSh0HAACgTSh4k3zmM5/JwQcfnB49emx1fdiwYbnyyiuTJEuWLMmSJUtKEQ9a7KSTTspdd92VW2+9NRdddFH69OmT5cuXp1evXs1jxo8fn2OPPXareevWrUtdXV2uueaa9o4MFMmWLVtyyy235IgjjshOO+2Ud77znRkwYEB23333fP3rX88zzzxT6ohFt3Tp0px55pnp379/6urq8nd/93fZaaedcvTRR+euu+5KU1NTqSMCAAC0moL3bQwdOrT5142NjSVMAttu8ODBOeSQQzJq1KicddZZmTt3bhYuXJiTTz65ecz06dOzYMGCzJ49u/naKaeckgMOOCAnnHBCKWIDbey5557Lxz/+8YwZMya33nprCoVC82fPPvts/uM//iN77LFHZs6cWcKUxVMoFDJt2rQMGTIk3/3ud/Pcc881f9bU1JQbb7wxhx12WI444oi88MILJUwKAADQegret7FgwYIkSU1NTd773veWOA20zsiRI3PiiSfm2muvzf3335/klZetXXnllTn11FOzcuXKzJkzJ/Pnz8+MGTNKnBZoCw0NDfnEJz6RX/3qV285bsuWLfniF7+YH/zgB+2UrP1MmzYtp59++lbF9hu5/fbbc9RRR+Wll15qp2QAAABtR8H7BpqamrJq1apcffXV+dznPpckueCCC1JbW1vaYLAdzj333HTt2jXnnXde87XDDz88xx57bCZMmJDJkydn1qxZ6du3bwlTAm3l/PPPz8KFC7d5/KRJk7J8+fIiJmpfTzzxRM4888xtHj9//vxMmzatiIkAAACKQ8H7GjNmzEhVVVW6du2a3XffPZ/97GdTX1+fuXPn5stf/nKp48F22WOPPTJ+/Pjcc889ue+++5qvT506NUuXLs2oUaNyxBFHlDAh0FZeeumlFu/I3bJlS6faxTtjxoy33bn7RnO2bNlSpEQAAADFoeB9jbq6unzkIx/Jhz70oey+++6pqqrKo48+mp/+9Kd5/vnnSx0PttvZZ5+dLl26bLWLt6amJoMGDcqwYcNKmAxoSzfeeGPWrl3b4nkzZ87sFC8ce+mll/KjH/2oxfP++Mc/5s477yxCIgAAgOKpKrR0e0sFeeyxx3LKKafkvvvuy0c+8pH8+te/btV99ttvv6xevbqN09GZvXpMSJJs2LAhNTU1Rf16Bx54YMaMGdOib2dOXjnj89WjS+rq6tKlS8f/O6NVq1alqakpXbp0SV1dXanjtDvrr4z1/+1vf2v1S8PK5b/Lb2Xz5s1Zs2ZNq+buvPPOjmQCAADa3YABA/LQQw+1am63Ns7SqQwbNiy33HJLBg0alAULFuTuu+/OIYcc0uL7rF69OitWrChCQug4Xi2ky0VTU1NF//fS+it7/W+l3P673Naef/5537UDAACUFQXv29hxxx3zsY99LP/1X/+VRx55pFUF74ABA4qQjM7stTt4y0W57PqrlB2cb8b6K2P9GzZsaHVJ+eoRReVse/4d2rt376J/1wQAAMD/tT39oYJ3G2zevDlJWv3ildZur6Zyvfbog/Ywf/787b7HU089VRalSH19fVasWJG6urosX7681HHanfVXxvqXL1+ed73rXS3+361jjz021157bZFSta9Ro0bl9ttvb9Gcnj17ZunSpenbt2+RUgEAALS9jr/drsTWrVuXX/3qV0mSffbZp7RhAGAb1NfX58gjj2zxvMmTJxchTWm0Zi3jx49X7gIAAGWn4gvehx56KOedd16WLl36us8WLVqUUaNGZf369Rk2bFg+/vGPlyAhALTcv/7rv6a6unqbxx9xxBH5//6//6+IidrX6NGjc+CBB27z+N69e+cb3/hG8QIBAAAUScUXvBs2bMi3vvWtDB48OP37989+++2XD33oQxk4cGCGDx+eBx98MEOGDMmNN96Yrl27ljouAGyTvffeOzfeeOM2HZ1y0EEH5Wc/+1nZn737Wl27ds0NN9yQESNGvO3YnXfeOXPnzs2QIUPaIRkAAEDbqviCd++9986ll16acePGZaeddsqTTz6ZRYsWZcuWLTnkkENy+eWX55FHHsmgQYNKHRUAWuTQQw/N/fffn2OPPTbdur3+2P13vOMdOf/883P77be367nf7aV379755S9/mSlTprzhS/V69OiRCRMm5Le//W0OOOCAEiQEAADYflWFQqFQ6hDA1l77krUNGzZ02JeXlUvO13r1JVsDBw7s1C/ZejPWX7nrX7VqVW666aacddZZeeGFF9KnT5+sWbPmDYvfzmjTpk255ZZb8tnPfjZ/+9vf0rt37zz55JPZddddSx0NAABgu1T8Dl4AqAR1dXU5+eSTs9NOOyVJdthhh4opd5Oke/fuGTduXHbcccckSU1NjXIXAADoFBS8UGHmzJmTSZMmZePGjRk3blyGDBmSvffeO4ceeugbvmwQAAAAgI5LwQsV5oYbbsi4ceOSJCeddFKeeOKJPPLIIxk7dmwmTpxY2nAAAAAAtIiCFzqZ9evXp76+Pn379s0+++yToUOHpmfPnpk4cWI2bdqUBQsW5OCDD06vXr0yevToVFVVJUlGjBiRZ555prThAQAAAGgRBS90Mr17987xxx+f0047LYsXL84ll1ySESNGZNasWZk3b15GjhyZ7t27v27epZdemrFjx5YgMQAAAACtpeCFTmjx4sXZd999kyQPP/xw869vvPHGHH300a8bf8EFF2Tp0qW58MIL2zUnAAAAANtHwQud0BsVvIVCIXfccUdGjRq11dipU6fm+uuvz2233Zbq6upSxAUAAACglRS80MmsWLEiVVVVGThwYJLk0UcfzbBhw/Lggw9m6NChqa2tbR578cUXZ/bs2bnrrrvSu3fvEiUGAAAAoLW6lToA0LYWLVrUvHs3eeVM3unTp6dfv34ZN25c8/Xly5fnjDPOyKBBg3LQQQclSXr27JkHHnigvSMDAAAA0EoKXuhkxowZkzFjxjT/fuHChUmSvfbaK/PmzWu+Xl9fn0Kh0O75AAAAAGg7Cl6oEI8//nipIwAAAADQxhS80ME1NDSUOsKb6sjZAAAAACqBghc6uP79+5c6AgAAAAAdVJdSBwAAAAAAoHXs4IUOqLq6Ohs2bCh1jBaprq4udQQAAACAiqPghQ6oqqoqNTU1pY4BAAAAQAfniAYAAAAAgDKl4AUAAAAAKFMKXgAAAACAMqXgBQAAAAAoUwpeAAAAAIAypeAFAAAAAChTCl4AAAAAgDKl4AUAAAAAKFMKXgAAAACAMqXgBQAAAAAoUwpeAAAAAIAypeAFAAAAAChTCl4AAAAAgDKl4AUAAAAAKFMKXgAAAACAMqXgBQAAAAAoUwpeAAAAAIAypeAFAAAAAChT3UodAOCNFAqFNDY2tvl9m5qamn9uaGho03tXV1enqqqqTe8JAAAA8FYUvECH1NjYmNra2qLdf9WqVW1+/w0bNqSmpqZN7wkAAADwVhzRAAAAAABQpuzgBTq8NWvWdNidsQ0NDenfv3+pYwAAAAAVSsELdHg1NTUdtuAFAAAAKCVHNAAAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACncb8+fNTVVW11Y/a2toMHz4806ZNy+bNm0sdEQAAAKBNdSt1AIC2dtxxx2X06NEpFApZvXp1rr766px++ulZsmRJZs6cWep4AAAAAG1GwQt0OsOHD8+ECROafz958uTsueeemTVrVs4///zsuuuuJUwHAAAA0HYc0QB0ejU1NRkxYkQKhUKWLVtW6jgAAAAAbUbB+yZ+8IMfNJ/heeCBB5Y6DrCdXi12+/TpU+IkAAAAAG3HEQ1vYPXq1TnrrLNKHQNopcbGxqxdu7b5DN4ZM2Zk0aJF2X///TNkyJBSxwMAAABoMwreN/ClL30pf/vb3zJmzJjcfPPNpY4DtNCUKVMyZcqUra4dc8wxufzyy0uUCKC0nn/++Vx99dW555578sILL6SmpiYHHHBAPv/5z6dfv36ljld0TU1N+eUvf5kf//jHWblyZbp27Zp3v/vd+ad/+qfst99+pY4HAADbRcH7f/ziF7/InDlz8qUvfSl9+vRR8EIZOumkk/KpT30qmzZtymOPPZaLLrooy5cvT69evZrHjB8/Pk1NTbnuuuuar61bty577bVXpk6dmhNOOKEU0QHa1ObNm/P1r3893//+99PQ0LDVZ3Pnzs15552Xz372s7nkkkuyww47lChlcd1+++3553/+5zz55JOv+2zGjBn54Ac/mJkzZ2afffZp/3AAANAGnMH7Gi+88EJOOeWU7L777vn3f//3UscBWmnw4ME55JBDMmrUqJx11lmZO3duFi5cmJNPPrl5zPTp07NgwYLMnj27+dopp5ySAw44QLkLdAqbNm3KMccck6lTp76u3H3VSy+9lJkzZ+awww5LY2NjOycsvp/97GcZM2bMG5a7r1q4cGE++tGPZsGCBe2YDAAA2o6C9zW+/vWvZ/ny5bnkkkuy0047lToO0EZGjhyZE088Mddee23uv//+JK+8bO3KK6/MqaeempUrV2bOnDmZP39+ZsyYUeK0AG3ja1/7WubOnbtNY3/961/ni1/8YpETta/f/e53+cxnPpMtW7a87dgNGzbkqKOOyurVq9shGQAAtC0F7//6zW9+k+9///sZNWpUPvWpT5U6DtDGzj333HTt2jXnnXde87XDDz88xx57bCZMmJDJkydn1qxZ6du3bwlTArSN5557Lt///vdbNOeaa67JM888U5xAJXDxxRdn06ZN2zx+3bp1+cEPflDERAAAUBwK3rzyLYxf+MIX0rNnz1x22WWljgMUwR577JHx48fnnnvuyX333dd8ferUqVm6dGlGjRqVI444ooQJAdrOVVddlRdffLFFcwqFQmbOnFmkRO3rL3/5S37+85+3eN4VV1yRzZs3FyERAAAUj4I3yX/8x3/k8ccfzznnnJNBgwaVOg5QJGeffXa6dOmy1S7empqaDBo0KMOGDSthMoC2ddddd7XrvI7mvvvuy8svv9zieStWrMiSJUuKkAgAAIqnW6kDlNoTTzyR888/P0OHDs1XvvKVonyN/fbbz5lu0EJNTU0tnnPggQemUCi86edDhw7dprMYW2vw4MHp0qVj/73ZqlWrmn+ur68vcZr2V+nrTzyDSln/s88+26p5ixYt6hTP5c1eKrctDj744PTs2bMN0wAAwNsbMGBAHnrooVbNrfiCd9KkSXnppZcyY8aMdO/evShfY/Xq1VmxYkVR7g10HK8WR+Wgqampov+9VOnrTzyDSl//m9myZUvFP5e1a9eWOgIAALRIxRe8v/vd79KlS5cce+yxr/tsw4YNSZL7778/AwYMSJI8+eST2WmnnVr0NV6dC2y7pqamsipMk6Surq4sdvA2NTWlS5cuqaurK3Wcdlfp6088g0pZ/9/+9re88MILLZ5XU1OT3r17t32gdrZ58+asWbOmxfOqqqpSV1eXqqqqIqQCAIA3tz39YVXhrb6fuQL07t07zz///DaPf+655zrFH3ygo2toaEhtbW2SV/6ypaampsSJ3li55HxVfX19VqxYkYEDB2b58uWljtPuKn39iWdQKetfuXJl3vnOd7b4hWG///3vs9deexUpVfs66qijMnfu3BbNOfPMM/Od73ynSIkAAKA4OvZWs3awfv36FAqFN/wxZcqUJMnHPvax5mvKXQCgo9t9991z3HHHtWjOJz7xiU5T7ibJv/zLv7RofK9evTJp0qQipQEAgOKp+IIXAKAzmj59evbbb79tGjtkyJD8+Mc/LnKi9nXQQQfl29/+9jaN7dq1a37yk59k0KBBRU4FAABtT8ELANAJ1dbW5pe//GU++clPvuW4Qw89NL/+9a+z6667tlOy9vOVr3wlV1xxxVu+P2HAgAGZO3fu2z4nAADoqBS8AACd1I477pg5c+bkySefzOmnn573v//96dq1a5Kkuro6jzzySO68885OWe6+6qSTTsrKlSszc+bMfPSjH21ef8+ePXPdddflT3/6U0aNGlXilAAA0HoV/5I1oGMql5eXlUvOV1XKC6beTKWvP/EMKn39iWdQ6esHAKDzsYMXqDhz5szJpEmTsnHjxowbNy5DhgzJ3nvvnUMPPTRLly4tdTwAAACAbabgBSrODTfckHHjxiV55Vt3n3jiiTzyyCMZO3ZsJk6cWNpwAAAAAC2g4AU6nfXr16e+vj59+/bNPvvsk6FDh6Znz56ZOHFiNm3alAULFuTggw9Or169Mnr06FRVVSVJRowYkWeeeaa04QEAAABaQMELdDq9e/fO8ccfn9NOOy2LFy/OJZdckhEjRmTWrFmZN29eRo4cme7du79u3qWXXpqxY8eWIDEAAABA6yh4gU5p8eLF2XfffZMkDz/8cPOvb7zxxhx99NGvG3/BBRdk6dKlufDCC9s1JwAAAMD2UPACndIbFbyFQiF33HFHRo0atdXYqVOn5vrrr89tt92W6urqUsQFAAAAaBUFL9DprFixIlVVVRk4cGCS5NFHH82wYcPy4IMPZujQoamtrW0ee/HFF2f27Nm566670rt37xIlBgAAAGidbqUOANDWFi1a1Lx7N3nlTN7p06enX79+GTduXPP15cuX54wzzsigQYNy0EEHJUl69uyZBx54oL0jAwAAALSKghfodMaMGZMxY8Y0/37hwoVJkr322ivz5s1rvl5fX59CodDu+QAAAADaioIXqBiPP/54qSMAAAAAtCkFL9DhNTQ0lDrCm+rI2QAAAIDOT8ELdHj9+/cvdQQAAACADqlLqQMAAAAAANA6dvACHVJ1dXU2bNhQ6hgtUl1dXeoIAAAAQIVR8AIdUlVVVWpqakodAwAAAKBDc0QDAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUqW6lDgDA6xUKhTQ2Nrb5fZuampp/bmhoaNN7V1dXp6qqqk3uVenrBwAAgG2l4AXogBobG1NbW1u0+69atarN779hw4bU1NS0yb0qff0AAACwrRzRAAAAAABQpuzgBejg1qxZ02F3hjY0NKR///5F/RqVvn4AAAB4KwpegA6upqamwxac7aHS1w8AAABvxRENAAAAAABlSsELAAAAAFCmFLwAAAAAAGVKwQsAAAAAUKYUvACdyPz581NVVbXVj9ra2gwfPjzTpk3L5s2bSx2xqCp9/QAAAFSebqUOAEDbO+644zJ69OgUCoWsXr06V199dU4//fQsWbIkM2fOLHW8oqv09QMAAFA5FLwAndDw4cMzYcKE5t9Pnjw5e+65Z2bNmpXzzz8/u+66awnTFV+lrx8AAIDK4YgGgApQU1OTESNGpFAoZNmyZaWO0+4qff0AAAB0XgreJJ/73Oded2bj//3xP//zP6WOCbBdXi02+/TpU+IkpVHp6wcAAKBzckTDawwePDi77bbbG35WXV3dzmkAWq+xsTFr165tPoN2xowZWbRoUfbff/8MGTKk1PGKrtLXDwAAQOVQ8L7GN77xjXzuc58rdQyA7TZlypRMmTJlq2vHHHNMLr/88hIlal+Vvn6AN/LUU0/l0UcfzYsvvphddtklH/vYx1JbW1vqWO1mw4YN+dWvfpXnnnsuO+ywQ/bee+/ssccepY4FALDdHNEA0AmddNJJueuuu3LrrbfmoosuSp8+fbJ8+fL06tWrecz48eNz7LHHbjVv3bp1qauryzXXXNPekdtUpa8f4LXmzp2bQw89NEOGDMk//MM/5MQTT8yYMWMycODA/PM//3P+8Ic/lDpiUT399NP50pe+lN133z1jxozJiSeemH/4h3/I4MGDc9hhh+Xmm28udUQAgO2i4AXohAYPHpxDDjkko0aNyllnnZW5c+dm4cKFOfnkk5vHTJ8+PQsWLMjs2bObr51yyik54IADcsIJJ5Qidpup9PUDJEmhUMjpp5+eo446KnfffffrPv/b3/6W//f//l+GDx+e++67rwQJi+/ee+/N8OHDc9lll+WFF1543ed33XVXjjzyyJx55pkpFAolSAgAsP0UvK8xZ86cjBs3LgcffHCOPfbYXHzxxXn22WdLHQtgu40cOTInnnhirr322tx///1JXnnZ2JVXXplTTz01K1euzJw5czJ//vzMmDGjxGnbXqWvH6hMU6ZMybRp09523Pr163PEEUfk0UcfbYdU7eeRRx7JEUcckeeff/5tx373u9/NN7/5zXZIBQDQ9hS8r3HLLbfkpptuyrx58/Lzn/88Z5xxRt797nfnJz/5SamjAWy3c889N127ds15553XfO3www/PsccemwkTJmTy5MmZNWtW+vbtW8KUxVPp6wcqyx//+Mecf/752zz+hRdeyNe+9rUiJmp/Z511VjZs2LDN47/1rW9l+fLlRUwEAFAcCt4kQ4YMybRp07J48eKsX78+DQ0Nuffee3PYYYeloaEhn/nMZ3LLLbeUOibAdtljjz0yfvz43HPPPVt9K+7UqVOzdOnSjBo1KkcccUQJExZXpa8fqCwzZ85MU1NTi+bcfvvtWbZsWZESta+nnnoqd955Z4vmNDU1ZebMmUVKBABQPAreJN/4xjdy2mmnZe+9987OO++c6urqfPSjH83tt9+esWPHplAo5LTTTnMuF1D2zj777HTp0mWrXaw1NTUZNGhQhg0bVsJk7aPS1w9UjquvvrrFcwqFQqd5yWRrvwOvNc8NAKDUqgpay7f0xBNPZM8990zyyjle73//+1t8j/322y+rV69u62hAJ9bU1JRVq1YlSTZs2JCampqifr0DDzwwY8aMyZlnntmieQ0NDamtrU2S1NXVpUuXtvl7w0pffzGtWrUqTU1N6dKlS+rq6kodp91V+voTz6AS1l8oFLJy5cpWza2urs4uu+zSxona33PPPZfGxsZWzd19991TVVXVxokAAN7agAED8tBDD7Vqbrc2ztLpvPe9702fPn2ybt26PPXUU60qeFevXp0VK1YUIR1Ax/FqIVupym39TU1NFf2/TZW+/sQzqPT1v5nGxsZWF6OdRWvLcQCAUlHwboPu3bsnSTZv3tyq+QMGDGjLOEAFeO0O1nJRrB285cIO3vJQ6etPPINKWf/q1auzZcuWFs/baaedsuOOOxYhUft64YUX8re//a3F87p165b+/fsXIREAwFvbnv7QEQ1v49lnn03//v1TKBTy61//Oh/5yEdKHQmoAK/91v/2OKKgtYqVs9LXX0z19fVZsWJFBg4cWJFvi6/09SeeQaWs/4ILLsjZZ5/dojldu3bNn/70p+y+++5FStV+li9fnne9610tLrn/4z/+I1/96leLlAoAoDg6/lajEvvud7+bQqGQnXfeOR/84AdLHQcAAN7WxIkTm78LbVsdffTRnaLcTV4p8o866qgWzenZs2f+6Z/+qUiJAACKp+IL3rvuuitf+9rXsmzZsq2uNzY25t/+7d/y7W9/O0ny9a9/PT169ChFRAAAaJHddtst06ZN2+bx/fv3z3e+850iJmp/U6dOzW677bbN46dNm5Z+/foVMREAQHFU/Bm8DQ0Nueiii3LRRRelrq4uAwcOTFNTU5YsWZIXX3wxSXLSSSflrLPOKnFSAADYdqeccko2btyYM8888y3HveMd78itt96ad73rXe0TrJ0MGjQod999d0aPHv2Wx3FUVVXlu9/9biZNmtSO6QAA2k7F7+D9wAc+kHPOOScf//jH06NHj/z3f/93Hn/88ey666759Kc/nbvvvjtXXHFFqqqqSh0VAABa5IwzzshDDz2Uf/zHf0yvXr22+uzd7353vv3tb2fx4sX5+7//+xIlLK5hw4Zl8eLFueiii96wwP785z+fhx56KP/yL//S/uEAANqIl6wBdEDl8vIuL1krj5yvVSkvmHozlb7+xDOo5PU/99xzee9735tnn302u+22W1atWpUuXSpnv8eWLVvy+OOP5+Mf/3jWrl2burq6rFy5stSxAAC2W+X8PzoAkiRz5szJpEmTsnHjxowbNy5DhgzJ3nvvnUMPPTRLly4tdbyiq/T1A5Vrl112aX6nRPfu3Suq3E2Srl275v3vf3969uyZJBW3fgCg8/L/agAqzA033JBx48YleeWM8SeeeCKPPPJIxo4dm4kTJ5Y2XDuo9PUDAADQuSh4ATqZ9evXp76+Pn379s0+++yToUOHpmfPnpk4cWI2bdqUBQsW5OCDD06vXr0yevTo5jPGR4wYkWeeeaa04dtApa8fAACAyqLgBehkevfuneOPPz6nnXZaFi9enEsuuSQjRozIrFmzMm/evIwcOTLdu3d/3bxLL700Y8eOLUHitlXp6wcAAKCyKHgBOqHFixdn3333TZI8/PDDzb++8cYbc/TRR79u/AUXXJClS5fmwgsvbNecxVLp6wcAAKByKHgBOqE3KjgLhULuuOOOjBo1aquxU6dOzfXXX5/bbrst1dXVpYjb5ip9/QAAAFQOBS9AJ7NixYpUVVVl4MCBSZJHH300w4YNy4MPPpihQ4emtra2eezFF1+c2bNn56677krv3r1LlLhtVfr6AQAAqCzdSh0AgLa1aNGi5t2ryStn0k6fPj39+vXLuHHjmq8vX748Z5xxRgYNGpSDDjooSdKzZ8888MAD7R25TVX6+gEAAKgsCl6ATmbMmDEZM2ZM8+8XLlyYJNlrr70yb9685uv19fUpFArtnq/YKn39AAAAVBYFL0CFePzxx0sdoaQqff0AAAB0Ts7gBQAAAAAoU3bwAnRwDQ0NpY7wptojW6WvHwAAAN6Kghegg+vfv3+pI5RUpa8fAAAA3oojGgAAAAAAypQdvAAdUHV1dTZs2FDqGC1SXV3dpveq5PUDAADAtlLwAnRAVVVVqampKXWMkqn09QMAAMC2ckQDAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmepW6gAAwOsVCoU0Nja2+X2bmpqaf25oaGjTe1dXV6eqqqpN7wkAAMBbU/ACQAfU2NiY2traot1/1apVbX7/DRs2pKampk3vCQAAwFtzRAMAAAAAQJmygxcAOrg1a9Z02J2xDQ0N6d+/f6ljAAAAVCwFLwB0cDU1NR224AUAAKC0HNEAAAAAAFCmFLwAAAAAAGVKwQsAAAAAUKYUvAAAAAAAZUrBCwAAAABQphS8ANCJzJ8/P1VVVVv9qK2tzfDhwzNt2rRs3ry51BEBAABoQ91KHQAAaHvHHXdcRo8enUKhkNWrV+fqq6/O6aefniVLlmTmzJmljgcAAEAbUfACQCc0fPjwTJgwofn3kydPzp577plZs2bl/PPPz6677lrCdAAAALQVRzT8HzfeeGOOPPLI1NXVpWfPnqmrq8tBBx2U73znO6WOBgCtVlNTkxEjRqRQKGTZsmWljgMAAEAbsYP3f7388ss54YQTMmfOnCTJoEGD8o53vCNr1qzJfffdl8ceeyxf+cpXSpwSAFrv1WK3T58+JU4CAABAW1Hw/q+JEydmzpw5Ofzww3PZZZflPe95T/Nn69evz7333lvCdADQMo2NjVm7dm3zGbwzZszIokWLsv/++2fIkCGljgcAAEAbcURDkjvvvDM//vGP86EPfShz587dqtxNkt69e+eoo44qUToAaLkpU6Zk1113zW677Zb3v//9mT59eo455pjcdNNNpY4GQDtbt25dvvvd72avvfZKTU1NdthhhwwaNChTpkzJ8uXLSx2v6LZs2ZJbbrklY8aMyS677JIePXqkb9+++fSnP51f/epXKRQKpY4IANtFwZtk2rRpSZJzzjkn3brZ1AxA+TvppJNy11135dZbb81FF12UPn36ZPny5enVq1fzmPHjx+fYY4/dat66detSV1eXa665pr0jA1AEV155ZQYOHJgzzzwz//3f/53GxsZs3Lgxf/jDH/Jv//Zvede73pV//dd/7bQl59KlSzNs2LCMGTMmt9xyS9avX59NmzZl3bp1ue6663LggQdm5MiRWbNmTamjAkCrVXzB++KLL+buu+9Oly5dctBBB+WBBx7IySefnEMOOSTjxo3Lf/zHf2Tt2rWljgkALTJ48OAccsghGTVqVM4666zMnTs3CxcuzMknn9w8Zvr06VmwYEFmz57dfO2UU07JAQcckBNOOKEUsQFoQ5dffnkmTpyYjRs3vumYLVu25Jvf/GanfN/I008/nQMOOCBLlix5y3G//e1v89GPftSf+wAoWxVf8D7yyCPZvHlz+vbtm8suuywf/vCHc8UVV+See+7JTTfdlK9//esZPHhw5s2bV+qoANBqI0eOzIknnphrr702999/f5JXXrZ25ZVX5tRTT83KlSszZ86czJ8/PzNmzChxWgC216OPPpovf/nL2zz+u9/9bn7xi18UMVH7KhQKGT9+/DbvzH3qqafyhS98ocipAKA4Kr7gXbVqVZLkueeey9e+9rWMHj06jz/+eF566aU8+uijOfjgg7N+/focc8wxFXE+FQCd17nnnpuuXbvmvPPOa752+OGH59hjj82ECRMyefLkzJo1K3379i1hSgDawmWXXZampqYWzfne975XpDTt74EHHsjChQtbNOemm27KM888U5xAAFBEFV/wNjQ0JEk2b96c97znPbnhhhvyvve9Lz169MiwYcMyd+7cDBgwIOvXr88ll1xS2rAAsB322GOPjB8/Pvfcc0/uu+++5utTp07N0qVLM2rUqBxxxBElTAhAW/jb3/7WqrPU77777jz55JNFSNT+vv/977d4TqFQyBVXXFGENABQXBX/RrHXvmzm1FNPTffu3bf6vLq6OpMmTcqUKVNy++23Z+rUqS3+Gvvtt19Wr1693VkBqBwt3XW1rc4+++zMnj075513XvPxQzU1NRk0aFCGDRu2XfcePHhwunTp2H93/Op37qxatSr19fUlTlMalf4MrL+y159UxjN4+eWX09jY2Kq5H/7wh7PDDju0caL219qXpk2bNi0//vGP2zgNALy9AQMG5KGHHmrV3IoveHfZZZfmXw8dOvQNx7x6/Q9/+EOrvsbq1auzYsWKVs0FgJY48MAD3/JN6EOHDs2WLVuK8rVfLU3KQVNTU8X/b3OlPwPrr+z1J57Bm1m3bl2pI5TUSy+95J8LAMpOxRe8e+65Z/Ove/To8YZjXt3l29o/EA8YMKBV8wCoXE1NTWVVmCZJXV1dWezgbWpqSpcuXVJXV1fqOCVR6c/A+it7/UllPINNmzblL3/5S6vm9unTp1Ps4P3LX/6STZs2tXher169nEUPQElsT39Y8QXvwIED83d/93f505/+lKeffjoHHXTQ68YsW7YsSVr9LVyt3V4NQOVqaGhIbW1tqWO0yFNPPZWamppSx3hL9fX1WbFiRerq6ir25amV/gysv7LXn1TGM2hqasoee+zR4u9ArK2tzR/+8IfstNNORUrWfr71rW9t9VLRbXX55Zfn85//fBESAUDxdOxtNu3k2GOPTZJcddVVr/usUCjkP//zP5MkBx98cHvGAoB2M3/+/Jx55pmljgFAG+jSpUsmTZrU4nknnnhipyh3k2TixInp1q1l+5l69+6d8ePHFykRABSPgjfJV77yley0006577778q1vfav5KIbNmzfnq1/9ah555JH07Nkz//Iv/1LipAAAAG/vn/7pn1r0HYg77rhjp/rzTl1dXU4++eQWzfnqV7+a6urqIiUCgOJR8CbZbbfd8rOf/Sw9e/bMeeedl7q6unzoQx/KgAED8p3vfCfdunXLrFmz3vQlbAAAAB1Jnz59ctttt2W33XZ727HV1dW54YYbMnjw4HZI1n4uvvjijB07dpvGfvGLX8xXv/rVIicCgOJQ8P6vUaNGZdGiRZkwYUK6deuWRYsWpVu3bjn22GPzwAMPZMKECaWOCAAAsM3+/u//Pr/97W8zduzYN30J5sEHH5x77703H//4x9s5XfF17949//Vf/5V//dd/Tb9+/d5wTH19fS699NJ8//vfT1VVVTsnBIC2UfEvWXutoUOH5sc//nGpYwAAALSJd7/73bnxxhvz5z//OVdddVUuvPDCNDY2pra2Ng8++GCn/y7Frl27ZsqUKfna176Wn//85zn55JPT0NCQmpqa/OQnP8mYMWNafFYvAHQ0dvACAAB0cu94xztyzjnnZJdddkmS7Lzzzp2+3H2tnj17ZsKECendu3eSV16oNm7cOOUuAJ2CghcAKsycOXMyadKkbNy4MePGjcuQIUOy995759BDD83SpUtLHQ8AAIAWUPACQIW54YYbMm7cuCTJSSedlCeeeCKPPPJIxo4dm4kTJ5Y2HAAAAC2i4AWATmb9+vWpr69P3759s88++2To0KHp2bNnJk6cmE2bNmXBggU5+OCD06tXr4wePbr5pTIjRozIM888U9rwAAAAtIiCFwA6md69e+f444/PaaedlsWLF+eSSy7JiBEjMmvWrMybNy8jR45M9+7dXzfv0ksvzdixY0uQGAAAgNZS8AJAJ7R48eLsu+++SZKHH364+dc33nhjjj766NeNv+CCC7J06dJceOGF7ZoTAACA7aPgBYBO6I0K3kKhkDvuuCOjRo3aauzUqVNz/fXX57bbbkt1dXUp4gIAANBKCl4A6GRWrFiRqqqqDBw4MEny6KOPZtiwYXnwwQczdOjQ1NbWNo+9+OKLM3v27Nx1113p3bt3iRIDAADQWt1KHQAAaFuLFi1q3r2bvHIm7/Tp09OvX7+MGzeu+fry5ctzxhlnZNCgQTnooIOSJD179swDDzzQ3pEBAABoJQUvAHQyY8aMyZgxY5p/v3DhwiTJXnvtlXnz5jVfr6+vT6FQaPd8AAAAtB0FLwBUiMcff7zUEQAAAGhjCl4A6OAaGhpKHeFNdeRsAAAAlUDBCwAdXP/+/UsdAQAAgA6qS6kDAAAAAADQOnbwAkAHVF1dnQ0bNpQ6RotUV1eXOgIAAEDFUfACQAdUVVWVmpqaUscAAACgg3NEAwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlKlupQ4AAPB/FQqFNDY2tvl9m5qamn9uaGho03tXV1enqqqqTe8JAADwdhS8AECH09jYmNra2qLdf9WqVW1+/w0bNqSmpqZN7wkAAPB2HNEAAAAAAFCm7OAFADq0NWvWdNidsQ0NDenfv3+pYwAAABVMwQsAdGg1NTUdtuAFAAAoNUc0AAAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAncb8+fNTVVW11Y/a2toMHz4806ZNy+bNm0sdEQAAoE11K3UAAIC2dtxxx2X06NEpFApZvXp1rr766px++ulZsmRJZs6cWep4AAAAbUbBCwB0OsOHD8+ECROafz958uTsueeemTVrVs4///zsuuuuJUwHAADQdhzRAAB0ejU1NRkxYkQKhUKWLVtW6jgAAABtpuIL3meeeeZ1Z/W92Y9vfvObpY4LALTSq8Vunz59SpwEAACg7VT8EQ29evXKRz7ykTf9/IUXXsijjz6aJBk5cmR7xQIAtkNjY2PWrl3bfAbvjBkzsmjRouy///4ZMmRIqeMBAAC0mYoveAcMGJBf//rXb/r5t7/97Tz66KOpr6/Pxz/+8XZMBgC01pQpUzJlypStrh1zzDG5/PLLS5QIAErr8ccfz7XXXpu//OUv6d69e9773vfmhBNOyC677FLqaO3i+eefz09/+tMsWbIkL7/8cnbdddf8wz/8Q/bee+9SRwPYbhVf8L6dq6++Okly4oknpkuXij/RAgDKwkknnZRPfepT2bRpUx577LFcdNFFWb58eXr16tU8Zvz48Wlqasp1113XfG3dunXZa6+9MnXq1JxwwgmliA4AbWrBggU5++yz86tf/ep1n5111lk54YQTctFFF3XaI4yef/75fO1rX8uPf/zjNDQ0bPXZv//7v+cjH/lI/v3f/z0HHnhgaQICtAGN5Vt4+OGH8/jjjydJPvvZz5Y4DQCwrQYPHpxDDjkko0aNyllnnZW5c+dm4cKFOfnkk5vHTJ8+PQsWLMjs2bObr51yyik54IADlLsAdAo33HBDDj744Dcsd5PkxRdfzKxZszJy5MisWrWqndMV31/+8pcccMABmTFjxuvK3VctWLAghx56aH72s5+1czqAtqPgfQtXXXVVkuRDH/pQ3vve95Y4DQDQWiNHjsyJJ56Ya6+9Nvfff3+SV162duWVV+bUU0/NypUrM2fOnMyfPz8zZswocVoA2H4PPfRQjjvuuLz88stvO/aJJ57IEUcckU2bNrVDsvaxZcuWHHXUUfn973//tmM3b96cz3zmM1mwYEE7JANoewreN7Fp06bmHT2f+9znShsGANhu5557brp27Zrzzjuv+drhhx+eY489NhMmTMjkyZMza9as9O3bt4QpAaBtXHDBBXnppZe2efyiRYty4403Fi9QO7v11lvzwAMPbPP4TZs25d///d+LmAigeBS8b+KWW27J2rVr07Nnz3z6058udRwAYDvtscceGT9+fO65557cd999zdenTp2apUuXZtSoUTniiCNKmBAA2sby5ctz0003tXje9OnTi5CmNFqzlttvvz3Lli0rQhqA4lLwvolXX6521FFHVcxbRQGgszv77LPTpUuXrXbx1tTUZNCgQRk2bFgJkwFA27n55pvT1NTU4nnz58/P+vXr2z5QO9u4cWNuv/32Vs39xS9+0cZpAIqvqlAoFEodoqP561//mt133z0vv/xybrnllowePXq77rfffvtl9erVbZQOADq/pqam5pe9bNiwITU1NUX9egceeGDGjBmTM888s0XzGhoaUltbmySpq6tLly4d/+/OV61alaampnTp0iV1dXWljtPurL+y1594BtZfGet/4YUX8re//a1Vc/v3759u3bq1caL2tWXLllb/GXzHHXfMTjvt1MaJAN7egAED8tBDD7Vqbnn/W7tIZs+enZdffjkDBgzIJz7xie2+3+rVq7NixYo2SAYAdFTl9vbxpqamiv7/J9Zf2etPPAPrr+z1v5U1a9aUOkJJvfDCC3nhhRdKHQOgRRS8b+Cqq65Kkpxwwgnp2rXrdt9vwIAB230PAKgkr93BWy7s4C0P1l/Z6088A+uvjPVv3Lgxf/3rX1s8r0uXLhkwYECqqqqKkKr9FAqFrFmzJlu2bGnx3D59+mSHHXYoQiqAt7Y9/aEjGv6P//7v/85ee+2VJHnsscfy93//9yVOBACV57VHH7THEQ2tVS45X6u+vj4rVqzIwIEDs3z58lLHaXfWX9nrTzwD66+M9Tc1NWXo0KF58sknWzTvvPPOyze/+c0ipWpfF154Yb7xjW+0aM7f/d3f5emnn26TjV4A7anjbzNpZ6++XG348OHKXQAAAMpOly5dcuqpp7ZoTo8ePfKFL3yhSIna3z/90z+1eCfu5MmTlbtAWVLwvkZTU1N+8pOfJEk++9nPljgNAAAAtM7kyZNzzDHHbPP4//zP/0x9fX0RE7Wv3XbbLddcc802H580evTonHHGGUVOBVAcCt7XuPvuu7NixYp07949xx9/fKnjAAAAQKt07do1s2fPzj/+4z++5bjq6upcd911Oe6449opWfs5+uijc/311zcfp/Rmjj/++Fx//fXp1s1rioDypOB9jVdfrnbEEUekX79+JU4DAAAArdejR4/88Ic/zO9///uccsop6du3b/Nn3bp1yyWXXJLly5fnU5/6VAlTFtfYsWOzfPnyfO9739vqGMaqqqp88YtfzOLFi3PNNdekZ8+eJUwJsH0UvK9xzTXXpFAo5IYbbih1FAAAAGgTe+21Vy677LKsXbs2u+++e5Kkf//++ed//ufssssuJU5XfDvvvHNOPfXUPPbYY83r33333TNjxozsvffeJU4HsP0UvABARZkzZ04mTZqUjRs3Zty4cRkyZEj23nvvHHrooVm6dGmp4wFAUVVVVZU6QklV+vqBzknBCwBUlBtuuCHjxo1Lkpx00kl54okn8sgjj2Ts2LGZOHFiacMBAAC0kIIXAOhU1q9fn/r6+vTt2zf77LNPhg4dmp49e2bixInZtGlTFixYkIMPPji9evXK6NGjm3fyjBgxIs8880xpwwMAALSQghcA6FR69+6d448/PqeddloWL16cSy65JCNGjMisWbMyb968jBw5Mt27d3/dvEsvvTRjx44tQWIAAIDWU/ACAJ3O4sWLs++++yZJHn744eZf33jjjTn66KNfN/6CCy7I0qVLc+GFF7ZrTgAAgO2l4AUAOp03KngLhULuuOOOjBo1aquxU6dOzfXXX5/bbrst1dXVpYgLAADQagpeAKBTWbFiRaqqqjJw4MAkyaOPPpphw4blwQcfzNChQ1NbW9s89uKLL87s2bNz1113pXfv3iVKDAAA0HrdSh0AAKAtLVq0qHn3bvLKmbzTp09Pv379Mm7cuObry5cvzxlnnJFBgwbloIMOSpL07NkzDzzwQHtHBgAAaDUFLwDQqYwZMyZjxoxp/v3ChQuTJHvttVfmzZvXfL2+vj6FQqHd8wEAALQlBS8AUBEef/zxUkcAAABoc87gBQAAAAAoU3bwAgAdWkNDQ6kjvKmOnA0AAKgMCl4AoEPr379/qSMAAAB0WI5oAAAAAAAoU3bwAgAdTnV1dTZs2FDqGC1SXV1d6ggAAEAFUvACAB1OVVVVampqSh0DAACgw3NEAwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAAAAAJQpBS8AAAAAQJnqVuoAAAC8XqFQSGNjY5vft6mpqfnnhoaGNrtvdXV1qqqq2ux+5bb+pO2fAQAAbAsFLwBAB9TY2Jja2tqi3X/VqlVtev8NGzakpqamze5XbutP2v4ZAADAtnBEAwAAAABAmbKDFwCgg1uzZk2H3Bna0NCQ/v37F/3rdNT1J+33DAAA4M0oeAEAOriampoOW3C2h0pfPwAAvBVHNAAAAAAAlCkFLwAAAABAmVLwAgAAAACUKQUvAAAAAECZUvACAHQS8+fPT1VV1VY/amtrM3z48EybNi2bN28udcSi8wwAAKg03UodAACAtnXcccdl9OjRKRQKWb16da6++uqcfvrpWbJkSWbOnFnqeO3CMwAAoFIoeAEAOpnhw4dnwoQJzb+fPHly9txzz8yaNSvnn39+dt111xKmax+eAQAAlcIRDQAAnVxNTU1GjBiRQqGQZcuWlTpOSXgGAAB0Vgre/7V27dp89atfzbBhw1JTU5OePXvmne98Z0488cT87ne/K3U8AIDt8mqp2adPnxInKR3PAACAzsgRDUmeeOKJHHjggVm9enW6dOmSd7/73amtrc2yZcvyk5/8JLNnz85VV12VE044odRRAQDeVmNjY9auXdt8/uyMGTOyaNGi7L///hkyZEip47ULzwAAgEqh4E0yadKkrF69Ou9973tz4403Zs8990ySNDQ05PTTT8/MmTNz8sknZ9SoUXZ8AAAd3pQpUzJlypStrh1zzDG5/PLLS5So/XkGALC1LVu25Mknn8zzzz+fmpqaDB48OL169Sp1rHa1cuXKrFy5MlVVVamvr0///v1LHQnaRMUf0fDCCy9k/vz5SZLvfOc7zeVu8spZbZdffnn69euXDRs25N577y1RSgCAbXfSSSflrrvuyq233pqLLrooffr0yfLly7f6Q9z48eNz7LHHbjVv3bp1qauryzXXXNPekducZwAAr3j22Wdz4YUX5j3veU/e97735cMf/nDe//73Z+DAgfnKV77S6c+m37JlS2688cYcdthhGThwYD74wQ9mv/32S11dXY488sjceuutaWpqKnVM2C4VX/C+9NJLKRQKSZJBgwa97vNu3brlne98Z5Jk06ZN7ZoNAKA1Bg8enEMOOSSjRo3KWWedlblz52bhwoU5+eSTm8dMnz49CxYsyOzZs5uvnXLKKTnggAM6xbFUngEAJA8++GD22muvfOMb38gf//jHrT5bt25dpk6dmr322is///nPS5SwuBoaGjJu3LgcffTRueuuu7b6rFAo5Oabb84RRxyRE044IS+99FKJUsL2q/iCt1+/fhk4cGCS5P7773/d5+vWrcv//M//pEuXLhk+fHh7xwMA2G4jR47MiSeemGuvvbb5/+/06dMnV155ZU499dSsXLkyc+bMyfz58zNjxowSpy0OzwCASvP444/nsMMOy7PPPvuW41566aWMHz8+N998czslax+bN2/OP/zDP2zTun72s5/lM5/5jJ28lK2KL3iT5IILLkhVVVW+8pWv5Ec/+lHWrFmThoaGLFiwIGPGjGk+i/c973lPqaMCALTKueeem65du+a8885rvnb44Yfn2GOPzYQJEzJ58uTMmjUrffv2LWHK4vIMAKgkJ598cp5//vltGtvU1JTPf/7znWoX69VXX53bb799m8dfd911ufHGG4sXCIpIwZvkM5/5TG644YYMHjw4n//85zNgwIDU1tbmgAMOyMqVK3P11VfnO9/5TqljAgC02h577JHx48fnnnvuyX333dd8ferUqVm6dGlGjRqVI444ooQJi88zAKBSPProo/n1r3/dojnPPvts/uu//qtIidpXoVBo1YtVv//97xchDRSfgjev/Bd/2bJlefbZZ9OlS5e8613vyvvf//5UV1fnj3/8Y6644oosWbKk1DEBALbL2WefnS5dumy1g7WmpiaDBg3KsGHDSpis/XgGAFSCH/7wh62aN2vWrDZOUhqPPvpofve737V43t13351nnnmm7QNBkXUrdYCOYNKkSbniiivywQ9+MHfeeWeGDBmSJHnxxRczZcqUfOc738mHP/zhPPbYY3nHO97R4vvvt99+Wb16dVvHBgA6sdacAXfggQc2vzz2jQwdOjRbtmzZnlhvavDgwenSpe32DrT2DLzO9AyKYdWqVc0/19fXlzhNaVT6M7D+yl5/4hlUyvr/+te/tmrevffe2ymey4svvtjquR/84AfTs2fPNkwD22bAgAF56KGHWjW34gveRx55JDNnzkz37t3z85//PO985zubP9thhx3y7W9/O7/73e9yzz335IILLmjVdv3Vq1dnxYoVbRkbAKBDefUPzJWsnJ5BU1NTxf//00p/BtZf2etPPINKX/+b2bJlS8U/l7Vr15Y6ArRYxRe8CxYsSKFQyODBg7cqd1/rsMMOyz333JOFCxe26msMGDBgeyICABWoqamprArDurq6Nt/BW07rT9r+GRTDqlWr0tTUlC5duqSurq7UcUqi0p+B9Vf2+hPPoFLW/9xzz6WxsbHF87p3757ddtutCIna10svvdTqona33XZL9+7d2zgRvL3t6Q8rvuB94YUXtnnsxo0bW/U1Wru9GgCoXA0NDamtrW2XrzV//vztvsdTTz2Vmpqa7Q/zv9pz/UnHfAbFUF9fnxUrVqSuri7Lly8vdZySqPRnYP2Vvf7EM6iU9c+fPz8HHXRQi+d997vfzZe+9KUiJGpfTU1N2WOPPfKHP/yhRfP23XffPPzww6mqqipSMiiOjr3FoB28et7uU089lT/+8Y9vOObOO+9Mkrz3ve9tt1wAAAAArfGxj30s73vf+1o0p6amJp/5zGeKlKh9denSJZMmTWrxvMmTJyt3KUsVX/Aedthh2W233bJp06Z86lOfypNPPtn82Ysvvpizzjor99xzT5J0mn/RAQAAAJ1XVVVVLrnkknTt2nWb51xwwQXZeeedi5iqfX3xi1/MsGHDtnn8hz70oZxwwglFTATFU/EFb01NTa655prU1NRk4cKFGTp0aAYNGpS99947/fr1y3e+850kySmnnJKxY8eWOC0AAADA2zv00ENzzTXXpEePHm879t/+7d/y5S9/uR1StZ+ddtopt912W/baa6+3Hbvffvtl7ty52WGHHdohGbS9ii94k+SQQw7Jo48+mlNPPTVDhgzJ6tWrs2TJkuy8884ZO3Zsbr755lx22WWljgkAAACwzT796U/nN7/5TY4//vg3fHHY4Ycfnttvvz3nnntuCdIV38CBA7NgwYJ861vfSn19/es+f/e7352LLroo8+fPz6677lqChNA2Kv4la68aNGhQvve975U6BgAAAECbGT58eK655ppMmzYt8+bNy8knn5z169enf//+ue2220odr+h23nnnnHPOOfna176WX/7yl/n0pz+d9evXp1+/fnnqqadadIwFdFR28AIAAAB0crvttls+/elPp6amJknSrVtl7fnr1q1bDjvssOb19+zZU7lLp6HgBQCoMHPmzMmkSZOycePGjBs3LkOGDMnee++dQw89NEuXLi11vKKr9PUDANC5KHgBACrMDTfckHHjxiVJTjrppDzxxBN55JFHMnbs2EycOLG04dpBpa8fAIDORcELANDJrF+/PvX19enbt2/22WefDB06ND179szEiROzadOmLFiwIAcffHB69eqV0aNHp6qqKkkyYsSIPPPMM6UN3wYqff0AAFQWBS8AQCfTu3fvHH/88TnttNOyePHiXHLJJRkxYkRmzZqVefPmZeTIkW/4Ju1LL700Y8eOLUHitlXp6wcAoLIoeAEAOqHFixdn3333TZI8/PDDzb++8cYbc/TRR79u/AUXXJClS5fmwgsvbNecxVLp6wcAoHIoeAEAOqE3KjgLhULuuOOOjBo1aquxU6dOzfXXX5/bbrst1dXVpYjb5ip9/QAAVA4FLwBAJ7NixYpUVVVl4MCBSZJHH300w4YNy4MPPpihQ4emtra2eezFF1+c2bNn56677krv3r1LlLhtVfr6AQCoLN1KHQAAgLa1aNGi5t2ryStn0k6fPj39+vXLuHHjmq8vX748Z5xxRgYNGpSDDjooSdKzZ8888MAD7R25TVX6+gEAqCwKXgCATmbMmDEZM2ZM8+8XLlyYJNlrr70yb9685uv19fUpFArtnq/YKn39AABUFgUvAECFePzxx0sdoaQqff0AAHROCl4AgA6uoaGh1BHeUHvl6qjrTzp2NgAAKoOCFwCgg+vfv3+pI5RUpa8fAADeSpdSBwAAAAAAoHXs4AUA6ICqq6uzYcOGUsfYZtXV1W1+v3Jaf9L2zwAAALaFghcAoAOqqqpKTU1NqWOUTKWvHwAAtpUjGgAAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMqUghcAAAAAoEwpeAEAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMqUghcAAAAAoEwpeAEAAAAAypSCFwAAAACgTCl4AQAAAADKlIIXAAAAAKBMKXgBAAAAAMqUghcAAAAAoEx1K3UAAABga4VCIY2NjW1+36ampuafGxoa2vTe1dXVqaqqarP7eQYAANtGwQsAAB1MY2Njamtri3b/VatWtfn9N2zYkJqamja7n2cAALBtHNEAAAAAAFCm7OAFAIAObM2aNR12V2hDQ0P69+9f9K/jGQAAvDkFLwAAdGA1NTUdttxsL54BAMCbc0QDAAAAAECZUvACAAAAAJQpBS8AAAAAQJlS8AIAAAAAlCkFLwAAdBLz589PVVXVVj9qa2szfPjwTJs2LZs3by51xKKq9PUDAJWpW6kDAAAAbeu4447L6NGjUygUsnr16lx99dU5/fTTs2TJksycObPU8Yqu0tcPAFQWBS8AAHQyw4cPz4QJE5p/P3ny5Oy5556ZNWtWzj///Oy6664lTFd8lb5+AKCyOKLhfz377LM566yzMnTo0Oywww7ZZZdd8v/9f/9ffvrTn5Y6GgAAbJeampqMGDEihUIhy5YtK3Wcdlfp6wcAOjc7eJMsWbIkhxxySFauXJnu3bvn7//+77Nx48b8+te/zn333Zd77rknV155ZaljAgBAq71abPbp06fESUqj0tcPAHReFV/wbtmyJZ/85CezcuXKHHDAAfn5z3+eAQMGJEkee+yxjBkzJj/84Q8zYsSIfOELXyhxWgAAeHuNjY1Zu3Zt8xm0M2bMyKJFi7L//vtnyJAhpY5XdJW+fgCgslT8EQ233nprlixZkp49e+bHP/5xc7mbJMOGDcvll1+eJPnXf/3XbNmypVQxAQBgm02ZMiW77rprdtttt7z//e/P9OnTc8wxx+Smm24qdbR2UenrB4D/a/HixTnppJPygQ98IO973/sycuTInH/++VmzZk2po7WLdevW5eKLL85HP/rRvO9978vw4cPz2c9+Nr/5zW9SKBRKHW+7VXzB++tf/zpJst9+++Vd73rX6z4fM2ZMampqsnLlytx3333tnA4AAFrupJNOyl133ZVbb701F110Ufr06ZPly5enV69ezWPGjx+fY489dqt569atS11dXa655pr2jtymKn39APCq5cuX52Mf+1j23Xff/OAHP8jvfve7LFmyJL/5zW9yzjnn5B3veEe+/OUvZ9OmTaWOWhRNTU0599xzM3DgwJxxxhn59a9/nSVLlmTRokW5+uqrM3LkyHzwgx/MU089Veqo26XiC95169YlSQYOHPimY1797P7772+XTAAAsD0GDx6cQw45JKNGjcpZZ52VuXPnZuHChTn55JObx0yfPj0LFizI7Nmzm6+dcsopOeCAA3LCCSeUInabqfT1A0CS/OlPf8qHP/zh3HvvvW86ZtOmTfne976XT33qU9m8eXM7piu+QqGQiRMn5t///d+zcePGNx338MMP58Mf/nCWLFnSjunaVsUXvL17906SrFix4k3HvPrZE0880R6RAACgTY0cOTInnnhirr322uZNC3369MmVV16ZU089NStXrsycOXMyf/78zJgxo8Rp216lrx+AylMoFDJu3LgsX758m8bfdNNN+da3vlXkVO3r8ssvz49+9KNtGvvXv/41RxxxRF5++eUipyqOii94P/jBDyZJHnroofzxj3983ee33nprGhoakiTPPfdcu2YDAIC2cu6556Zr164577zzmq8dfvjhOfbYYzNhwoRMnjw5s2bNSt++fUuYsngqff0AVJZ58+Zl0aJFLZpz2WWX5cUXXyxSova1ZcuWXHzxxS2a84c//CE33nhjcQIVWcUXvGPHjk19fX1eeumljB8/Pn/+85+bP/u/38bV2NhYiogAALDd9thjj4wfPz733HPPVu+WmDp1apYuXZpRo0bliCOOKGHC4qr09QNQWaZPn97iOevWrct1111XhDTt7/bbb88f/vCHFs+7/PLLi5Cm+LqVOkCp9ezZM9ddd11GjRqV3/72t3n3u9+dwYMHZ+PGjXnmmWfSt2/fHHPMMbn++uuz4447tupr7Lffflm9enUbJwcAoLNqamoqyn3PPvvszJ49O+edd17mzZuXJKmpqcmgQYMybNiw7br34MGD06VL2+0fKcYzKOb6k7Z/BsWwatWq5p/r6+tLnKb9Vfr6E8+g0tefeAaVsv5X19lSkydPztlnn93Gadrf888/36p59957bwYOHJiqqqo2TvT2BgwYkIceeqhVcyu+4E2SD3/4w1m0aFH+4z/+I3fccUeefvrp7LLLLvnc5z6Xf/u3f8sFF1yQ5JUH3RqrV69+yzN+AQCgLRx44IEpFApv+vnQoUOzZcuWonzt1v5Bsi2Vcv1Jx3gG26qpqami/4xS6etPPINKX3/iGVT6+t9MY2NjxX8H+8qVK0sdocUUvP/r3e9+d6644oo3/Ozxxx9P8spO3NZobTEMAEBlampqKquyMEnq6urafAdvpT+DYli1alWamprSpUuX1NXVlTpOu6v09SeeQaWvP/EMKmX9r66zpaqrq7PLLrsUIVH7ev7557Nhw4ZWzd19991LtoO3tRS8b2Pt2rX5zW9+k27dumX06NGtukdrt1cDAFCZGhoaUltbW+oYLfLUU0+lpqamze7nGRRHfX19VqxYkbq6um1+s3pnUunrTzyDSl9/4hlUyvpPOOGE/PSnP23xvCuvvDLjx48vQqL2dffdd+fQQw9t8bzDDjssd9xxRxESFZeC922cc8452bx5c0444YRO/Tc7AABUrvnz55c6QklV+voB6HwmT57c4oJ3t912yzHHHFOkRO3r4IMPzpAhQ/Lkk0+2aN7kyZOLlKi4Ovb3D7WTW2+9NQsWLNjq2vr163PaaafliiuuyK677prvfve7JUoHAAAAANtu5MiR+chHPtKiOaeffnp69OhRpETtq0uXLjnrrLNaNOd973tfjjjiiCIlKi4Fb5I777wzBxxwQHbeeefsvffe2XvvvdO/f/9ceumlGThwYO65557079+/1DEBAAAA4G1VVVXlv/7rvzJ48OBtGn/iiSfmK1/5SpFTta/Pf/7zOe2007Zp7MCBA3PzzTen2/+vvbsPsrJK0AP+XBCa7e6ZMNAKrZ0vRogdixGRcboYk0VXMzZSobVqKUTMshOWILpTlmZN7aowyUQdqxiESoYhbpNsrJqgW6wfwyiljIGN22YUDeiMcR3bCUk10k6pMbt0B0T75g9jZ4mfwO1++977+1V1dd/3vu+5zznlPz6cOve06jzsQMGbpKurK0uXLk1LS0teffXV/Lf/9t/yd//u382/+Bf/Ii+//HJmz55ddEQAAAAA+NymTZuWp59+Ov/wH/7DT/zSsObm5qxduzZ/9Ed/NOa/KPRElUqlbNiwId/73vc+9YvjfuM3fiM//elP87f/9t8exXSVVZ21dIUtWLAgCxYsKDoGAAAAAFRMS0tLHnnkkfzyl7/Mv/k3/yabNm3K0aNH09DQkA0bNuTaa6/NF77whaJjjphSqZSbbropq1evzgMPPJAHH3wwTzzxRN599900NTVl7969aW9vLzrmKautah4AAAAAOM6MGTNy9913p6WlJckHxe+aNWtqutz9qxobG/Pbv/3b2bFjR04//fQkyeTJk2ui3E0UvAAAUFe2b9+e6667LkeOHElXV1dmzZqV8847L5dddll6e3uLjjcqrAEAUEsUvAAAUEceeuihdHV1JUlWrVqVV155JS+88EIWL16clStXFhtulFgDAKCWKHgBAKCGvPPOO2lra8vUqVMzZ86ctLe3p6GhIStXrsyxY8fS09OTSy65JJMmTcrChQuHv3Slo6MjBw4cKDZ8hVgDAKCeKHgBAKCGTJ48OcuWLcuNN96Y/fv3Z+PGjeno6Eh3d3d2796d+fPnZ8KECR95btOmTVm8eHEBiSvPGgAA9UTBCwAANWb//v05//zzkyTPP//88N8PP/xwrrzyyo/cf+edd6a3tzd33XXXqOYcSdYAAKgXCl4AAKgxH1dulsvlPP744+ns7Dzu3vXr1+fBBx/Mzp0709jYWETcEWENAIB6oeAFAIAacvDgwZRKpZx11llJkhdffDGzZ8/Os88+m/b29jQ3Nw/fu2HDhmzbti27du3K5MmTC0pcedYAAKgnpxUdAAAAqJx9+/YN71xNPjiPdvPmzWlpaUlXV9fw9b6+vtx8882ZMWNGLr744iRJQ0NDnnnmmdGOXHHWAACoJwpeAACoIYsWLcqiRYuGX+/duzdJcu6552b37t3D19va2lIul0c932iwBgBAPVHwAgBAHXjppZeKjlA4awAA1CIFLwAAjGEDAwNFR/hEo5XNGgAAfDIFLwAAjGHTpk0rOkLhrAEAwCcbV3QAAAAAAABOjh28AAAwxjQ2Nubw4cNFxzghjY2NFR+v3tcAAODzUPACAMAYUyqV0tTUVHSMQlkDAIDPxxENAAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpU4rOgAAAADHK5fLGRwcrPi4Q0NDw78HBgYqOnZjY2NKpVJFxwQAPpuCFwAAYIwZHBxMc3PziI1/6NChio9/+PDhNDU1VXRMAOCzOaIBAAAAAKBK2cELAAAwhr3xxhtjdmfswMBApk2bVnQMAKhrCl4AAIAxrKmpacwWvABA8RzRAAAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAFAj9uzZk1KpdNxPc3Nz5s6dm3vuuSfvvfde0REBgAo7regAAAAAVNbVV1+dhQsXplwup7+/P/fdd19uuummvPzyy7n33nuLjgcAVJCCFwAAoMbMnTs3y5cvH369Zs2anHPOOenu7s4dd9yR008/vcB0AEAlOaIBAACgxjU1NaWjoyPlcjmvvfZa0XEAgAqqqYL3wIED2bp1a1avXp0LLrggEydOTKlUyooVKz7X80888UQuv/zyTJ06NY2NjZk9e3buuuuuvPvuuyMbHAAAYIR9WOxOmTKl4CQAQCXV1BENGzduzKZNm07q2e9973v5p//0nyZJ/ubf/Jv5G3/jb+TnP/95/uAP/iA//vGP85Of/CS/9mu/Vsm4AAAAI2JwcDBvvvnm8Bm8W7Zsyb59+3LhhRdm1qxZRccDACqopnbwtrS0ZOHChVm3bl127NiRNWvWfK7nnn322fze7/1eSqVS/uiP/igHDhzIvn378ud//uc5++yz8/TTT+f3f//3Rzg9AABAZaxbty6nn356zjjjjHzlK1/J5s2bc9VVV+WRRx4pOhoAUGE1VfDedtttefTRR/Ptb387ixYtype+9KXP9dx3vvOdlMvl/PZv/3Z+67d+a/j6l7/85WzdujVJ8oMf/CC/+tWvRiQ3AABAJa1atSq7du3KY489lrvvvjtTpkxJX19fJk2aNHzP0qVLs2TJkuOee/vtt9Pa2pof/vCHox0ZADhJNVXwnoy//Mu/zBNPPJEk+Z3f+Z2PvP/3//7fz6xZs/Luu+/mRz/60WjHAwAAOGEzZ87MpZdems7Oztxyyy3ZsWNH9u7dm9WrVw/fs3nz5vT09GTbtm3D166//vpcdNFFueaaa4qIDQCchLovePft25d33303DQ0NmTdv3sfec9FFFyVJfvrTn45mNAAAgIqYP39+rr322jzwwAN5+umnk3zwZWtbt27NDTfckNdffz3bt2/Pnj17smXLloLTAgAnou4L3l/84hdJPvhitdNO+/jvnPvyl7983L0AAADV5vbbb8/48eOzdu3a4WuXX355lixZkuXLl2fNmjXp7u7O1KlTC0wJAJyoui94/+f//J9J8qnn9X743of3AgAAVJuzzz47S5cuzZNPPpmnnnpq+Pr69evT29ubzs7OXHHFFQUmBABORt0XvEeOHEmSTJw48RPvaWhoSJL87//9v0clEwAAwEi49dZbM27cuON28TY1NWXGjBmZPXt2gckAgJP18WcS1JEPv0X23Xff/cR7jh49miT5tV/7tZP6jHnz5qW/v/+kngUAAOrP0NDQST23YMGClMvlT3y/vb0977///snG+lQzZ87MuHFjew/RoUOHhn+3tbUVnKYY9b4G9T7/xBqYf33PPxm7azB9+vQ899xzJ/Vs3Re8n+f4hc9zjMOn6e/vz8GDB0/qWQAAgGrw4f8wV4OhoaG6/3+0el+Dep9/Yg3Mv77nn9TWGtR9wTtr1qwkyX//7/8977333sd+0dprr7123L0navr06ScfEAAAqDtDQ0NVVZgmSWtra1Xs4B0aGsq4cePS2tpadJxC1Psa1Pv8E2tg/vU9/2TsrsGp9Id1X/Cef/75mThxYo4ePZrnnnsuHR0dH7nnz/7sz5IkX/va107qM052ezUAAFCfBgYG0tzcPGqft2fPnlMe49VXX01TU9OphxlBbW1tOXjwYFpbW9PX11d0nELU+xrU+/wTa2D+9T3/pDbXYGz/8+oo+MIXvpDLLrssSfKHf/iHH3n/P/2n/5Rf/OIXmThxYhYvXjza8QAAAAAAPlHdF7xJctttt6VUKuXf/bt/l3//7//98PXXXnst//gf/+MkyT/5J/8kZ5xxRlERAQAAAAA+oqYK3p6enrS0tAz/bNiwIUly//33H3e9p6fnuOc6Ojry3e9+N+VyOStWrMjf+lt/K+eff37OOeec9Pb25mtf+1q++93vFjElAAAAAIBPVFNn8B47dixvvfXWR64fPXo0R48ePe6+/98tt9yS8847L9/73veyd+/evPHGG5k1a1auueaa3HzzzWloaBjR7AAAAAAAJ6qmCt4FCxakXC6f9PPf+MY38o1vfKOCiQAAAAAARk5NHdEAAADAp9u+fXuuu+66HDlyJF1dXZk1a1bOO++8XHbZZent7S06HgBwghS8AAAAdeShhx5KV1dXkmTVqlV55ZVX8sILL2Tx4sVZuXJlseEAgBOm4AUAAKgh77zzTtra2jJ16tTMmTMn7e3taWhoyMqVK3Ps2LH09PTkkksuyaRJk7Jw4cKUSqUkH3z59IEDB4oNDwCcMAUvAABADZk8eXKWLVuWG2+8Mfv378/GjRvT0dGR7u7u7N69O/Pnz8+ECRM+8tymTZuyePHiAhIDAKdCwQsAAFBj9u/fn/PPPz9J8vzzzw///fDDD+fKK6/8yP133nlnent7c9ddd41qTgDg1Cl4AQAAaszHFbzlcjmPP/54Ojs7j7t3/fr1efDBB7Nz5840NjYWERcAOAUKXgAAgBpy8ODBlEqlnHXWWUmSF198MbNnz86zzz6b9vb2NDc3D9+7YcOGbNu2Lbt27crkyZMLSgwAnIrTig4AAABA5ezbt294927ywZm8mzdvTktLS7q6uoav9/X15eabb86MGTNy8cUXJ0kaGhryzDPPjHZkAOAUKHgBAABqyKJFi7Jo0aLh13v37k2SnHvuudm9e/fw9ba2tpTL5VHPBwBUloIXAACgDrz00ktFRwAARoAzeAEAAAAAqpQdvAAAAGPYwMBA0RE+0VjOBgD1QsELAAAwhk2bNq3oCADAGOaIBgAAAACAKmUHLwAAwBjT2NiYw4cPFx3jhDQ2NhYdAQDqkoIXAABgjCmVSmlqaio6BgBQBRzRAAAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKVOKzoAAAAA/P/K5XIGBwcrOubQ0NDw74GBgYqO3djYmFKpVNExAeDzUPACAAAw5gwODqa5uXlExj506FDFxz58+HCampoqOiYAfB6OaAAAAAAAqFJ28AIAADCmvfHGG2Nyd+zAwECmTZtWdAwA6pyCFwAAgDGtqalpTBa8ADAWOKIBAAAAAKBKKXgBAAAAAKqUghcAAAAAoEopeAEAAAAAqpSCFwAAgJqwZ8+elEql436am5szd+7c3HPPPXnvvfeKjggAFXda0QEAAACgkq6++uosXLgw5XI5/f39ue+++3LTTTfl5Zdfzr333lt0PACoKAUvAAAANWXu3LlZvnz58Os1a9bknHPOSXd3d+64446cfvrpBaYDgMpyRAMAAAA1rampKR0dHSmXy3nttdeKjgMAFVVTBe+BAweydevWrF69OhdccEEmTpyYUqmUFStWjMhzAAAAVIcPi90pU6YUnAQAKqumjmjYuHFjNm3aNGrPAQAAMPYMDg7mzTffHD6Dd8uWLdm3b18uvPDCzJo1q+h4AFBRNVXwtrS0ZOHChfnqV7+aefPmZefOndm8efOIPQcAAMDYs27duqxbt+64a1dddVW+//3vF5QIAEZOTRW8t91223Gvf/rTn47ocwAAAIw9q1atym/+5m/m2LFj+dnPfpa77747fX19mTRp0vA9S5cuzdDQUP74j/94+Nrbb7+dc889N+vXr88111xTRHQAOGE1dQYvAAAAzJw5M5deemk6Oztzyy23ZMeOHdm7d29Wr149fM/mzZvT09OTbdu2DV+7/vrrc9FFFyl3AagqCl4AAABq2vz583PttdfmgQceyNNPP53kgy9b27p1a2644Ya8/vrr2b59e/bs2ZMtW7YUnBYAToyCFwAAgJp3++23Z/z48Vm7du3wtcsvvzxLlizJ8uXLs2bNmnR3d2fq1KkFpgSAE6fgBQAAoOadffbZWbp0aZ588sk89dRTw9fXr1+f3t7edHZ25oorrigwIQCcHAUvAAAAdeHWW2/NuHHjjtvF29TUlBkzZmT27NkFJgOAk3da0QHqwbx589Lf3190DAAAgKoxNDR0ws8sWLAg5XL5E99vb2/P+++/fyqxPtHMmTMzbtzY30N16NCh4d9tbW0Fpxl99T7/xBqYf33PPxm7azB9+vQ899xzJ/WsgncU9Pf35+DBg0XHAAAAYIR8WBhUi6Ghobr+/9R6n39iDcy/vuef1NYaKHhHwfTp04uOAAAAUFWGhoaqqjRtbW2tmh28Q0NDGTduXFpbW4uOM+rqff6JNTD/+p5/MnbX4FT6QwXvKDjZ7dUAAAD1amBgIM3NzaPyWXv27DnlMV599dU0NTWdepgR1tbWloMHD6a1tTV9fX1Fxxl19T7/xBqYf33PP6nNNRj7/7wIAAAAAMDHUvACAAAAAFSpmip4e3p60tLSMvyzYcOGJMn9999/3PWenp6KPAcAAAAAUKSaOoP32LFjeeuttz5y/ejRozl69Ohx91XiOQAAAACAItVUwbtgwYKUy+VRew4AAAAAoEg1dUQDAAAAAEA9UfACAABQN7Zv357rrrsuR44cSVdXV2bNmpXzzjsvl112WXp7e4uOBwAnTMELAABA3XjooYfS1dWVJFm1alVeeeWVvPDCC1m8eHFWrlxZbDgAOAkKXgAAAGrGO++8k7a2tkydOjVz5sxJe3t7GhoasnLlyhw7diw9PT255JJLMmnSpCxcuDClUilJ0tHRkQMHDhQbHgBOgoIXAACAmjF58uQsW7YsN954Y/bv35+NGzemo6Mj3d3d2b17d+bPn58JEyZ85LlNmzZl8eLFBSQGgFOj4AUAAKCm7N+/P+eff36S5Pnnnx/+++GHH86VV175kfvvvPPO9Pb25q677hrVnABQCQpeAAAAasrHFbzlcjmPP/54Ojs7j7t3/fr1efDBB7Nz5840NjYWERcATomCFwAAgJpx8ODBlEqlnHXWWUmSF198MbNnz86zzz6b9vb2NDc3D9+7YcOGbNu2Lbt27crkyZMLSgwAp+a0ogMAAABApezbt294927ywZm8mzdvTktLS7q6uoav9/X15eabb86MGTNy8cUXJ0kaGhryzDPPjHZkADglCl4AAABqxqJFi7Jo0aLh13v37k2SnHvuudm9e/fw9ba2tpTL5VHPBwCVpuAFAACg5r300ktFRwCAEaHgBQAAYEwbGBgoOsLHGqu5AKgvCl4AAADGtGnTphUdAQDGrHFFBwAAAAAA4OTYwQsAAMCY09jYmMOHDxcd43NrbGwsOgIAdUrBCwAAwJhTKpXS1NRUdAwAGPMc0QAAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAABQpRS8AAAAAABVSsELAAAAAFClFLwAAAAAAFXqtKIDAAAAAMcrl8sZHBys+LhDQ0PDvwcGBio6dmNjY0qlUkXGqvf5A5wIBS8AAACMMYODg2lubh6x8Q8dOlTx8Q8fPpympqaKjFXv8wc4EY5oAAAAAACoUnbwAgAAwBj2xhtvjNmdoQMDA5k2bdqIfka9zx/gsyh4AQAAYAxramoaswXnaKj3+QN8Fkc0AAAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAECN2LNnT0ql0nE/zc3NmTt3bu6555689957RUccUfU+f6A+nVZ0AAAAAKCyrr766ixcuDDlcjn9/f257777ctNNN+Xll1/OvffeW3S8EVfv8wfqi4IXAAAAaszcuXOzfPny4ddr1qzJOeeck+7u7txxxx05/fTTC0w38up9/kB9cUQDAAAA1LimpqZ0dHSkXC7ntddeKzrOqKv3+QO1raYK3gMHDmTr1q1ZvXp1LrjggkycODGlUikrVqz4xGfK5XJ6enryz/7ZP8v8+fMzZcqUTJgwIdOmTcuiRYvyox/9aPQmAAAAACPkw2JzypQpBScpRr3PH6hdNXVEw8aNG7Np06YTeuY//sf/mEsvvTRJUiqV8uUvfzkzZsxIb29vHn300Tz66KP55je/me7u7pRKpZGIDQAAABU1ODiYN998c/gM2i1btmTfvn258MILM2vWrKLjjbh6nz9QX2pqB29LS0sWLlyYdevWZceOHVmzZs1nPlMulzNjxoz8q3/1r/KrX/0qr776ap577rm89dZbueeee1IqlfJv/+2/zQ9+8INRmAEAAACcunXr1uX000/PGWecka985SvZvHlzrrrqqjzyyCNFRxsV9T5/oL7UVMF722235dFHH823v/3tLFq0KF/60pc+85kLL7wwf/7nf54bbrghLS0tw9fHjx+fG2+8MatWrUoS37IJAABA1Vi1alV27dqVxx57LHfffXemTJmSvr6+TJo0afiepUuXZsmSJcc99/bbb6e1tTU//OEPRztyRdX7/IH6UlMF78n44he/mAkTJnzi+9/4xjeSJK+88spoRQIAAIBTMnPmzFx66aXp7OzMLbfckh07dmTv3r1ZvXr18D2bN29OT09Ptm3bNnzt+uuvz0UXXZRrrrmmiNgVU+/zB+pL3Re8n+XIkSNJksbGxoKTAAAAwMmZP39+rr322jzwwAN5+umnk3zwZWNbt27NDTfckNdffz3bt2/Pnj17smXLloLTVl69zx+obQrez/DAAw8kSf7e3/t7BScBAACAk3f77bdn/PjxWbt27fC1yy+/PEuWLMny5cuzZs2adHd3Z+rUqQWmHDn1Pn+gdil4P8Vjjz02fAD7LbfcUnAaAAAAOHlnn312li5dmieffDJPPfXU8PX169ent7c3nZ2dueKKKwpMOLLqff5A7VLwfoLXXnst1157bZLkW9/6VubPn19wIgAAADg1t956a8aNG3fcLtampqbMmDEjs2fPLjDZ6Kj3+QO16bSiA4xF/f39ufzyy/P222/nH/yDf5D169ef0njz5s1Lf39/hdIBAABQ64aGhk7quQULFqRcLn/i++3t7Xn//fdPNtanmjlzZsaNq8w+snqf/0g6dOjQ8O+2traC04w+86/v+Sdjdw2mT5+e55577qSeVfD+fz4sdXt7e/P1r389Dz30UCZMmHBKY/b39+fgwYMVSggAAABjz4elSb2qtvkPDQ3VdVdh/vU9/6S21kDB+1f8xV/8RS6//PL87Gc/y9y5c/Poo4+msbHxlMedPn16BdIBAABQL4aGhqquMGxtba3oDt56nv9IOnToUIaGhjJu3Li0trYWHWfUmX99zz8Zu2twKv2hgvf/GhwczKJFi7J37960t7fn8ccfz1/7a3+tImOf7PZqAAAA6tPAwECam5tH7fP27NlzymO8+uqraWpqOvUwMf+R1NbWloMHD6a1tTV9fX1Fxxl15l/f809qcw3G/j8tjYJ33303V155ZZ566ql8+ctfzk9+8pO0tLQUHQsAAAAA4FPVfcH7/vvvZ9myZXniiSfS1taWn/zkJznzzDOLjgUAAAAA8Jlq6oiGnp6eLF68ePj14OBgkuT+++/Pj3/84+HrjzzySL7+9a8nSf74j/84f/Inf5IkmThxYpYvX/6J42/fvt15ugAAAADAmFFTBe+xY8fy1ltvfeT60aNHc/To0ePu+6vvfeiXv/xlfvnLX37i+EeOHKlQUgAAAACAU1dTBe+CBQtSLpdP6JkVK1ZkxYoVIxMIAAAAAGAE1f0ZvAAAAFBPtm/fnuuuuy5HjhxJV1dXZs2alfPOOy+XXXZZent7i4434up9/kDtUfACAABAHXnooYfS1dWVJFm1alVeeeWVvPDCC1m8eHFWrlxZbLhRUO/zB2qPghcAAABqyDvvvJO2trZMnTo1c+bMSXt7exoaGrJy5cocO3YsPT09ueSSSzJp0qQsXLgwpVIpSdLR0ZEDBw4UG74C6n3+QP1R8AIAAEANmTx5cpYtW5Ybb7wx+/fvz8aNG9PR0ZHu7u7s3r078+fPz4QJEz7y3KZNm7J48eICEldWvc8fqD8KXgAAAKgx+/fvz/nnn58kef7554f/fvjhh3PllVd+5P4777wzvb29ueuuu0Y150ip9/kD9UXBCwAAADXm4wrOcrmcxx9/PJ2dncfdu379+jz44IPZuXNnGhsbi4hbcfU+f6C+KHgBAACghhw8eDClUilnnXVWkuTFF1/M7Nmz8+yzz6a9vT3Nzc3D927YsCHbtm3Lrl27Mnny5IISV1a9zx+oP6cVHQAAAAConH379g3vXk0+OJN28+bNaWlpSVdX1/D1vr6+3HzzzZkxY0YuvvjiJElDQ0OeeeaZ0Y5cUfU+f6D+KHgBAACghixatCiLFi0afr13794kybnnnpvdu3cPX29ra0u5XB71fCOt3ucP1B8FLwAAANSBl156qegIhar3+QO1yxm8AAAAAABVyg5eAAAAGMMGBgaKjvCJRiNbvc8f4LMoeAEAAGAMmzZtWtERClXv8wf4LI5oAAAAAACoUnbwAgAAwBjT2NiYw4cPFx3jhDQ2NlZ0rHqeP8CJUPACAADAGFMqldLU1FR0jMLU+/wBToQjGgAAAAAAqpSCFwAAAACgSil4AQAAAACqlIIXAAAAAKBKKXgBAAAAAKqUghcAAAAAoEopeAEAAAAAqpSCFwAAAACgSil4AQAAAACqlIIXAAAAAKBKKXgBAAAAAKqUghcAAAAAoEopeAEAAAAAqpSCFwAAAACgSil4AQAAAACqlIIXAAAAAKBKKXgBAAAAAKrUaUUHAAAAAOB45XI5g4ODFR93aGho+PfAwEBFx25sbEypVKrIWPU+fzgRCl4AAACAMWZwcDDNzc0jNv6hQ4cqPv7hw4fT1NRUkbHqff5wIhzRAAAAAABQpezgBQAAABjD3njjjTG7M3RgYCDTpk0b0c+o9/nDZ1HwAgAAAIxhTU1NY7bgHA31Pn/4LI5oAAAAAACoUgpeAAAAAIAqpeAFAAAAAKhSCl4AAAAAgCql4AUAAACoAXv27EmpVDrup7m5OXPnzs0999yT9957r+iII84aUI9OKzoAAAAAAJVz9dVXZ+HChSmXy+nv7899992Xm266KS+//HLuvffeouONCmtAPVHwAgAAANSQuXPnZvny5cOv16xZk3POOSfd3d254447cvrppxeYbnRYA+qJIxoAAAAAalhTU1M6OjpSLpfz2muvFR2nENaAWlZTBe+BAweydevWrF69OhdccEEmTpyYUqmUFStWfOpzP/rRj3LdddflwgsvzFlnnZWGhoZ84QtfyJw5c/IHf/AHefPNN0dnAgAAAAAj4MNSc8qUKQUnKY41oFbV1BENGzduzKZNm074uQ0bNuRP//RPM3HixJx55pn5yle+kl/96ld58cUX88ILL6S7uztPPPFE5syZU/nQAAAAABU0ODiYN998c/j82S1btmTfvn258MILM2vWrKLjjQprQD2pqYK3paUlCxcuzFe/+tXMmzcvO3fuzObNmz/zuW9+85tZu3ZtLrrookycOHH4+s9+9rMsW7YsP//5z7Ns2bL81//6X0cyPgAAAMApW7duXdatW3fctauuuirf//73C0o0+qwB9aSmjmi47bbb8uijj+bb3/52Fi1alC996Uuf67l/9I/+US655JLjyt0kmT17drZu3Zokefnll/Pyyy9XPDMAAABAJa1atSq7du3KY489lrvvvjtTpkxJX19fJk2aNHzP0qVLs2TJkuOee/vtt9Pa2pof/vCHox254qwB9aSmCt6R0N7ePvz34OBggUkAAAAAPtvMmTNz6aWXprOzM7fcckt27NiRvXv3ZvXq1cP3bN68OT09Pdm2bdvwteuvvz4XXXRRrrnmmiJiV5Q1oJ4oeD9DT09Pkg++bfHv/J2/U3AaAAAAgBMzf/78XHvttXnggQfy9NNPJ/ngi8a2bt2aG264Ia+//nq2b9+ePXv2ZMuWLQWnHRnWgFqm4P0YQ0NDOXToUO67776sWLEiSXLnnXemubm52GAAAAAAJ+H222/P+PHjs3bt2uFrl19+eZYsWZLly5dnzZo16e7uztSpUwtMObKsAbVKwftXbNmyJaVSKePHj8+ZZ56Z3/qt30pbW1t27NiRb33rW0XHAwAAADgpZ599dpYuXZonn3wyTz311PD19evXp7e3N52dnbniiisKTDjyrAG1SsH7V7S2tubrX/96vva1r+XMM89MqVTKiy++mP/wH/5D/tf/+l9FxwMAAAA4abfeemvGjRt33A7WpqamzJgxI7Nnzy4w2eixBtSi04oOMJYsXrw4ixcvHn79s5/9LNdff322bduW//E//kf+7M/+7KTGnTdvXvr7+ysVEwAAAKhxQ0NDJ/zMggULUi6XP/H99vb2vP/++6cS61PNnDkz48ZVZi/hycw/KXYNKjn/kXLo0KHh321tbQWnKcZYXYPp06fnueeeO6lnFbyfYvbs2Xn00UczY8aM9PT05Cc/+UkuvfTSEx6nv78/Bw8eHIGEAAAAAGPDh8VZvaqm+Q8NDdV9V1VLa6Dg/Qxf+MIX8uu//uv5kz/5k7zwwgsnVfBOnz59BJIBAAAAterDL4CvJq2trRXdwVvP8x8phw4dytDQUMaNG5fW1tai4xRirK7BqfSHCt7P4b333kuSk97Cf7LbqwEAAID6NDAwkObm5lH5rD179lRknFdffTVNTU0VGWs0559UZg0qOf+R0tbWloMHD6a1tTV9fX1FxylELa7B2P5nhTHg7bffzp/+6Z8mSebMmVNsGAAAAACAv6LuC97nnnsua9euTW9v70fe27dvXzo7O/POO+9k9uzZ+Y3f+I0CEgIAAAAAfLyaOqKhp6cnixcvHn49ODiYJLn//vvz4x//ePj6I488kq9//etJksOHD+c73/lOvvOd7+SMM87IX//rfz3jx49PX19fXn/99STJrFmz8vDDD2f8+PGjOBsAAAAAgE9XUwXvsWPH8tZbb33k+tGjR3P06NHj7vvQeeedl02bNmX37t35+c9/nl/84hc5cuRIpkyZkksvvTRXXnllvvnNb2bSpEmjMgcAAAAAgM+rpgreBQsWpFwun9AzX/rSl/Ktb30r3/rWt0YoFQAAAADAyKj7M3gBAAAAAKqVghcAAACgjmzfvj3XXXddjhw5kq6ursyaNSvnnXdeLrvsso/9EvpaU+/zp/YoeAEAAADqyEMPPZSurq4kyapVq/LKK6/khRdeyOLFi7Ny5cpiw42Cep8/tUfBCwAAAFBD3nnnnbS1tWXq1KmZM2dO2tvb09DQkJUrV+bYsWPp6enJJZdckkmTJmXhwoUplUpJko6Ojhw4cKDY8BVQ7/On/ih4AQAAAGrI5MmTs2zZstx4443Zv39/Nm7cmI6OjnR3d2f37t2ZP39+JkyY8JHnNm3alMWLFxeQuLLqff7UHwUvAAAAQI3Zv39/zj///CTJ888/P/z3ww8/nCuvvPIj9995553p7e3NXXfdNao5R0q9z5/6ouAFAAAAqDEfV3CWy+U8/vjj6ezsPO7e9evX58EHH8zOnTvT2NhYRNyKq/f5U18UvAAAAAA15ODBgymVSjnrrLOSJC+++GJmz56dZ599Nu3t7Wlubh6+d8OGDdm2bVt27dqVyZMnF5S4sup9/tSf04oOAAAAAEDl7Nu3b3j3avLBmbSbN29OS0tLurq6hq/39fXl5ptvzowZM3LxxRcnSRoaGvLMM8+MduSKqvf5U39K5XK5XHQIAAAAAP6fgYGB4Z2mhw8fTlNT0ymPee6552b37t0544wzTnmsD41EzpEat5rmP1La2tpy8ODBnHXWWenr6ys6TiFqcQ3s4AUAAACoAy+99FLREQpV7/Ondil4AQAAAMawgYGBoiN8otHIVu/zh8+i4AUAAAAYw6ZNm1Z0hELV+/zhs4wrOgAAAAAAACfHDl4AAACAMaaxsTGHDx8uOsYJaWxsrOhY9Tx/OBEKXgAAAIAxplQqpampqegYhan3+cOJcEQDAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlTqt6AAAAAAAwP9TLpczODhY8XGHhoaGfw8MDFR07MbGxpRKpYqNZw0+v1K5XC6P+qcCAAAAAB9rYGAgzc3NRcc4IYcPH05TU1PFxrMGn58jGgAAAAAAqpQjGgAAAABgjHrjjTcK2RX6eQwMDGTatGkj/jnW4NMpeAEAAABgjGpqahqz5eZosQafzhENAAAAAABVSsELAAAAAFClFLwAAAAAAFVKwQsAAAAAUKUUvAAAAAAAVUrBCwAAAAA1YM+ePSmVSsf9NDc3Z+7cubnnnnvy3nvvFR1xxNXjGpxWdAAAAAAAoHKuvvrqLFy4MOVyOf39/bnvvvty00035eWXX869995bdLxRUU9roOAFAAAAgBoyd+7cLF++fPj1mjVrcs4556S7uzt33HFHTj/99ALTjY56WoOaOaLhwIED2bp1a1avXp0LLrggEydOTKlUyooVK054rD/8wz8c3sK9YMGCimcFAAAAgNHS1NSUjo6OlMvlvPbaa0XHKUQtr0HN7ODduHFjNm3adMrj9Pf355ZbbqlAIgAAAAAYGz4sNadMmVJwkuLU6hrUTMHb0tKShQsX5qtf/WrmzZuXnTt3ZvPmzSc8zu/+7u/mL/7iL7Jo0aL8+Mc/HoGkAAAAADByBgcH8+abbw6fP7tly5bs27cvF154YWbNmlV0vFFRT2tQMwXvbbfddtzrn/70pyc8xo9+9KNs3749v/u7v5spU6YoeAEAAACoOuvWrcu6deuOu3bVVVfl+9//fkGJRl89rUHNnMF7qv7yL/8y119/fc4888z8y3/5L4uOAwAAAAAnZdWqVdm1a1cee+yx3H333ZkyZUr6+voyadKk4XuWLl2aJUuWHPfc22+/ndbW1vzwhz8c7cgVV09roOD9v37/938/fX192bhxY774xS8WHQcAAAAATsrMmTNz6aWXprOzM7fcckt27NiRvXv3ZvXq1cP3bN68OT09Pdm2bdvwteuvvz4XXXRRrrnmmiJiV1Q9rYGCN8l//s//OT/4wQ/S2dmZ3/zN3yw6DgAAAABUzPz583PttdfmgQceyNNPP53kgy8a27p1a2644Ya8/vrr2b59e/bs2ZMtW7YUnHZk1PIa1H3Be+zYsfzO7/xOGhoa8q//9b8uOg4AAAAAVNztt9+e8ePHZ+3atcPXLr/88ixZsiTLly/PmjVr0t3dnalTpxaYcmTV6hrUfcH73e9+Ny+99FJuu+22zJgxo+g4AAAAAFBxZ599dpYuXZonn3wyTz311PD19evXp7e3N52dnbniiisKTDjyanUNTis6QJFeeeWV3HHHHWlvb8/v/d7vjdjnzJs3L/39/SM2PgAAAAC1Y2hoaETGvfXWW7Nt27asXbs2u3fvTpI0NTVlxowZmT179imNPXPmzIwbV7m9pPW2BtOnT89zzz13Us/WdcF73XXX5ejRo9myZUsmTJgwYp/T39+fgwcPjtj4AAAAALBgwYKUy+VPfL+9vT3vv//+iHz2oUOHRmTcE1WPa1DXBe9/+S//JePGjcuSJUs+8t7hw4eTJE8//XSmT5+eJPnFL36RL37xiyf8OR8+DwAAAACfZWhoaMwUpp9Xa2trxXfw1tManEp/WNcFb/LBfyxvvPHGJ75/7Nix4fdPdmv4yW6vBgAAAKD+DAwMpLm5uegYJ+TVV19NU1NTxcazBp9fXRe877zzzie+9+1vfzv//J//8/z6r/969uzZM2qZAAAAAGA06b6qew0qt28aAAAAAIBRVTMFb09PT1paWoZ/NmzYkCS5//77j7ve09NTcFIAAAAAgMqomSMajh07lrfeeusj148ePZqjR48edx8AAAAAQC0olcvlctEhAAAAAIAP/NUvGDt8+HAhX9z1eYxkTmvw+dXMEQ0AAAAAAPVGwQsAAAAAdWL79u257rrrcuTIkXR1dWXWrFk577zzctlll6W3t7foeKOi1tZAwQsAAAAAdeKhhx5KV1dXkmTVqlV55ZVX8sILL2Tx4sVZuXJlseFGSa2tgYIXAAAAAGrEO++8k7a2tkydOjVz5sxJe3t7GhoasnLlyhw7diw9PT255JJLMmnSpCxcuDClUilJ0tHRkQMHDhQbvkLqbQ0UvAAAAABQIyZPnpxly5blxhtvzP79+7Nx48Z0dHSku7s7u3fvzvz58zNhwoSPPLdp06YsXry4gMSVV29roOAFAAAAgBqyf//+nH/++UmS559/fvjvhx9+OFdeeeVH7r/zzjvT29ubu+66a1RzjqR6WgMFLwAAAADUkI8rN8vlch5//PF0dnYed+/69evz4IMPZufOnWlsbCwi7oiopzVQ8AIAAABAjTh48GBKpVLOOuusJMmLL76Y2bNn59lnn017e3uam5uH792wYUO2bduWXbt2ZfLkyQUlrrx6W4PTig4AAAAAAFTGvn37hneuJh+cR7t58+a0tLSkq6tr+HpfX19uvvnmzJgxIxdffHGSpKGhIc8888xoR664eluDUrlcLhcdAgAAAAD4wMDAwPAu08OHD6epqemUxzz33HOze/funHHGGac81odGIudIjl1ta/B52cELAAAAADXupZdeKjpC4Wp1DRS8AAAAADBGDQwMFB3hE41WNmvw6RS8AAAAADBGTZs2regIhbMGn25c0QEAAAAAADg5vmQNAAAAAMaQcrmcwcHBomOckMbGxpRKpYqNZw0+PwUvAAAAAECVckQDAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECVUvACAAAAAFQpBS8AAAAAQJVS8AIAAAAAVCkFLwAAAABAlVLwAgAAAABUKQUvAAAAAECV+j9XPT8dPkSgDgAAAABJRU5ErkJggg==" + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize register with A=0, B=1, C=2, ...\n", + "qr = [QuantumRegister(1, name=str(i)) for i in range(15)]\n", + "qc_pac = QuantumCircuit(*qr, name='Pachinko')\n", + "# Angle for controlled-rotation gates\n", + "rotation_angle = np.pi / 2\n", + "# Specify control qubits\n", + "c_qubits=list(range(10))+list(range(10))\n", + "c_qubits.sort()\n", + "# Specify target qubits\n", + "offset = 1\n", + "t_qubits = list()\n", + "for d in range(5):\n", + " offset += d\n", + " for i in range(d+1):\n", + " t_qubits.append(i+offset)\n", + " if (i != 0) and (i != d):\n", + " t_qubits.append(i+offset)\n", + "\n", + "# Apply controlled rotation gates with the specified angle\n", + "for cq, tq in zip(c_qubits, t_qubits):\n", + " qc_pac.cry(rotation_angle, control_qubit=qr[cq], target_qubit=qr[tq])\n", + " \n", + "# Draw circuit\n", + "qc_pac.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-08T23:55:50.894094Z", + "start_time": "2023-11-08T23:55:50.615238Z" + } + }, + "id": "7000db4359eed86a" + }, + { + "cell_type": "markdown", + "source": [ + "Assume that you have seen the ball at node E. Now inference the probability that the ball will land at node M." + ], + "metadata": { + "collapsed": false + }, + "id": "b10379ad3c6087cf" + }, + { + "cell_type": "code", + "execution_count": 9, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", + "k: 0\n", + "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", + "k: 1\n", + "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", + "k: 2\n", + "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", + "k: 3\n" + ] + }, + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", + "\u001B[0;31mKeyboardInterrupt\u001B[0m Traceback (most recent call last)", + "Cell \u001B[0;32mIn[9], line 6\u001B[0m\n\u001B[1;32m 4\u001B[0m qbayesian \u001B[38;5;241m=\u001B[39m QBayesian(circuit\u001B[38;5;241m=\u001B[39mqc_pac)\n\u001B[1;32m 5\u001B[0m \u001B[38;5;66;03m# Inference\u001B[39;00m\n\u001B[0;32m----> 6\u001B[0m \u001B[43mqbayesian\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43minference\u001B[49m\u001B[43m(\u001B[49m\u001B[43mquery\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mquery\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mevidence\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mevidence\u001B[49m\u001B[43m)\u001B[49m\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:255\u001B[0m, in \u001B[0;36mQBayesian.inference\u001B[0;34m(self, query, evidence, shots, limit)\u001B[0m\n\u001B[1;32m 239\u001B[0m \u001B[38;5;250m\u001B[39m\u001B[38;5;124;03m\"\"\"\u001B[39;00m\n\u001B[1;32m 240\u001B[0m \u001B[38;5;124;03mPerforms inference on the query variables given the evidence. It uses rejection sampling if evidence\u001B[39;00m\n\u001B[1;32m 241\u001B[0m \u001B[38;5;124;03mis provided and calculates the probability of the query.\u001B[39;00m\n\u001B[0;32m (...)\u001B[0m\n\u001B[1;32m 252\u001B[0m \u001B[38;5;124;03m ValueError: If evidence is required for rejection sampling and none is provided.\u001B[39;00m\n\u001B[1;32m 253\u001B[0m \u001B[38;5;124;03m\"\"\"\u001B[39;00m\n\u001B[1;32m 254\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m evidence \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[0;32m--> 255\u001B[0m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mrejectionSampling\u001B[49m\u001B[43m(\u001B[49m\u001B[43mevidence\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mshots\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mlimit\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 256\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n\u001B[1;32m 257\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39msamples:\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:201\u001B[0m, in \u001B[0;36mQBayesian.rejectionSampling\u001B[0;34m(self, evidence, shots, limit)\u001B[0m\n\u001B[1;32m 199\u001B[0m k \u001B[38;5;241m+\u001B[39m\u001B[38;5;241m=\u001B[39m \u001B[38;5;241m1\u001B[39m\n\u001B[1;32m 200\u001B[0m \u001B[38;5;66;03m# Create circuit with 2^k times grover operator\u001B[39;00m\n\u001B[0;32m--> 201\u001B[0m qc, E \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mpowerGrover\u001B[49m\u001B[43m(\u001B[49m\u001B[43mgroverOp\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mgroverOp\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mevidence\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mevidence\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mk\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mk\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 202\u001B[0m \u001B[38;5;66;03m# Test number of\u001B[39;00m\n\u001B[1;32m 203\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mlen\u001B[39m(e\u001B[38;5;241m.\u001B[39mintersection(E)) \u001B[38;5;241m>\u001B[39m best_inter:\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:153\u001B[0m, in \u001B[0;36mQBayesian.powerGrover\u001B[0;34m(self, groverOp, evidence, k)\u001B[0m\n\u001B[1;32m 151\u001B[0m qc_measure\u001B[38;5;241m.\u001B[39mmeasure([q \u001B[38;5;28;01mfor\u001B[39;00m q \u001B[38;5;129;01min\u001B[39;00m evidence_qubits], measurement_ecr)\n\u001B[1;32m 152\u001B[0m \u001B[38;5;66;03m# Run the circuit with the Grover operator and measurements\u001B[39;00m\n\u001B[0;32m--> 153\u001B[0m e_samples \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mrun_circuit\u001B[49m\u001B[43m(\u001B[49m\u001B[43mqc_measure\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mshots\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43m \u001B[49m\u001B[38;5;241;43m1024\u001B[39;49m\u001B[43m)\u001B[49m\n\u001B[1;32m 154\u001B[0m E_count \u001B[38;5;241m=\u001B[39m {\u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mlabel2qubit[e]: \u001B[38;5;241m0\u001B[39m \u001B[38;5;28;01mfor\u001B[39;00m e \u001B[38;5;129;01min\u001B[39;00m evidence}\n\u001B[1;32m 155\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m e_sample_key, e_sample_val \u001B[38;5;129;01min\u001B[39;00m e_samples\u001B[38;5;241m.\u001B[39mitems():\n\u001B[1;32m 156\u001B[0m \u001B[38;5;66;03m# Go through reverse binary that matches order of qubits\u001B[39;00m\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:117\u001B[0m, in \u001B[0;36mQBayesian.run_circuit\u001B[0;34m(self, circuit, shots)\u001B[0m\n\u001B[1;32m 115\u001B[0m \u001B[38;5;66;03m# Run the transpiled circuit on the simulator\u001B[39;00m\n\u001B[1;32m 116\u001B[0m job \u001B[38;5;241m=\u001B[39m simulator_backend\u001B[38;5;241m.\u001B[39mrun(transpiled_circuit, shots\u001B[38;5;241m=\u001B[39mshots)\n\u001B[0;32m--> 117\u001B[0m result \u001B[38;5;241m=\u001B[39m \u001B[43mjob\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mresult\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 118\u001B[0m \u001B[38;5;66;03m# Get the counts of quantum state results\u001B[39;00m\n\u001B[1;32m 119\u001B[0m counts \u001B[38;5;241m=\u001B[39m result\u001B[38;5;241m.\u001B[39mget_counts(transpiled_circuit)\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qbayesian/lib/python3.9/site-packages/qiskit_aer/jobs/utils.py:42\u001B[0m, in \u001B[0;36mrequires_submit.._wrapper\u001B[0;34m(self, *args, **kwargs)\u001B[0m\n\u001B[1;32m 40\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_future \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[1;32m 41\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m JobError(\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mJob not submitted yet!. You have to .submit() first!\u001B[39m\u001B[38;5;124m\"\u001B[39m)\n\u001B[0;32m---> 42\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[43mfunc\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43margs\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43mkwargs\u001B[49m\u001B[43m)\u001B[49m\n", + "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qbayesian/lib/python3.9/site-packages/qiskit_aer/jobs/aerjob.py:114\u001B[0m, in \u001B[0;36mAerJob.result\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 96\u001B[0m \u001B[38;5;129m@requires_submit\u001B[39m\n\u001B[1;32m 97\u001B[0m \u001B[38;5;28;01mdef\u001B[39;00m \u001B[38;5;21mresult\u001B[39m(\u001B[38;5;28mself\u001B[39m, timeout\u001B[38;5;241m=\u001B[39m\u001B[38;5;28;01mNone\u001B[39;00m):\n\u001B[1;32m 98\u001B[0m \u001B[38;5;66;03m# pylint: disable=arguments-differ\u001B[39;00m\n\u001B[1;32m 99\u001B[0m \u001B[38;5;250m \u001B[39m\u001B[38;5;124;03m\"\"\"Get job result. The behavior is the same as the underlying\u001B[39;00m\n\u001B[1;32m 100\u001B[0m \u001B[38;5;124;03m concurrent Future objects,\u001B[39;00m\n\u001B[1;32m 101\u001B[0m \n\u001B[0;32m (...)\u001B[0m\n\u001B[1;32m 112\u001B[0m \u001B[38;5;124;03m concurrent.futures.CancelledError: if job cancelled before completed.\u001B[39;00m\n\u001B[1;32m 113\u001B[0m \u001B[38;5;124;03m \"\"\"\u001B[39;00m\n\u001B[0;32m--> 114\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43m_future\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mresult\u001B[49m\u001B[43m(\u001B[49m\u001B[43mtimeout\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mtimeout\u001B[49m\u001B[43m)\u001B[49m\n", + "File \u001B[0;32m/Applications/Xcode.app/Contents/Developer/Library/Frameworks/Python3.framework/Versions/3.9/lib/python3.9/concurrent/futures/_base.py:440\u001B[0m, in \u001B[0;36mFuture.result\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 437\u001B[0m \u001B[38;5;28;01melif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_state \u001B[38;5;241m==\u001B[39m FINISHED:\n\u001B[1;32m 438\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m__get_result()\n\u001B[0;32m--> 440\u001B[0m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43m_condition\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mwait\u001B[49m\u001B[43m(\u001B[49m\u001B[43mtimeout\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 442\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_state \u001B[38;5;129;01min\u001B[39;00m [CANCELLED, CANCELLED_AND_NOTIFIED]:\n\u001B[1;32m 443\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m CancelledError()\n", + "File \u001B[0;32m/Applications/Xcode.app/Contents/Developer/Library/Frameworks/Python3.framework/Versions/3.9/lib/python3.9/threading.py:312\u001B[0m, in \u001B[0;36mCondition.wait\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 310\u001B[0m \u001B[38;5;28;01mtry\u001B[39;00m: \u001B[38;5;66;03m# restore state no matter what (e.g., KeyboardInterrupt)\u001B[39;00m\n\u001B[1;32m 311\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m timeout \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[0;32m--> 312\u001B[0m \u001B[43mwaiter\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43macquire\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 313\u001B[0m gotit \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;01mTrue\u001B[39;00m\n\u001B[1;32m 314\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n", + "\u001B[0;31mKeyboardInterrupt\u001B[0m: " + ] + } + ], + "source": [ + "query = {'12': 1}\n", + "evidence = {'4': 1, '3': 0, '5': 0, '6': 0, '9': 0, '10': 0, '14': 0}\n", + "# Initialize quantum bayesian inference framework\n", + "qbayesian = QBayesian(circuit=qc_pac)\n", + "# Inference\n", + "qbayesian.inference(query=query, evidence=evidence)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-08T23:59:55.688981Z", + "start_time": "2023-11-08T23:55:50.881925Z" + } + }, + "id": "f3ae346612ee10d" + }, { "cell_type": "code", "execution_count": null, @@ -326,11 +525,11 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-07T21:09:44.709280Z", - "start_time": "2023-11-07T21:09:44.708151Z" + "end_time": "2023-11-08T23:59:55.692314Z", + "start_time": "2023-11-08T23:59:55.691982Z" } }, - "id": "7000db4359eed86a" + "id": "6d2c15ce28c7d74a" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index fdf681a89..679fd568e 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -159,6 +159,7 @@ def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (Grov E_count[evidence_qubits[i]] += e_sample_val else: E_count[evidence_qubits[i]] += -e_sample_val + print(E_count) # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} return qc, E @@ -201,6 +202,7 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10 # Test number of if len(e.intersection(E)) > best_inter: best_qc = qc + print("k:",k) if e == E: self.converged = True @@ -233,7 +235,7 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10 return self.samples - def inference(self, query: dict, evidence: dict=None, shots: int=100000) -> float: + def inference(self, query: dict, evidence: dict=None, shots: int=100000, limit: int=10) -> float: """ Performs inference on the query variables given the evidence. It uses rejection sampling if evidence is provided and calculates the probability of the query. @@ -250,7 +252,7 @@ def inference(self, query: dict, evidence: dict=None, shots: int=100000) -> floa ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: - self.rejectionSampling(evidence, shots) + self.rejectionSampling(evidence, shots, limit) else: if not self.samples: raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") From ed23ab483570328b64bd7fe2586eac63b7af6f64 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 02:01:13 +0100 Subject: [PATCH 13/48] Bug in Pachinko game --- .../13_quantum_bayesian_inference.ipynb | 130 +++++++---------- .../algorithms/inference/qbayesian.py | 138 +++++++++--------- test/algorithms/inference/test_qbayesian.py | 18 ++- 3 files changed, 132 insertions(+), 154 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 200eb3f93..fefddb5c3 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -60,8 +60,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:45.204595Z", - "start_time": "2023-11-08T23:55:44.587163Z" + "end_time": "2023-11-09T23:56:49.329959Z", + "start_time": "2023-11-09T23:56:48.754530Z" } }, "id": "925af2a5fe37bf8c" @@ -86,8 +86,8 @@ "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-08T23:55:45.211204Z", - "start_time": "2023-11-08T23:55:45.203684Z" + "end_time": "2023-11-09T23:56:49.334795Z", + "start_time": "2023-11-09T23:56:49.331578Z" } }, "outputs": [], @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:45.723868Z", - "start_time": "2023-11-08T23:55:45.213325Z" + "end_time": "2023-11-09T23:56:49.778087Z", + "start_time": "2023-11-09T23:56:49.334596Z" } }, "id": "c4984e988c8ededd" @@ -171,17 +171,9 @@ "cell_type": "code", "execution_count": 4, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{Qubit(QuantumRegister(1, 'A'), 0): 0.931640625}\n", - "k: 0\n" - ] - }, { "data": { - "text/plain": "0.12168" + "text/plain": "0.11777" }, "execution_count": 4, "metadata": {}, @@ -201,8 +193,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:46.525097Z", - "start_time": "2023-11-08T23:55:45.721959Z" + "end_time": "2023-11-09T23:56:50.662173Z", + "start_time": "2023-11-09T23:56:49.779106Z" } }, "id": "8d7a132268680e61" @@ -226,7 +218,7 @@ { "data": { "text/plain": "
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}, "execution_count": 5, "metadata": {}, @@ -257,8 +249,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:46.923287Z", - "start_time": "2023-11-08T23:55:46.527817Z" + "end_time": "2023-11-09T23:56:51.053032Z", + "start_time": "2023-11-09T23:56:50.665313Z" } }, "id": "9021e193f69b0392" @@ -281,19 +273,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "{Qubit(QuantumRegister(1, '0'), 0): 0.62109375, Qubit(QuantumRegister(1, '1'), 0): 0.541015625, Qubit(QuantumRegister(1, '2'), 0): 0.47265625, Qubit(QuantumRegister(1, '3'), 0): 0.4453125, Qubit(QuantumRegister(1, '4'), 0): 0.4453125, Qubit(QuantumRegister(1, '5'), 0): 0.447265625, Qubit(QuantumRegister(1, '6'), 0): 0.40625, Qubit(QuantumRegister(1, '7'), 0): 0.376953125, Qubit(QuantumRegister(1, '8'), 0): 0.384765625}\n", - "k: 0\n", - "{Qubit(QuantumRegister(1, '0'), 0): 0.4609375, Qubit(QuantumRegister(1, '1'), 0): 0.380859375, Qubit(QuantumRegister(1, '2'), 0): 0.34765625, Qubit(QuantumRegister(1, '3'), 0): 0.298828125, Qubit(QuantumRegister(1, '4'), 0): 0.27734375, Qubit(QuantumRegister(1, '5'), 0): 0.23046875, Qubit(QuantumRegister(1, '6'), 0): 0.263671875, Qubit(QuantumRegister(1, '7'), 0): 0.244140625, Qubit(QuantumRegister(1, '8'), 0): 0.27734375}\n", - "k: 1\n", - "{Qubit(QuantumRegister(1, '0'), 0): -0.1015625, Qubit(QuantumRegister(1, '1'), 0): -0.14453125, Qubit(QuantumRegister(1, '2'), 0): -0.166015625, Qubit(QuantumRegister(1, '3'), 0): -0.1796875, Qubit(QuantumRegister(1, '4'), 0): -0.208984375, Qubit(QuantumRegister(1, '5'), 0): -0.21484375, Qubit(QuantumRegister(1, '6'), 0): -0.1875, Qubit(QuantumRegister(1, '7'), 0): -0.19140625, Qubit(QuantumRegister(1, '8'), 0): -0.20703125}\n", - "k: 2\n", - "{'1000000000': 0.53215, '0000000000': 0.46785}\n" + "{'1000000000': 0.33117, '0000000000': 0.66883}\n" ] }, { "data": { "text/plain": "
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" 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" }, "execution_count": 6, "metadata": {}, @@ -307,15 +293,15 @@ "# Initialize quantum bayesian\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", - "samples = qbayesian.rejectionSampling(evidence=evidence)\n", + "samples = qbayesian.rejection_sampling(evidence=evidence)\n", "print(samples)\n", "plot_histogram(samples)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:50.448531Z", - "start_time": "2023-11-08T23:55:46.923961Z" + "end_time": "2023-11-09T23:56:58.093487Z", + "start_time": "2023-11-09T23:56:51.061766Z" } }, "id": "352129ef4f8f6cff" @@ -387,8 +373,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:50.612524Z", - "start_time": "2023-11-08T23:55:50.456357Z" + "end_time": "2023-11-09T23:56:58.267794Z", + "start_time": "2023-11-09T23:56:58.102515Z" } }, "id": "44baa6f9eaf8b320" @@ -407,10 +393,17 @@ "cell_type": "code", "execution_count": 8, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 13, 13, 14]\n" + ] + }, { "data": { - "text/plain": "
", - "image/png": 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}, "execution_count": 8, "metadata": {}, @@ -422,23 +415,27 @@ "qr = [QuantumRegister(1, name=str(i)) for i in range(15)]\n", "qc_pac = QuantumCircuit(*qr, name='Pachinko')\n", "# Angle for controlled-rotation gates\n", - "rotation_angle = np.pi / 2\n", + "rotation_angle_0 = 2 * np.arcsin(0)\n", + "rotation_angle_1 = 2 * np.arcsin(1/2)\n", "# Specify control qubits\n", "c_qubits=list(range(10))+list(range(10))\n", "c_qubits.sort()\n", "# Specify target qubits\n", - "offset = 1\n", + "offset = 0\n", "t_qubits = list()\n", "for d in range(5):\n", " offset += d\n", " for i in range(d+1):\n", - " t_qubits.append(i+offset)\n", + " if (i+offset) != 0:\n", + " t_qubits.append(i+offset)\n", " if (i != 0) and (i != d):\n", " t_qubits.append(i+offset)\n", - "\n", + "print(t_qubits)\n", "# Apply controlled rotation gates with the specified angle\n", + "qc_pac.ry(rotation_angle_1, 0)\n", "for cq, tq in zip(c_qubits, t_qubits):\n", - " qc_pac.cry(rotation_angle, control_qubit=qr[cq], target_qubit=qr[tq])\n", + " qc_pac.cry(rotation_angle_1, control_qubit=qr[cq], target_qubit=qr[tq])\n", + " qc_pac.cry(rotation_angle_0, control_qubit=qr[cq], target_qubit=qr[tq])\n", " \n", "# Draw circuit\n", "qc_pac.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" @@ -446,8 +443,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:55:50.894094Z", - "start_time": "2023-11-08T23:55:50.615238Z" + "end_time": "2023-11-09T23:56:58.687930Z", + "start_time": "2023-11-09T23:56:58.269737Z" } }, "id": "7000db4359eed86a" @@ -467,42 +464,17 @@ "execution_count": 9, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", - "k: 0\n", - "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", - "k: 1\n", - "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", - "k: 2\n", - "{Qubit(QuantumRegister(1, '4'), 0): -1.0, Qubit(QuantumRegister(1, '3'), 0): -1.0, Qubit(QuantumRegister(1, '5'), 0): -1.0, Qubit(QuantumRegister(1, '6'), 0): -1.0, Qubit(QuantumRegister(1, '9'), 0): -1.0, Qubit(QuantumRegister(1, '10'), 0): -1.0, Qubit(QuantumRegister(1, '14'), 0): -1.0}\n", - "k: 3\n" - ] - }, - { - "ename": "KeyboardInterrupt", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", - "\u001B[0;31mKeyboardInterrupt\u001B[0m Traceback (most recent call last)", - "Cell \u001B[0;32mIn[9], line 6\u001B[0m\n\u001B[1;32m 4\u001B[0m qbayesian \u001B[38;5;241m=\u001B[39m QBayesian(circuit\u001B[38;5;241m=\u001B[39mqc_pac)\n\u001B[1;32m 5\u001B[0m \u001B[38;5;66;03m# Inference\u001B[39;00m\n\u001B[0;32m----> 6\u001B[0m \u001B[43mqbayesian\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43minference\u001B[49m\u001B[43m(\u001B[49m\u001B[43mquery\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mquery\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mevidence\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mevidence\u001B[49m\u001B[43m)\u001B[49m\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:255\u001B[0m, in \u001B[0;36mQBayesian.inference\u001B[0;34m(self, query, evidence, shots, limit)\u001B[0m\n\u001B[1;32m 239\u001B[0m \u001B[38;5;250m\u001B[39m\u001B[38;5;124;03m\"\"\"\u001B[39;00m\n\u001B[1;32m 240\u001B[0m \u001B[38;5;124;03mPerforms inference on the query variables given the evidence. It uses rejection sampling if evidence\u001B[39;00m\n\u001B[1;32m 241\u001B[0m \u001B[38;5;124;03mis provided and calculates the probability of the query.\u001B[39;00m\n\u001B[0;32m (...)\u001B[0m\n\u001B[1;32m 252\u001B[0m \u001B[38;5;124;03m ValueError: If evidence is required for rejection sampling and none is provided.\u001B[39;00m\n\u001B[1;32m 253\u001B[0m \u001B[38;5;124;03m\"\"\"\u001B[39;00m\n\u001B[1;32m 254\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m evidence \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[0;32m--> 255\u001B[0m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mrejectionSampling\u001B[49m\u001B[43m(\u001B[49m\u001B[43mevidence\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mshots\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mlimit\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 256\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n\u001B[1;32m 257\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39msamples:\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:201\u001B[0m, in \u001B[0;36mQBayesian.rejectionSampling\u001B[0;34m(self, evidence, shots, limit)\u001B[0m\n\u001B[1;32m 199\u001B[0m k \u001B[38;5;241m+\u001B[39m\u001B[38;5;241m=\u001B[39m \u001B[38;5;241m1\u001B[39m\n\u001B[1;32m 200\u001B[0m \u001B[38;5;66;03m# Create circuit with 2^k times grover operator\u001B[39;00m\n\u001B[0;32m--> 201\u001B[0m qc, E \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mpowerGrover\u001B[49m\u001B[43m(\u001B[49m\u001B[43mgroverOp\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mgroverOp\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mevidence\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mevidence\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mk\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mk\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 202\u001B[0m \u001B[38;5;66;03m# Test number of\u001B[39;00m\n\u001B[1;32m 203\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mlen\u001B[39m(e\u001B[38;5;241m.\u001B[39mintersection(E)) \u001B[38;5;241m>\u001B[39m best_inter:\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:153\u001B[0m, in \u001B[0;36mQBayesian.powerGrover\u001B[0;34m(self, groverOp, evidence, k)\u001B[0m\n\u001B[1;32m 151\u001B[0m qc_measure\u001B[38;5;241m.\u001B[39mmeasure([q \u001B[38;5;28;01mfor\u001B[39;00m q \u001B[38;5;129;01min\u001B[39;00m evidence_qubits], measurement_ecr)\n\u001B[1;32m 152\u001B[0m \u001B[38;5;66;03m# Run the circuit with the Grover operator and measurements\u001B[39;00m\n\u001B[0;32m--> 153\u001B[0m e_samples \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mrun_circuit\u001B[49m\u001B[43m(\u001B[49m\u001B[43mqc_measure\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mshots\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43m \u001B[49m\u001B[38;5;241;43m1024\u001B[39;49m\u001B[43m)\u001B[49m\n\u001B[1;32m 154\u001B[0m E_count \u001B[38;5;241m=\u001B[39m {\u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mlabel2qubit[e]: \u001B[38;5;241m0\u001B[39m \u001B[38;5;28;01mfor\u001B[39;00m e \u001B[38;5;129;01min\u001B[39;00m evidence}\n\u001B[1;32m 155\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m e_sample_key, e_sample_val \u001B[38;5;129;01min\u001B[39;00m e_samples\u001B[38;5;241m.\u001B[39mitems():\n\u001B[1;32m 156\u001B[0m \u001B[38;5;66;03m# Go through reverse binary that matches order of qubits\u001B[39;00m\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qiskit_machine_learning/algorithms/inference/qbayesian.py:117\u001B[0m, in \u001B[0;36mQBayesian.run_circuit\u001B[0;34m(self, circuit, shots)\u001B[0m\n\u001B[1;32m 115\u001B[0m \u001B[38;5;66;03m# Run the transpiled circuit on the simulator\u001B[39;00m\n\u001B[1;32m 116\u001B[0m job \u001B[38;5;241m=\u001B[39m simulator_backend\u001B[38;5;241m.\u001B[39mrun(transpiled_circuit, shots\u001B[38;5;241m=\u001B[39mshots)\n\u001B[0;32m--> 117\u001B[0m result \u001B[38;5;241m=\u001B[39m \u001B[43mjob\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mresult\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 118\u001B[0m \u001B[38;5;66;03m# Get the counts of quantum state results\u001B[39;00m\n\u001B[1;32m 119\u001B[0m counts \u001B[38;5;241m=\u001B[39m result\u001B[38;5;241m.\u001B[39mget_counts(transpiled_circuit)\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qbayesian/lib/python3.9/site-packages/qiskit_aer/jobs/utils.py:42\u001B[0m, in \u001B[0;36mrequires_submit.._wrapper\u001B[0;34m(self, *args, **kwargs)\u001B[0m\n\u001B[1;32m 40\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_future \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[1;32m 41\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m JobError(\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mJob not submitted yet!. You have to .submit() first!\u001B[39m\u001B[38;5;124m\"\u001B[39m)\n\u001B[0;32m---> 42\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[43mfunc\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43margs\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43mkwargs\u001B[49m\u001B[43m)\u001B[49m\n", - "File \u001B[0;32m~/PycharmProjects/qiskit-machine-learning/qbayesian/lib/python3.9/site-packages/qiskit_aer/jobs/aerjob.py:114\u001B[0m, in \u001B[0;36mAerJob.result\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 96\u001B[0m \u001B[38;5;129m@requires_submit\u001B[39m\n\u001B[1;32m 97\u001B[0m \u001B[38;5;28;01mdef\u001B[39;00m \u001B[38;5;21mresult\u001B[39m(\u001B[38;5;28mself\u001B[39m, timeout\u001B[38;5;241m=\u001B[39m\u001B[38;5;28;01mNone\u001B[39;00m):\n\u001B[1;32m 98\u001B[0m \u001B[38;5;66;03m# pylint: disable=arguments-differ\u001B[39;00m\n\u001B[1;32m 99\u001B[0m \u001B[38;5;250m \u001B[39m\u001B[38;5;124;03m\"\"\"Get job result. The behavior is the same as the underlying\u001B[39;00m\n\u001B[1;32m 100\u001B[0m \u001B[38;5;124;03m concurrent Future objects,\u001B[39;00m\n\u001B[1;32m 101\u001B[0m \n\u001B[0;32m (...)\u001B[0m\n\u001B[1;32m 112\u001B[0m \u001B[38;5;124;03m concurrent.futures.CancelledError: if job cancelled before completed.\u001B[39;00m\n\u001B[1;32m 113\u001B[0m \u001B[38;5;124;03m \"\"\"\u001B[39;00m\n\u001B[0;32m--> 114\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43m_future\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mresult\u001B[49m\u001B[43m(\u001B[49m\u001B[43mtimeout\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[43mtimeout\u001B[49m\u001B[43m)\u001B[49m\n", - "File \u001B[0;32m/Applications/Xcode.app/Contents/Developer/Library/Frameworks/Python3.framework/Versions/3.9/lib/python3.9/concurrent/futures/_base.py:440\u001B[0m, in \u001B[0;36mFuture.result\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 437\u001B[0m \u001B[38;5;28;01melif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_state \u001B[38;5;241m==\u001B[39m FINISHED:\n\u001B[1;32m 438\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m__get_result()\n\u001B[0;32m--> 440\u001B[0m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43m_condition\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mwait\u001B[49m\u001B[43m(\u001B[49m\u001B[43mtimeout\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 442\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39m_state \u001B[38;5;129;01min\u001B[39;00m [CANCELLED, CANCELLED_AND_NOTIFIED]:\n\u001B[1;32m 443\u001B[0m \u001B[38;5;28;01mraise\u001B[39;00m CancelledError()\n", - "File \u001B[0;32m/Applications/Xcode.app/Contents/Developer/Library/Frameworks/Python3.framework/Versions/3.9/lib/python3.9/threading.py:312\u001B[0m, in \u001B[0;36mCondition.wait\u001B[0;34m(self, timeout)\u001B[0m\n\u001B[1;32m 310\u001B[0m \u001B[38;5;28;01mtry\u001B[39;00m: \u001B[38;5;66;03m# restore state no matter what (e.g., KeyboardInterrupt)\u001B[39;00m\n\u001B[1;32m 311\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m timeout \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[0;32m--> 312\u001B[0m \u001B[43mwaiter\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43macquire\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 313\u001B[0m gotit \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;01mTrue\u001B[39;00m\n\u001B[1;32m 314\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n", - "\u001B[0;31mKeyboardInterrupt\u001B[0m: " - ] + "data": { + "text/plain": "0.12777000000000002" + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "query = {'12': 1}\n", - "evidence = {'4': 1, '3': 0, '5': 0, '6': 0, '9': 0, '10': 0, '14': 0}\n", + "evidence = {'4': 1}\n", "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc_pac)\n", "# Inference\n", @@ -511,22 +483,22 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:59:55.688981Z", - "start_time": "2023-11-08T23:55:50.881925Z" + "end_time": "2023-11-09T23:57:36.205130Z", + "start_time": "2023-11-09T23:56:58.737324Z" } }, "id": "f3ae346612ee10d" }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "outputs": [], "source": [], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-08T23:59:55.692314Z", - "start_time": "2023-11-08T23:59:55.691982Z" + "end_time": "2023-11-09T23:57:36.208046Z", + "start_time": "2023-11-09T23:57:36.205546Z" } }, "id": "6d2c15ce28c7d74a" diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 679fd568e..aca45bbdc 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -9,9 +9,7 @@ # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -import copy -import numpy as np from qiskit import QuantumCircuit, transpile, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator @@ -19,6 +17,7 @@ """Quantum Bayesian Inference""" + class QBayesian: r""" Implements Quantum Bayesian Inference algorithm. The algorithm has been developed in [1]. @@ -30,9 +29,9 @@ class QBayesian: Usage: ------ - To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. - You can then use the `inference` method to estimate probabilities given evidence, optionally using - rejection sampling and Grover's algorithm for amplification. + To use the `QBayesian` class, instantiate it with a quantum circuit that represents the + Bayesian network. You can then use the `inference` method to estimate probabilities given + evidence, optionally using rejection sampling and Grover's algorithm for amplification. Example: -------- @@ -52,12 +51,12 @@ class QBayesian: # Discrete quantum Bayesian network def __init__(self, circuit: QuantumCircuit): """ - Run the provided quantum circuit on the Aer simulator backend. For other simulator overwrite the method - run_circuit(). + Run the provided quantum circuit on the Aer simulator backend. For other simulator + overwrite the method run_circuit(). Args: - circuit (QuantumCircuit): The quantum circuit representing the Bayesian network. Each random variable - should be assigned to exactly one register of one qubit. + circuit (QuantumCircuit): The quantum circuit representing the Bayesian network. + Each random variable should be assigned to exactly one register of one qubit. Raises: ValueError: If any register in the circuit is not mapped to exactly one qubit. @@ -65,7 +64,7 @@ def __init__(self, circuit: QuantumCircuit): """ # Test valid input for qrg in circuit.qregs: - if qrg.size>1: + if qrg.size > 1: raise ValueError("Every register needs to be mapped to exactly one unique qubit") # Initialize QBayesian self.circ = circuit @@ -78,10 +77,10 @@ def __init__(self, circuit: QuantumCircuit): # True if rejection sampling converged after limit self.converged = bool - def getGroverOp(self, evidence: dict) -> GroverOperator: + def get_grover_op(self, evidence: dict) -> GroverOperator: """ - Constructs a Grover operator based on the provided evidence. The evidence is used to determine - the "good states" that the Grover operator will amplify. + Constructs a Grover operator based on the provided evidence. The evidence is used to + determine the "good states" that the Grover operator will amplify. Args: evidence (dict): A dictionary representing the evidence with keys as variable labels and values as states. @@ -91,23 +90,26 @@ def getGroverOp(self, evidence: dict) -> GroverOperator: # Evidence to reversed qubit index sorted by index num_qubits = self.circ.num_qubits e2idx = sorted( - [(num_qubits-self.label2qidx[e_key]-1, e_val) for e_key, e_val in evidence.items()], key=lambda x: x[0] + [(num_qubits - self.label2qidx[e_key] - 1, e_val) + for e_key, e_val in evidence.items()], key=lambda x: x[0] ) # Binary format of good states num_evd = len(e2idx) - bin_str = [format(i, f'0{(num_qubits-num_evd)}b') for i in range(2**(num_qubits-num_evd))] + bin_str = [ + format(i, f'0{(num_qubits - num_evd)}b') for i in range(2 ** (num_qubits - num_evd)) + ] # Get good states good_states = [] for b in bin_str: for e_idx, e_val in e2idx: - b = b[:e_idx]+str(e_val)+b[e_idx:] + b = b[:e_idx] + str(e_val) + b[e_idx:] good_states.append(b) - # Get statevector by transform good states like 010 regarding its idx (2+1=3) of statevector to 1 and o/w to 0 - oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2**num_qubits)]) + # Get statevector by transform good states w.r.t its idx to 1 and o/w to 0 + oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2 ** num_qubits)]) return GroverOperator(oracle, state_preparation=self.circ) def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: - """ Run the provided quantum circuit for the number of shots on the Aer simulator backend. """ + """ Run the quantum circuit for the number of shots on the Aer simulator backend. """ # Get the Aer simulator backend simulator_backend = AerSimulator() # Transpile the circuit for the given backend @@ -121,25 +123,29 @@ def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: relative_counts = {state: count / shots for state, count in counts.items()} return relative_counts - def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (GroverOperator, set): + def power_grover( + self, grover_op: GroverOperator, evidence: dict, k: int + ) -> (GroverOperator, set): """ - Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns - a tuple containing the updated quantum circuit and a set of the measured evidence qubits. + Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, + and returns a tuple containing the updated quantum circuit and a set of the measured + evidence qubits. Args: - groverOp (GroverOperator): The Grover operator to be applied. + grover_op (GroverOperator): The Grover operator to be applied. evidence (dict): A dictionary representing the evidence. k (int): The power to which the Grover operator is raised. Returns: - tuple: A tuple containing the updated quantum circuit and a set of the measured evidence qubits. + tuple: A tuple containing the updated quantum circuit and a set of the + measured evidence qubits. """ # Create circuit qc = QuantumCircuit(*self.circ.qregs) qc.append(self.circ, self.circ.qregs) # Apply grover operator 2^k times - qcGrover = QuantumCircuit(*self.circ.qregs) - qcGrover.append(groverOp, self.circ.qregs) - qcGrover = qcGrover.power(2 ** k) - qc.append(qcGrover, self.circ.qregs) + qc_grover = QuantumCircuit(*self.circ.qregs) + qc_grover.append(grover_op, self.circ.qregs) + qc_grover = qc_grover.power(2 ** k) + qc.append(qc_grover, self.circ.qregs) # Add quantum circuit for measuring qc_measure = QuantumCircuit(*self.circ.qregs) qc_measure.append(qc, self.circ.qregs) @@ -150,25 +156,25 @@ def powerGrover(self, groverOp: GroverOperator, evidence: dict, k: int) -> (Grov evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] qc_measure.measure([q for q in evidence_qubits], measurement_ecr) # Run the circuit with the Grover operator and measurements - e_samples = self.run_circuit(qc_measure, shots = 1024) - E_count = {self.label2qubit[e]: 0 for e in evidence} + e_samples = self.run_circuit(qc_measure, shots=1024*self.circ.num_qubits) + print(e_samples) + e_count = {self.label2qubit[e]: 0 for e in evidence} for e_sample_key, e_sample_val in e_samples.items(): # Go through reverse binary that matches order of qubits for i, char in enumerate(e_sample_key[::-1]): if int(char) == 1: - E_count[evidence_qubits[i]] += e_sample_val + e_count[evidence_qubits[i]] += e_sample_val else: - E_count[evidence_qubits[i]] += -e_sample_val - print(E_count) + e_count[evidence_qubits[i]] += -e_sample_val # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 - E = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in E_count.items()} - return qc, E + e_meas = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in e_count.items()} + return qc, e_meas - def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10) -> dict: + def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 10) -> dict: """ - Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures - all qubits. If evidence is provided, it uses the Grover operator for amplitude amplification and iterates - until the evidence matches or a limit is reached. + Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit + and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude + amplification and iterates until the evidence matches or a limit is reached. Args: evidence (dict): A dictionary representing the evidence. shots (int): The number of times the circuit will be executed. @@ -187,30 +193,30 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10 samples = self.run_circuit(qc, shots=shots) return samples # Get grover operator if evidence not empty - groverOp = self.getGroverOp(evidence) + grover_op = self.get_grover_op(evidence) # Amplitude amplification - e, E = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} - best_QC, best_inter = QuantumCircuit(), 0 + e, meas_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} + best_qc, best_inter = QuantumCircuit(), 0 self.converged = False k = -1 # If the measurement of the evidence qubits matches the evidence stop - while (e != E) and (k < limit): + while (e != meas_e) and (k < limit): # Increment power k += 1 # Create circuit with 2^k times grover operator - qc, E = self.powerGrover(groverOp=groverOp, evidence=evidence, k=k) + qc, meas_e = self.power_grover(grover_op=grover_op, evidence=evidence, k=k) # Test number of - if len(e.intersection(E)) > best_inter: + if len(e.intersection(meas_e)) > best_inter: best_qc = qc - print("k:",k) - if e == E: + if e == meas_e: self.converged = True # Create a classical register with the size of the evidence - measurement_qcr = ClassicalRegister(self.circ.num_qubits-len(evidence)) + measurement_qcr = ClassicalRegister(self.circ.num_qubits - len(evidence)) best_qc.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them - query_qubits = [(label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if label not in evidence] + query_qubits = [(label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if + label not in evidence] query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1]) # Measure query variables and return their count best_qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) @@ -218,8 +224,8 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10 counts = self.run_circuit(best_qc, shots=shots) # Build default string with evidence query_string = '' - varIdxSorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] - for var in varIdxSorted: + var_idx_sorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] + for var in var_idx_sorted: if var in evidence: query_string += str(evidence[var]) else: @@ -234,32 +240,34 @@ def rejectionSampling(self, evidence: dict, shots: int = 100000, limit: int = 10 self.samples[query] = val return self.samples - - def inference(self, query: dict, evidence: dict=None, shots: int=100000, limit: int=10) -> float: + def inference( + self, query: dict, evidence: dict = None, shots: int = 100000, limit: int = 10 + ) -> float: """ - Performs inference on the query variables given the evidence. It uses rejection sampling if evidence - is provided and calculates the probability of the query. + Performs inference on the query variables given the evidence. It uses rejection sampling if + evidence is provided and calculates the probability of the query. Args: - query (dict): The query variables with keys as variable labels and values as states. If Q is a real subset - of X\E, it will be marginalized. - evidence (dict, optional): The evidence variables. If provided, rejection sampling is executed. If you want - to indicate no evidence - insert an empty list. + query (dict): The query variables with keys as variable labels and values as states. + If Q is a real subset of X without E, it will be marginalized. + evidence (dict, optional): The evidence variables. If provided, rejection sampling is + executed. If you want to indicate no evidence insert an empty list. shots (int): The number of times the circuit will be executed. + limit (int): The maximum number of 2^k times the Grover operator is integrated Returns: float: The probability of the query given the evidence. Raises: ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: - self.rejectionSampling(evidence, shots, limit) + self.rejection_sampling(evidence, shots, limit) else: if not self.samples: - raise ValueError("Provide evidence for rejection sampling or indicate no evidence with empty list") + raise ValueError("Provide evidence or indicate no evidence with empty list") # Get sorted indices of query qubits query_indices_rev = [ (self.circ.num_qubits-self.label2qidx[q_key]-1, q_val) for q_key, q_val in query.items() ] + print([(key, val) for key, val in self.samples.items() if val>0.05]) # Get probability of query res = 0 for sample_key, sample_val in self.samples.items(): @@ -271,9 +279,3 @@ def inference(self, query: dict, evidence: dict=None, shots: int=100000, limit: if add: res += sample_val return res - - - - - - diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 27a6ee59b..2cc5c9653 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -18,8 +18,10 @@ from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister + class TestQBayesianInference(QiskitMachineLearningTestCase): """Test QBayesianInference Algorithm""" + def setUp(self): super().setUp() algorithm_globals.random_seed = 10598 @@ -64,7 +66,6 @@ def setUp(self): # Quantum Bayesian inference self.qbayesian = QBayesian(qcA) - def test_rejection_sampling(self): """Test rejection sampling with different amount of evidence""" test_cases = [{'A': 0, 'B': 0}, {'A': 0}, {}] @@ -73,9 +74,9 @@ def test_rejection_sampling(self): {'000': 0.36, '100': 0.04, '010': 0.18, '110': 0.42}, {'000': 0.27, '001': 0.03375, '010': 0.135, '011': 0.0175, '100': 0.03, '101': 0.04125, '110': 0.315, '111': 0.1575} - ] + ] for e, res in zip(test_cases, true_res): - samples = self.qbayesian.rejectionSampling(evidence=e) + samples = self.qbayesian.rejection_sampling(evidence=e) self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.1) for sample_key, sample_val in samples.items()])) @@ -107,14 +108,14 @@ def test_inference(self): def test_parameter(self): """Tests parameter of QBayesian methods""" # Test set limit - self.qbayesian.rejectionSampling(evidence={'B': 1}, limit=1) + self.qbayesian.rejection_sampling(evidence={'B': 1}, limit=1) # Test set shots self.qbayesian.inference(query={'B': 1}, evidence={'A': 0, 'C': 0}, shots=10) # Create a quantum circuit with a register that has more than one qubit - with self.assertRaises(ValueError, msg="QBayesian constructor did not raise ValueError with invalid input."): + with self.assertRaises(ValueError, msg="No ValueError in constructor with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(2, 'qr'))) # Test invalid inference without evidence or generated samples - with self.assertRaises(ValueError, msg="QBayesian inference did not raise ValueError with invalid input."): + with self.assertRaises(ValueError, msg="No ValueError in inference with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(1, 'qr'))).inference({'A': 0}) def test_trivial_circuit(self): @@ -137,7 +138,10 @@ def test_trivial_circuit(self): # Initialize quantum bayesian qb = QBayesian(circuit=qc) # Inference - self.assertTrue(np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.05))) + self.assertTrue( + np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.05)) + ) + if __name__ == "__main__": unittest.main() From be09b49ecd33d887e6d10931ab50bd91eea32299 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 02:53:47 +0100 Subject: [PATCH 14/48] Add Burglary Earthquake Example --- .../13_quantum_bayesian_inference.ipynb | 332 +++++++++++++++--- .../algorithms/inference/qbayesian.py | 2 - 2 files changed, 275 insertions(+), 59 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index fefddb5c3..bddba2ee8 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -29,7 +29,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 40, "outputs": [ { "data": { @@ -60,8 +60,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:49.329959Z", - "start_time": "2023-11-09T23:56:48.754530Z" + "end_time": "2023-11-10T01:53:06.075105Z", + "start_time": "2023-11-10T01:53:03.964957Z" } }, "id": "925af2a5fe37bf8c" @@ -81,13 +81,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 41, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-09T23:56:49.334795Z", - "start_time": "2023-11-09T23:56:49.331578Z" + "end_time": "2023-11-10T01:53:06.075307Z", + "start_time": "2023-11-10T01:53:04.049355Z" } }, "outputs": [], @@ -114,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 42, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, - "execution_count": 3, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:49.778087Z", - "start_time": "2023-11-09T23:56:49.334596Z" + "end_time": "2023-11-10T01:53:06.075447Z", + "start_time": "2023-11-10T01:53:04.056015Z" } }, "id": "c4984e988c8ededd" @@ -169,13 +169,93 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 43, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00906 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.02694 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 5.19609 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.001s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.001s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.002s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 5.42998 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.01788 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.04697 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.01574 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.04101 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00381 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 2.39205 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.06199 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09704 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.03028 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01574 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00715 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.39403 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03767 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.08988 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02670 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.02003 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.01693 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.26696 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03886 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09084 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02623 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01693 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.01788 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 37.86802 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00477 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00072 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.00811 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 3.83615 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.001s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.001s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 4.67014 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.01431 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.10109 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.05722 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.98174 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.13614 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09704 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02813 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01597 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.59574 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.07105 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.10395 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02694 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01812 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00405 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.44100 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03791 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09394 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02599 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.02408 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.01812 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 32.92513 (ms)\n" + ] + }, { "data": { - "text/plain": "0.11777" + "text/plain": "0.11922" }, - "execution_count": 4, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -193,8 +273,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:50.662173Z", - "start_time": "2023-11-09T23:56:49.779106Z" + "end_time": "2023-11-10T01:53:06.077940Z", + "start_time": "2023-11-10T01:53:04.128656Z" } }, "id": "8d7a132268680e61" @@ -213,14 +293,14 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 44, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 5, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -249,8 +329,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:51.053032Z", - "start_time": "2023-11-09T23:56:50.665313Z" + "end_time": "2023-11-10T01:53:06.093229Z", + "start_time": "2023-11-10T01:53:04.244818Z" } }, "id": "9021e193f69b0392" @@ -267,21 +347,175 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 45, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00620 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01907 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 281.26693 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.002s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.010s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 17.19189 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.35095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.86808 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.34261 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 33.26821 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 1.72710 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 3.97491 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.87595 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.35095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 34.79385 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 1.88112 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 4.23598 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.85235 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.34213 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 36.93390 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 2.03085 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 4.22120 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.88501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00811 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.40007 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.39315 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 450.05584 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01407 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 232.22804 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.003s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.017s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 27.04120 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.66090 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.60432 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.66400 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 64.04185 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.42512 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.89809 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.58596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.68402 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 63.49897 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.40509 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.62796 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.61505 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.65899 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 63.62295 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.32594 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.77507 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.68180 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.67306 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.67830 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 515.87081 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01717 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 587.18991 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.005s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.033s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 51.32413 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 1.31083 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.22413 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.31989 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 133.64792 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.69782 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.83910 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.23009 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.36399 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 129.71878 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 6.80709 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.44499 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.13973 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.35517 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 127.05207 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.74693 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.60783 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.17287 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.28102 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00381 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 1.26791 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 1234.83801 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00525 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00119 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01001 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 762.33602 (ms)\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.006s.\n", + "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.033s.\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 55.11713 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 1.33991 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.41511 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.39093 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 125.62895 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.15208 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.98597 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.48496 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00787 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.52016 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 150.48409 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.29823 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 16.40582 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.73816 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00906 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.53112 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 132.76291 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 6.85596 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.81717 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.26610 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.41692 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00739 (ms)\n", + "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 1.53494 (ms)\n", + "INFO:qiskit.compiler.transpiler:Total Transpile Time - 1358.55627 (ms)\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "{'1000000000': 0.33117, '0000000000': 0.66883}\n" + "{'1000000000': 0.40371, '0000000000': 0.59629}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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" 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iRYtyvb/Lly/j6+uLwWCgQ4cOt+1jMBiy/Kdfv365PraIiIhIYWKf2y9GRUXx888/M3PmTBYuXMiiRYuoUKECL730Ev369aN06dK5Lmrjxo20b98eZ2dnevfuTdGiRVmyZAm9evUiIiKC4cOH53ifr732GrGxsXft5+/vf9uwV6dOnRwfU0RERKQwMpjNZvO97uTgwYP88MMPzJ8/n8uXL2Nvb0/nzp0ZMGAAHTp0wGAwZHtfqampVK1alTNnzrB9+3ZL8IqNjSUoKIhTp05x7Ngx/P39s73PJUuW0L17d6ZPn85rr71G+/bt+euvvzL1MxgMtGjRgr///jvb+76TuLg4PDw8iI2Nxd3dPU/2easBX+bLbkVybcYQa1cgImKbcpI78uQlkJo1azJt2jTOnTvHTz/9RLNmzfjjjz/o3Lkz/v7+jB07lrNnz2ZrXxs2bCAsLIw+ffpkuOrm4eHByJEjSU5OZu7cudmuLTo6mldeeYXnnnuOTp065XRoIiIiIg+cPH0L2MnJifbt29OxY0dKly6N2WzmzJkzjB07looVKzJ48GCuX79+x32kX31r165dpm3t27cHYNOmTdmu6eWXX8bOzo6pU6dmq/+VK1f44YcfGD9+PN999x0HDx7M9rFERERE7ge5fgbwVmvWrGHmzJksW7aMlJQUypQpw4cffsjzzz/Pnj17mDJlCt999x3Xr19n9uzZWe4nNDQUgICAgEzbSpcujZubm6XP3cybN4/ffvuNpUuX4unpma1nAPfv38+gQYMytHXo0IG5c+fi5eV1x+8mJSWRlJRk+RwXFwdASkoKKSkpABiNRuzs7EhLS8NkMln6prenpqZy8115Ozs7jEZjlu0ihU36f+vp7O1vnGZSU1MztDs4OGAymUhLS7O0GQwG7O3ts2zP6u8mr/6eslu7xqQxaUwaU2EcU07cUwA8e/Yss2bNYvbs2Zw+fRq4ceVu0KBBdOnSBTs7OwAqVqxI9+7d6dKlC3/88ccd95ke0jw8PG673d3dPVtB7ty5c7zxxhs8/fTTdO3aNVvjGT58ON26daNy5co4Ojpy6NAhxo0bx6pVq+jcuTPBwcGWMd3OhAkTGDt2bKb2NWvW4OLiAoCfnx+BgYEcOHCA8PBwS58qVapQtWpVdu7cSXR0tKW9Tp06+Pv7s3nzZq5evWppb9y48V0DqYg1rFy5MsPnjh07kpCQwMaNGy1t9vb2dOrUiZiYGIKDgy3tRYsWpXXr1kRERLBv3z5Le6lSpWjSpAmhoaGEhIRY2vP672nNmjUZTtitWrWiSJEiGpPGpDFpTPfFmHx8fMiuXL8E0rlzZ1avXk1aWhre3t688MILDBw4kPLly2f5nQkTJvDBBx9kSLi3ateuHWvXriU0NJRKlSpl2u7r68u1a9fuGgI7duzIv//+y+HDhylZsiQAp06dokKFClm+BHI7JpOJ1q1bs2nTJpYsWcJTTz2VZd/bXQEsV64cMTExlocx8/rXiF4CkcLmm8G6AqgxaUwak8ZkjTHFx8dn+yWQXF8BXLlyJa1bt2bQoEE8+eSTlsHeSZcuXe6aTtOv/GUV8OLi4vD09LzjPubOncuqVatYvHixJfzlltFoZMCAAWzatImtW7feMQA6OTnh5OSUqd3BwQEHB4cMbXZ2dre9mpjV/47Z+d9XpDC49b/1O7Ubjcbb3rbIqj2rv5u8+nvKSe1ZtWtMGhNoTFnVmNN2jSnnY8quXD9EduzYMdatW0ePHj2yHU4efvhhnn/++Tv2SX/273bP+UVFRXHt2rXbPh94s7179wLQo0ePDJM5V6hQAYDVq1djMBiyPbdfeoiMj4/PVn8REZHC4uuvv6Z8+fI4OzvTsGFDdu7cma3vLViwAIPBwBNPPJGh3Ww2M2rUKMqUKUORIkVo27Ztls/mJyUlUadOHQwGQ4bbm2J9uQ6A48ePZ9myZXfss3z5cvr375+j/bZo0QK48dzcrVavXp2hT1YaN27Miy++mOmfXr16AVC2bFlefPHFO17Nu9mOHTsA7nh7W0REpLBZuHAhw4YNY/To0ezZs4fatWvTvn17Lly4cMfvnTp1irfeeotHHnkk07ZJkybx1Vdf8d1337Fjxw5cXV1p3749iYmJmfq+8847OXouTQpOrp8BNBqNjBkzhlGjRmXZ55NPPmHUqFF3fObvVqmpqVSpUoWzZ89mORF0SEiIJYxFRkYSGxtLmTJlsnxxJN2dngE8ePAgVatWzXS5dtu2bTz66KOkpKRw5MgRHnrooWyPRRNBiy3SRNAihUfDhg1p0KAB06dPB248116uXDlef/113nvvvdt+Jy0tjebNm9O/f3/++ecfrly5wtKlS4EbV/98fHwYPnw4b731FnDj/z57e3szZ84cevfubdnPqlWrGDZsGEuWLKFGjRrs3btXq2rlswKfCDoriYmJOX52zd7enpkzZ2IymWjevDkDBw5k+PDh1K5dm2PHjjF+/PgMV+JGjBhBtWrV+P333++p1ilTpuDj48OTTz7JG2+8wfDhw+nQoQPNmjUjMTGRr776KkfhT0RExJqSk5P5999/adu2raXNaDTStm3bDG+h3uqjjz7Cy8uLF198MdO2kydPEhUVlWGfHh4eNGzYMMM+z58/z4ABA/jpp58ss2BI4XJPbxZktcSb2WwmIiKCVatW5erSb6tWrdiyZQujR49m4cKFpKSkULNmTSZOnGi5jZvXunbtypUrV9i/fz9r164lOTmZ0qVL07t3b4YMGUJQUFC+HFdERCQ/xMTEWGbquJm3tzdHjx697Xe2bNnCjz/+mOXzelFRUZZ93LrP9G1ms5l+/frx8ssvU79+fU6dOnVvA5F8kaMAaDQaM4S+MWPGMGbMmCz7m81m3n333VwVFhQUxKpVq+7ab86cOcyZMydb+yxfvjxZ3fF+8sknefLJJ3NSooiIyAPj6tWrPPfcc8yYMeOeZtCYNm0aV69eZcSIEXlYneS1HAXA5s2bWwLg5s2b8fPzu+2LEXZ2dhQvXpzWrVszYMCAPClUREREsq9kyZLY2dlx/vz5DO3nz5+ndOnSmfqHhYVx6tQpunTpYmlLn2fO3t6ekJAQy/fOnz9PmTJlMuwz/fm+DRs2EBwcnGlatPr16/PMM88wd+7cPBmf3JscBcD0dXrhxtXAF1544Y4vgYiIiIh1ODo6Uq9ePdavX2+ZysVkMrF+/Xpee+21TP2rVq3KwYMHM7R98MEHXL16lalTp1KuXDkcHBwoXbo069evtwS+uLg4duzYwSuvvALAV199xccff2zZx7lz52jfvj0LFy6kYcOG+TNYybFcPwN48+zTIiIiUvgMGzaM559/nvr16xMUFMSXX35JfHw8L7zwAgB9+/bF19eXCRMm4OzszMMPP5zh+8WKFQPI0D5kyBA+/vhjAgICqFChAh9++CE+Pj6WkOnn55dhH25ubgA89NBDlC1bNp9GKjml5SVEREQeUL169SI6OppRo0YRFRVFnTp1+OuvvywvcYSHh9929Yk7eeedd4iPj2fgwIFcuXKFZs2a8ddff+Hs7JwfQ5B8ku15APv374/BYGD8+PF4e3tne4Jng8HAjz/+eE9F3q80D6DYIs0DKCJiHTnJHdkOgOlvAB85coTKlStn+xeDwWDI0UTQDxIFQLFFCoAiItaRk9yR7VvAJ0+eBMDX1zfDZxERERG5v2Q7APr7+9/xs4iIiIjcH/J1KTgRERERKXyyfQUwPDw81we59ZVwEREREbGebAfA8uXLZ7n2750YDAZSU1Nz/D0RERERyR/ZDoB9+/bNVQAUERERkcIl2wFwzpw5+ViGiIiIiBQUvQQiIiIiYmMUAEVERERsTLZvAWspOBEREZEHg5aCy0daCk5skZaCExGxDi0FJyIiIiJZ0lJwIiIiIjYm2wFQRETkfqPHZKQwKUyPyNzzW8C///47Xbt2xc/PDw8PD/z8/HjiiSdYunRpHpQnIiIiInkt11cAU1NT6dOnD0uWLMFsNmNvb0+JEiWIiopi2bJl/Pnnn3Tr1o358+djb68LjSIiIiKFRa6vAE6YMIFff/2VRx55hH/++YfExEQiIyNJTExk8+bNNGvWjCVLlvDpp5/mZb0iIiIico9yHQBnz55N1apVWbduHU2bNrVMC2M0GmnWrBnr1q2jcuXKzJo1K8+KFREREZF7l+sAGBkZSZcuXbK8vevg4ECXLl2IjIzMdXEiIiIikvdyHQDLlSvHtWvX7tgnPj4ePz+/3B5CRERERPJBrgPgSy+9xKJFi7K8wnf27FkWLlzISy+9lOviRERERCTvZfv13PDw8Ayfe/bsydatWwkMDGTIkCE0a9YMb29vzp8/zz///MPUqVNp1qwZPXr0yPOiRURERCT3sh0Ay5cvj8FgyNRuNpt5//33b9u+bNkyli9fTmpq6r1VKSIiIiJ5JtsBsG/fvrcNgCIiIiJyf8l2AJwzZ04+liEiIiIiBeWel4ITERERkfuLAqCIiIiIjbmnRXqvXr3K9OnTWbduHefOnSMpKSlTH4PBQFhY2L0cRkRERETyUK4DYHR0NE2aNCEsLAx3d3fi4uLw8PAgOTmZhIQEAHx8fHBwcMizYkVERETk3uX6FvCYMWMICwvjf//7H5cvXwZg6NChxMfHs2PHDoKCgihfvjyHDx/Os2JFRERE5N7lOgCuXLmSNm3a8Oyzz2aaHqZBgwasWrWKU6dOMXbs2HsuUkRERETyTq4DYGRkJIGBgZbPdnZ2llu/AJ6enjz22GMsWrTo3ioUERERkTyV6wDo4eFBSkqK5bOnpydnzpzJ0Mfd3Z3z58/nvjoRERERyXO5DoAVK1bk1KlTls+BgYGsXbuWixcvApCQkMCff/6Jn5/fPRcpIiIiInkn1wGwXbt2rF+/nuvXrwMwaNAgLly4QO3atenRowcPP/wwYWFh9OvXL69qFREREZE8kOsA+PLLLzNjxgxLAHzqqaf47LPPiI+PZ8mSJURFRTFs2DDefvvtPCtWRERERO5drucBLFOmDL169crQNnz4cIYMGUJMTAxeXl6Z3g4WEREREeu7p5VAbsfOzg5vb++83q2IiIiI5JF7DoCRkZEsWLCAvXv3Ehsbi4eHB4GBgfTu3ZsyZcrkRY0iIiIikofuKQB+/fXXvP322yQlJWE2my3t8+bN4/3332fy5Mm8+uqr91ykiIiIiOSdXAfABQsW8Prrr1OyZEnef/99HnnkEby9vTl//jybN29m6tSplu09e/bMy5pFRERE5B7kOgBOmjSJkiVLsm/fPnx8fCztVapUoXnz5vTr14/AwEAmTpyoACgiIiJSiOR6GpgjR47Qs2fPDOHvZmXLlqVHjx4cOXIk18WJiIiISN7LdQAsVqwYrq6ud+zj5uZGsWLFcnsIEREREckHuQ6Ajz/+OH/++Sepqam33Z6SksKff/5J165dc12ciIiIiOS9XAfASZMm4erqSrt27di+fXuGbcHBwbRr146iRYvy6aef3nORIiIiIpJ3sv0SSMWKFTO1JScns2fPHpo2bYq9vT0lS5YkJibGclWwTJky1K1bl7CwsLyrWERERETuSbYDoMlkyrS0m4ODA35+fhnabn0pxGQy3UN5IiIiIpLXsh0AT506lY9liIiIiEhByfUzgCIiIiJyf7rntYABUlNTCQkJIS4uDnd3d6pUqYK9fZ7sWkRERETy2D1dAbx06RIDBgzAw8ODWrVq0axZM2rVqkWxYsUYOHAgFy9ezKs6RURERCSP5Poy3aVLl2jUqBHHjx+nePHiPPLII5QpU4aoqCh2797NzJkz2bRpE8HBwRQvXjwvaxYRERGRe5DrK4Djxo3j+PHjvP3225w+fZq//vqL2bNns2rVKk6fPs27775LaGgon3zySV7WKyIiIiL3KNcB8I8//qBly5ZMnDgx05JwLi4uTJgwgZYtW/L777/fc5EiIiIikndyHQDPnTtH48aN79incePGnDt3LreHEBEREZF8kOsA6OHhwenTp+/Y5/Tp03h4eOT2ECIiIiKSD3IdAFu0aMHixYtZt27dbbevX7+exYsX07Jly9weQkRERETyQa7fAh49ejQrVqygffv2dOzYkRYtWuDt7c358+f5+++/WbVqFS4uLowaNSov6xURERGRe5TrAFijRg1Wr15Nv379WLFiBStWrMBgMGA2mwF46KGHmDNnDjVq1MizYkVERETk3t3Tch3NmjUjNDSUrVu3snfvXstKIIGBgTRt2hSDwZBXdYqIiIhIHsl1AOzfvz81a9Zk6NChNGvWjGbNmuVlXSIiIiKST3L9Esj8+fO5cOFCXtYiIiIiIgUg1wHwoYceIjIyMi9rEREREZECkOsA2L9/f1asWMHZs2fzsh4RERERyWe5fgawW7dubNy4kSZNmvDOO+/QoEEDvL29b/vih5+f3z0VKSIiIiJ5J9cBsGLFipZpX954440s+xkMBlJTU3N7GBERERHJY7kOgH379s3XaV527drF6NGj2bZtGykpKdSsWZNhw4bRs2fPbH1/1apVzJ07l3379hEVFUVycjJ+fn40bdqUd999l8qVK9/2e6tXr2b8+PHs2bMHg8FAvXr1+OCDD2jTpk1eDk9ERETEanIdAOfMmZOHZWS0ceNG2rdvj7OzM71796Zo0aIsWbKEXr16ERERwfDhw++6j5UrV7J9+3YaNmzIY489hoODA0eOHGHu3Ln8/PPPrFy5ktatW2f4zrx583juuecoVaoU/fr1A2DhwoU8+uijLFq0iO7du+fHcEVEREQKlMGcvnRHIZGamkrVqlU5c+YM27dvp06dOgDExsYSFBTEqVOnOHbsGP7+/nfcT2JiIs7Ozpna169fT9u2balfvz67du2ytF++fJmKFStib2/P3r17KVu2LABnzpwhMDAQgBMnTlC0aNFsjyUuLg4PDw9iY2Nxd3fP9vdyYsCX+bJbkVybMcTaFYj8H50jpTDJ7/NjTnJHrt8CTpeUlMTvv//OqFGjePPNNxk1ahS///47SUlJudrfhg0bCAsLo0+fPpbwB+Dh4cHIkSNJTk5m7ty5d93P7cIfQJs2bfD09OT48eMZ2hcvXsyVK1d4/fXXLeEPoGzZsrz22mvExMTw+++/52pMIiIiIoXJPS0Ft2zZMgYOHEh0dDQ3X0g0GAx4eXnxww8/0KVLlxzt8++//wagXbt2mba1b98egE2bNuW65uDgYC5fvpxp5ZK7HXfMmDFs2rSJvn375vrYIiIiIoVBrgPg+vXr6datG3Z2dvTv359HHnkEb29vzp8/z+bNm5k3bx5PPfUUq1evzvSs3Z2EhoYCEBAQkGlb6dKlcXNzs/TJjjVr1rBt2zaSkpIIDQ1l+fLllCxZki+++CLbx01vu9txk5KSMlz5jIuLAyAlJYWUlBQAjEYjdnZ2pKWlYTKZLH3T21NTUzOEaTs7O4xGY5btIoVN+n/r6eztb5xmbp0NwMHBAZPJRFpamqXNYDBgb2+fZXtWfzd59feU3do1pvtpTFqTXgqX/Px7yolcB8DRo0dTpEgRtm3bxsMPP5xhW9++fXnjjTdo2rQpo0ePzlEAjI2NBW7c8r0dd3d3S5/sWLNmDVOmTLF8rlSpEgsWLKBevXrZPm76ffS7HXfChAmMHTv2tjW4uLgAN+ZEDAwM5MCBA4SHh1v6VKlShapVq7Jz506io6Mt7XXq1MHf35/Nmzdz9epVS3vjxo3x8vK6Yz0i1rBy5coMnzt27EhCQgIbN260tNnb29OpUydiYmIIDg62tBctWpTWrVsTERHBvn37LO2lSpWiSZMmhIaGEhISYmnP67+nNWvWZAgRrVq1okiRIhrTfTwmcECkMMnPvycfH59s15Hrl0BcXV3p06cPM2bMyLLPiy++yIIFC4iPj8/2ftu1a8fatWsJDQ2lUqVKmbb7+vpy7dq1HIVAgGvXrvHff//x0UcfsW7dOmbNmkWfPn0s2ytXrkxoaCgpKSmWX5PpUlJScHR0pFatWuzfvz/LY9zuCmC5cuWIiYmxhMi8/iWsB5ylsPlmsK4AakyFZ0wDp+oKoBQeM4bk7xXA+Pj4bL8EkusrgC4uLpQqVeqOfby8vCxXvrIr/QpcVgEvLi4OT0/PHO0TwM3NjaCgIJYuXUr9+vUZOHAgjz76qGUMNx+3RIkSmY55c5+sODk54eTklKndwcEBB4eMv0Lt7Oyws7PL1PfW8Hm3dpHC5tb/1u/UbjQab3vbIqv2rP5u8urvKSe1Z9WuMRW+MYkUJvn995TtOnL7xbZt27Ju3bo79lm3bh2PPvpojvZ7p+ftoqKiuHbt2m2f08sue3t7WrVqRXx8PLt3787Wce/0fKCIiIjI/SbXAXDy5MlcuHCBvn37EhERkWFbREQEzz33HDExMUyePDlH+23RogVw47m5W61evTpDn9w6d+4ckPHXYkEcV0RERKQwyPUzgK1bt+by5cscOHAAOzs7/Pz8LG8Bh4eHk5aWRq1atTLdrjUYDKxfvz7L/aamplKlShXOnj2b5UTQISEhlC9fHoDIyEhiY2MpU6ZMhlu0u3fvpn79+pn2v3r1arp06YKrqytnzpzB1dUVuDERdIUKFXBwcNBE0CL3QBNBS2Gic6QUJoVpIuhcP1iWPm8e3AhtJ06c4MSJExn63O6FibutH2xvb8/MmTNp3749zZs3z7AU3OnTp5k8ebIl/AGMGDGCuXPnMnv2bMvybQANGjTg4YcfplatWpQtW5b4+HgOHDjAP//8g4ODA7NmzbKEPwBPT0+mT5/Oc889R926denVqxdwYym4ixcvsnDhwhyFPxEREZHCKtcB8OY3T/Jaq1at2LJlC6NHj2bhwoWkpKRQs2ZNJk6caAlmdzN+/Hg2btzIpk2biI6Oxmg04ufnx8CBAxkyZAjVqlXL9J1nn32WkiVLMn78eGbPno3BYKBevXp88MEHtG3bNq+HKSIiImIVhW4t4AeJbgGLLdItYClMdI6UwqQw3QLOs6UkwsPD2bx5c17tTkRERETySZ4FwNmzZ9OqVau82p2IiIiI5BMtJisiIiJiYxQARURERGyMAqCIiIiIjcmzAOjh4YGfn19e7U5ERERE8kmeBcAhQ4Zw8uTJvNqdiIiIiOQT3QIWERERsTHZXgkkfY6/oKAgnJ2dczTnX/PmzXNemYiIiIjki2wHwJYtW2IwGDhy5AiVK1e2fM6OtLS0XBcoIiIiInkr2wFw1KhRGAwGSpYsmeGziIiIiNxfsh0Ax4wZc8fPIiIiInJ/0EsgIiIiIjYm1wHw6tWrnDhxgpSUlAztCxcu5JlnnuHFF19kz54991ygiIiIiOStbN8CvtU777zDvHnzOH/+PA4ODgB8++23vPbaa5jNZgAWLFjAv//+S9WqVfOmWhERERG5Z7m+Arhp0ybatm2Li4uLpe3TTz/F19eXzZs3s2jRIsxmM5999lmeFCoiIiIieSPXVwAjIyPp0KGD5fORI0eIiIhg0qRJNGvWDIBff/01R/MFioiIiEj+y/UVwKSkJBwdHS2fN23ahMFgoF27dpa2ihUrcvbs2XurUERERETyVK4DYNmyZTlw4IDl8/LlyylevDi1atWytF28eBE3N7d7q1BERERE8lSubwE/9thjfP3117z11ls4Ozvz119/0bdv3wx9jh07hp+f3z0XKSIiIiJ5J9cBcMSIEfz55598/vnnAJQpU4aPPvrIsv3ChQts3bqV11577d6rFBEREZE8k+sAWLp0aQ4fPsz69esBaN68Oe7u7pbtMTExfPbZZ7Rv3/7eqxQRERGRPJPrAAhQpEgROnfufNtt1atXp3r16veyexERERHJB1oKTkRERMTG3NMVwLS0NBYtWsS6des4d+4cSUlJmfoYDAbLbWIRERERsb5cB8D4+HjatWvH9u3bMZvNGAwGyxJwgOWzwWDIk0JFREREJG/k+hbwxx9/THBwMGPHjiUmJgaz2cyYMWOIjIxk4cKFVKxYkR49etz2qqCIiIiIWE+uA+Bvv/1Go0aN+OCDDyhevLil3dvbmx49erBx40bWrVuntYBFRERECplcB8Dw8HAaNWr0fzsyGjNc7StbtiydOnVi7ty591ahiIiIiOSpXAdAV1dXjMb/+7qHhweRkZEZ+pQuXZrw8PDcVyciIiIieS7XAdDf3z9DuHv44YfZsGGD5Sqg2Wxm/fr1lClT5t6rFBEREZE8k+sA2KZNGzZu3EhqaioAzz//POHh4TRu3Ji3336bZs2asW/fPrp165ZnxYqIiIjIvcv1NDADBgygRIkSREdHU6ZMGfr378/evXv55ptv2LdvHwDdunVjzJgxeVSqiIiIiOSFXAfAgIAA3n333Qxt06ZNY9SoUZw4cQJ/f39Kly59zwWKiIiISN66p5VAbqdUqVKUKlUqr3crIiIiInlEawGLiIiI2JhcXwGsWLFitvoZDAbCwsJyexgRERERyWO5DoAmk+m26/zGxsZy5coVAMqUKYOjo2OuixMRERGRvJfrAHjq1Kk7bhs2bBjnz59n7dq1uT2EiIiIiOSDfHkGsHz58ixcuJDLly/z/vvv58chRERERCSX8u0lEAcHBx599FEWLVqUX4cQERERkVzI17eAr1+/zqVLl/LzECIiIiKSQ/kWAP/55x9++eUXqlSpkl+HEBEREZFcyPVLIK1bt75te2pqKmfPnrW8JDJq1KjcHkJERERE8kGuA+Dff/9923aDwYCnpyft2rVj2LBhPProo7k9hIiIiIjkg3uaB1BERERE7j/3vBbwhQsXOHv2LCaTCV9fX0qXLp0XdYmIiIhIPsnVSyBJSUlMmjSJgIAAypQpQ/369QkKCsLX15eSJUsydOjQO04ULSIiIiLWk+MAGBERQYMGDRgxYgRhYWGUKVOGoKAggoKCKFOmDJcuXWLq1KnUr1+fdevWWb4XGRmpOQFFRERECoEcBcCUlBQ6duzIoUOHePrppzly5AhnzpwhODiY4OBgzpw5w5EjR3jmmWe4dOkSTzzxBKdOnSIsLIxmzZpx9OjR/BqHiIiIiGRTjp4B/P777zl8+DCjR49m9OjRt+1TpUoVfvrpJypXrszo0aN55plnOHXqFDExMdSrVy9PihYRERGR3MvRFcBFixZRqVKlbM3t98EHHxAQEEBwcDCJiYmsXr2aTp065bpQEREREckbOQqA//33H+3atcNgMNy1r8FgsPTdsWMHLVu2zG2NIiIiIpKHchQAr127hoeHR7b7u7u7Y29vT6VKlXJcmIiIiIjkjxwFQC8vL44fP57t/mFhYXh5eeW4KBERERHJPzkKgI0bN2bVqlVERUXdtW9UVBQrVqygWbNmuS5ORERERPJejgLgyy+/zLVr13jyySeJiYnJst/Fixd58sknuX79OoMGDbrnIkVEREQk7+RoGphWrVoxYMAAZsyYQbVq1Rg0aBCtW7emXLlywI1JotevX8+MGTOIiYlh4MCBevlDREREpJDJ8VrA33zzDe7u7nzxxRdMmDCBCRMmZNhuNpsxGo289dZbmbaJiIiIiPXlOADa2dnx2WefMXDgQObMmUNwcLDlmcDSpUvTpEkTnn/+eQICAvK8WBERERG5dzkOgOkCAgL45JNP8rIWERERESkAOXoJRERERETufwqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYmEIbAHft2kXHjh0pVqwYrq6uNGrUiEWLFmX7+2FhYYwZM4bHH38cX19fDAYD5cuXv+N3DAZDlv/069fv3gYkIiIiUkjYW7uA29m4cSPt27fH2dmZ3r17U7RoUZYsWUKvXr2IiIhg+PDhd93HP//8w9ixY7Gzs6NatWpERUVl69j+/v63DXt16tTJ4ShERERECqdCFwBTU1MZMGAARqORzZs3W4LXqFGjCAoKYuTIkXTv3h1/f/877qd58+YEBwdTu3ZtihQpgrOzc7aOX758ecaMGXOPoxAREREpvArdLeANGzYQFhZGnz59Mlx18/DwYOTIkSQnJzN37ty77qdixYo0atSIIkWK5GO1IiIiIvefQncF8O+//wagXbt2mba1b98egE2bNuXb8a9cucIPP/xATEwMxYsXp2nTptSsWTPfjiciIiJS0ApdAAwNDQUgICAg07bSpUvj5uZm6ZMf9u/fz6BBgzK0dejQgblz5+Ll5ZVvxxUREREpKIUuAMbGxgI3bvnejru7u6VPXhs+fDjdunWjcuXKODo6cujQIcaNG8eqVavo3LkzwcHB2NnZZfn9pKQkkpKSLJ/j4uIASElJISUlBQCj0YidnR1paWmYTCZL3/T21NRUzGazpd3Ozg6j0Zhlu0hhk/7fejp7+xunmdTU1AztDg4OmEwm0tLSLG0GgwF7e/ss27P6u8mrv6fs1q4x3U9jMiBSmOTn31NOFLoAaE2TJ0/O8Llx48YsX76c1q1bs2nTJv744w+eeuqpLL8/YcIExo4dm6l9zZo1uLi4AODn50dgYCAHDhwgPDzc0qdKlSpUrVqVnTt3Eh0dbWmvU6cO/v7+bN68matXr2aoTVckpTBauXJlhs8dO3YkISGBjRs3Wtrs7e3p1KkTMTExBAcHW9qLFi1K69atiYiIYN++fZb2UqVK0aRJE0JDQwkJCbG05/Xf05o1azKEiFatWlGkSBGN6T4eEzggUpjk59+Tj49PtuswmG/+eVUI9OjRg19//ZXdu3dTr169TNuLFi2Kp6dnhkFnh7OzM6VLl+bUqVM5runnn3/m2WefZdiwYUyZMiXLfre7AliuXDliYmJwd3cH8v6X8IAvczwckXz1zWBdAdSYCs+YBk7VFUApPGYMyd8rgPHx8Xh4eBAbG2vJHVkpdFcA05/9Cw0NzRQAo6KiuHbtGkFBQQVaU8mSJQGIj4+/Yz8nJyecnJwytTs4OODgkPFXqJ2d3W1vJ6efyLLbLlLY3Prf+p3ajUbjbW9bZNWe1d9NXv095aT2rNo1psI3JpHCJL//nrJdR66/mU9atGgB3LhteqvVq1dn6FNQduzYAXDXlURERERE7geFLgC2adOGihUrMn/+/Az3wmNjYxk/fjyOjo707dvX0h4ZGcnRo0fv+cWQgwcPZrqtALBt2zYmTpyIg4MDPXr0uKdjiIiIiBQGhe6+or29PTNnzqR9+/Y0b948w1Jwp0+fZvLkyRmuxI0YMYK5c+cye/bsDEu4xcTE8NZbb1k+p6SkEBMTk6HP5MmTLbd3p0yZwooVK2jWrBnlypXDwcGBw4cPs2bNGgwGA19//TUPPfRQfg9fREREJN8VugAIN97o2rJlC6NHj2bhwoWkpKRQs2ZNJk6cSK9evbK1j2vXrmVaMSQ+Pj5D25gxYywBsGvXrly5coX9+/ezdu1akpOTKV26NL1792bIkCEF/tyhiIiISH4pdG8BP0ji4uKy/TZObuktYClsZgyxdgUi/0fnSClM8vv8mJPcUeieARQRERGR/KUAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG1NoA+CuXbvo2LEjxYoVw9XVlUaNGrFo0aIc7SMpKYmPPvqIgIAAnJ2d8fHxYeDAgVy4cCHL7/z8888EBQXh6uqKp6cnnTt3Zs+ePfc6HBEREZFCo1AGwI0bN9K0aVO2bNlCz549efnll4mKiqJXr15MmTIlW/swmUx07dqV0aNHU7JkSYYMGULjxo2ZOXMmjRs3Jjo6OtN3PvnkE5599lkuXLjAyy+/TI8ePdi8eTNNmjRh69ateT1MEREREaswmM1ms7WLuFlqaipVq1blzJkzbN++nTp16gAQGxtLUFAQp06d4tixY/j7+99xP7Nnz6Z///48/fTT/PzzzxgMBgC+++47XnnlFQYOHMj3339v6R8aGkr16tWpWLEiO3fuxMPDA4B9+/bRqFEjKlasyKFDhzAas5+Z4+Li8PDwIDY2Fnd39xz+L5E9A77Ml92K5NqMIdauQOT/6BwphUl+nx9zkjsK3RXADRs2EBYWRp8+fSzhD8DDw4ORI0eSnJzM3Llz77qfGTNmADBhwgRL+AMYNGgQFStW5OeffyYhIcHSPnv2bFJTU3n//fct4Q+gTp06PP300xw5coQtW7bkwQhFRERErKvQBcC///4bgHbt2mXa1r59ewA2bdp0x30kJiayY8cOqlSpkulKocFg4NFHHyU+Pp7du3fn6XFFRERE7geFLgCGhoYCEBAQkGlb6dKlcXNzs/TJSlhYGCaT6bb7uHnfN+8nNDQUNzc3Spcuna3+IiIiIvcre2sXcKvY2FiADLdhb+bu7m7pcy/7uLlf+r97eXllu//tJCUlkZSUlKmOS5cukZKSAoDRaMTOzo60tDRMJpOlb3p7amoqNz+WaWdnh9FozLI9OfGOJYkUuIsXUzJ8tre/cZpJTU3N0O7g4IDJZCItLc3SZjAYsLe3z7I9q7+bvPp7Sv87vVvtGtP9M6bkRAMihUVcHPn69xQfHw9Adl7vKHQB8H42YcIExo4dm6m9QoUKVqhGxDr+N8LaFYiIFE4FdX68evVqlhfB0hW6AJhecFZX2+Li4vD09LznfdzcL/3fc9L/dkaMGMGwYcMsn00mE5cuXaJEiRIZXkSRwicuLo5y5coRERGRb29si4jcj3R+vH+YzWauXr2Kj4/PXfsWugB48/N29erVy7AtKiqKa9euERQUdMd9VKxYEaPRmOUze7d7zjAgIIDg4GCioqIyPQd4p+cSb+bk5ISTk1OGtmLFit3xO1K4uLu76wQnInIbOj/eH+52sSpdoXsJpEWLFgCsWbMm07bVq1dn6JOVIkWKEBQUREhICKdPn86wzWw2s3btWlxdXalfv36eHldERETkflDoAmCbNm2oWLEi8+fPZ9++fZb22NhYxo8fj6OjI3379rW0R0ZGcvTo0Uy3bwcOHAjcuC1788OQ33//PSdOnOCZZ56hSJEilvYXXngBe3t7Pvnkkwz72rdvH7/88gvVqlWjWbNmeT1cERERkQJX6G4B29vbM3PmTNq3b0/z5s3p3bs3RYsWZcmSJZw+fZrJkydTvnx5S/8RI0Ywd+5cZs+eTb9+/Sztzz//PAsXLuSXX37h5MmTtGjRguPHj/Pbb79RoUIFPv744wzHrVy5MmPGjOGDDz6gdu3adOvWjatXr7JgwQLgxsTSOVkFRO4vTk5OjB49OtMtfBERW6fz44Op0C0Fl27nzp2MHj2abdu2kZKSQs2aNRk2bBi9evXK0K9fv363DYBwY1qWTz/9lJ9++omIiAiKFy9O586d+fjjj/H29r7tcX/++We+/PJLDh8+jKOjI02bNmXcuHHUrVs3v4YqIiIiUqAKbQAUERERkfyhe5oiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEXuQfpL9GazGb1QLyIi9wsFQJFcSA97BoPB8v+m/7uIiNxw8w/jtLQ0K1Yit9I8gCK5tHr1ak6dOkVYWBjFixenefPmVKpUiZIlS1pWjTGbzQqGImLTEhMTcXZ2tnYZcotCtxScSGEXHh7OF198wVdffZXptq+/vz+dO3emT58+NG7cWOFPRGzWyZMnWbRoEYcOHSI6OppatWpRr149qlatir+/P8WKFQPAZDJpqVUr0BVAkRwaPHgws2bNomvXrjz77LN4eXmxY8cO9uzZw65du/jvv/8A6NSpEx9++CFBQUE6wYmITfnll18YN24cR48epUiRIiQkJFi2lS1blrZt2/L000/z6KOPWrFK26YAKJIDSUlJFC9enF69ejFr1qxM248ePcrGjRuZP38+W7dupVq1asydO5f69etboVoRkYKXlJRElSpVcHJy4v3336dTp06cO3eOQ4cOcejQIbZs2cLu3btJTEykW7dujBkzhurVq+uHcgHTLWCRHFi7di1paWk0b94cyPj2r9FopGrVqlStWpV+/foxe/Zshg0bxsCBA1m+fDk+Pj7WLF1EpED88ssvREZGMnv2bPr06QNAiRIlqFmzJiaTiRMnTrB161bmzZvHr7/+yunTp1myZAlly5a1cuW2RVFbJAfs7Owwm81ER0cDN95qMxgMll+tJpMJk8lEkSJFePXVVxk2bBj79u3jwIED1ixbRKTAbN26FS8vLxo0aADcOC+m/1g2Go1UqlSJ559/nl9//ZWPPvqIPXv28Oqrr1q5atujACiSA40aNcLR0ZFffvmF0NBQ7O3tM7zokR4G06c76NmzJy4uLmzfvt1aJYuIFCh/f3+io6M5c+YMkHnarPQw6OHhwQcffECnTp3YtWsX4eHhVqvZFikAimST2WzG09OTqVOnsm/fPlq2bMl3333HyZMnLYEv/QSX/vn06dOkpqbq1oaI2IzGjRuTnJzMpEmTiI6Oxs7OLkP4gxvnyvTzZNOmTbl27RrHjx+3Ws22SAFQJJvST2Ddu3dn5MiRXLp0ibfeeovXXnuN77//nuDgYMsvXkdHR06dOsWsWbOws7OjR48e1ixdRKRAmEwm2rRpw/vvv8/q1atp2LAh06dP59ixY5Z5UdPPpXZ2dgBERUWRkpKil+UKmN4CFsmlzZs3891337F27VouXbpE2bJlqVy5Mo6Ojri5ubFr1y6ioqIYOnQon3zyibXLFREpMOfOnWPSpElMnz4do9FI48aNad26NXXr1qVatWpUqlSJxMREfvrpJ95//30aN27MH3/8Ye2ybYoCoEg23G5FD7PZTEREBHv37mXHjh38+++/HDlyhDNnzuDq6oqfnx/vv/8+TzzxBC4uLlaqXETEerZv384PP/zAX3/9RVRUFEWLFqV48eI4ODjg5OTE4cOHqV+/PtOnTycoKMja5doUBUCRbLp+/Tr29vacPn2aIkWKZHiuLyEhgQsXLuDg4EBSUhKXLl2iXr16VqxWRKRg3e6HsslkIiYmhtDQUP7991+2b9/Orl27uHjxIjVq1CAgIIAJEybg7e1tpaptlwKgyF0kJSWxadMmpk+fzvbt23Fzc8NoNFK+fHkee+wxevfuja+vr7XLFBGxKpPJxLlz57h06RJRUVFUr149ww/lpKQkAJycnIiKisLNzQ03NzdA66ZbgwKgyF18+eWXjB07lqSkJOrUqWNZ+u38+fPAjQmge/TowSuvvEKzZs0sJzGdzETEVhw/fpxvvvmGuXPnEh8fT3JyMgaDgZo1a9KrVy+eeeYZ/Pz8MnxHoc+6FABF7iAxMREfHx9q1KjBokWLcHd3x9XVFYAdO3awePFiy6z3Pj4+TJgwgeeee87KVYuIFJzk5GQ6derEhg0baNKkCU2bNiUmJoZdu3YREhJCcnIyAN26dWP48OE0atTIyhULKACK3NG8efMYOHAg8+bN46mnngIy/2pNS0tj1qxZTJ48mdDQUGbOnEn//v2tVbKISIH68ccfefXVVxkzZgwjRozIsG3nzp2sWLGCJUuW8N9//+Hr68v06dPp2rWrlaqVdJoHUOQOQkJCMBqNlnV8U1JSLOHPZDKRlpaGnZ0dAwYM4Ntvv7VMFH358mVrli0iUmAWLVpEnTp16N27NwCpqamWSZ6DgoIYO3YsO3bsYNq0aaSlpdG/f3/++usva5YsKACK3FGTJk24fv06hw8fBsDBwcGyzWg0WiYyNZvNtG7dmlGjRnHkyBH27dtnjXJFRApUYmIiKSkpJCQkULp0aeDG88/p58b09dFdXV0ZPHgw06ZN4/Lly8ybNw/4v5VBpOApAIrcQd26dalevTqvvvoqX3/9NRcvXrxtv9TUVAA8PDwwmUzExsYWZJkiIlbh7OxM3bp1OXTokGXN8/TwBzd+KBuNRsv6v926daNjx47s3buXU6dO6SUQK1IAFLkDb29vxo4dS9GiRXnvvfd499132bZtm+X2Rrr0+f/279+P0WikdevWVqpYRKRgPffcc3h4eNCrVy++//57oqKiMvUxmUwYDAaSk5MpVaoUMTExeHl5WaFaSaeXQESyITg4mI8//phVq1YB0KhRIx5//HHq1q1rmdH+zz//5IsvvqB79+6W2xsiIrZg6tSpjBw5EqPRyJNPPknv3r0JDAykWLFiFClSxNJv+/btDBgwAB8fH1avXm3FikUBUOQOUlNTLbcwjh07xooVK1i2bBm7du3i+vXr2NnZ4ezsTHx8PADPPvssH374IQEBAVauXESkYAUHBzN+/HjWrl1Lamoq9erV45FHHqFChQo4OzsDMGXKFM6dO8fChQtp3769lSu2bQqAIjl0/fp1tm3bxt69e4mJiSEuLo60tDS6d+9O8+bNLSc6ERFbkJKSgoODA2azmdDQUDZu3Mj69evZtWsXUVFRlhVAADw9Pfnmm2/o1auXFSsWUAAUua1Lly6xe/dugoOD8fT0xMnJCV9fX+rVq0eZMmUs/ZKSknBycrJipSIi1nf9+nVcXFwsn2NjYzl8+DAREREkJSVx9uxZKlWqRJMmTbR0ZiGhAChyiy1btvDuu+8SHBwM3JjSwGw24+LiQvXq1Wnbti0dO3YkKCgIR0dHkpOTcXR0tHLVIiIFKzg4mN9++42YmBgcHR3x9PSkbt26tGnThhIlSli7PLkLBUCRmyQmJlKnTh2io6MZO3YsXl5e2NnZERUVxbp161i7di3Xr18nICCAV199lcGDB2Nvb2/tskVECkxqaiqffvopo0aNAqBYsWIkJSWRkJAAgL+/P507d+bpp5+mUaNGGI1Gy21iKTwUAEVuMnPmTN58802mT5/OCy+8kGn7yZMnWbx4MbNnzyYkJIQ+ffowbdo0PD09rVCtiEjB+/nnn3nhhRfo2LEjo0aNwmQyUaRIEY4cOcKCBQtYunQpJpMJf39/hgwZwptvvmntkuU2FABFbtKrVy/27t3LihUrCAgIuO2vVpPJxL///su4ceNYvnw5X375JW+88YaVKhYRKVhNmjTB3t6eH374gapVq2baHhcXx6xZs/j66685deoUb775JuPGjcswHYxYnyaCFvn/UlNTKVmyJOfOnbMsaXS7WxZGo5EGDRowZ84c6tWrx7Rp07h+/XpBlysiUuAuXbrEyZMn8ff3p3LlypYVPuD/1kd3d3dnyJAhLFy4kIYNG/L555+zadMmK1cut1IAFOHGepT29vY0bdqU69evM2zYMC5fvgz830ntZqmpqRQvXpzmzZsTHR1NSEiINcoWESlQZrOZMmXKcOLECYxGIwaDwbKc283ro8ONpTTnzZuHg4OD5bawFB4KgCJgOYG1aNGC5s2b8+OPPzJixAhOnTqV4aSWlpZmCYtJSUkYDAZMJpMmfhYRm1CiRAlat25NcHAwY8aM4dKlS0DmH8rp/+7r60vt2rXZt2+fZc10KRwUAEVu4uvry4IFC+jatSs//PADFStWpFevXixbtozk5GTs7Owstzs2btzIwoULad68OW5ublauXESkYPTv3x9/f38mTpzIhx9+yPHjxzNd/Uv/99DQUFJSUvD29tZ0WYWMXgIRuUlaWhp2dnacPHmSOXPm8O233xITEwNA0aJFadq0KQEBAezfv5+tW7dSvnx55syZQ9OmTa1cuYhIwQkNDWXo0KGsXLkSgE6dOtG/f39atGiBo6MjCQkJeHp68vLLLzNnzhyWLFlC165drVy13EwBUOT/M5vNllvB6VJSUli0aBE///wzu3btIj4+Hnt7e1JSUujSpQtvv/02DRo0sFLFIiIFLzU1FXt7e0JCQpg/fz7z588nLCwMABcXFwIDAzGZTPz333/ExsbSv39/Zs6caeWq5VYKgCL/n8lkIiIiAn9/f65cuYLRaMTd3d2y/dKlSxw6dAhPT0/LP66urrcNjiIitiI2NpaVK1eyatUqQkJCiI+P59KlSzz00EO88MIL9OzZU4/JFEIKgGLzEhIS+Pzzz1m9ejUHDx7E0dGR2rVrU6dOHerVq0fNmjWpWLEizs7O1i5VRKTA3fwj9/Dhw5hMJlxdXUlISMDX15dixYpZ+sbExHDlyhUqVKhAYmIirq6uVqpa7kYBUGxacnIyffr04bfffqN69eq4urpiMpm4cuUK4eHh2Nvb06BBA5555hmeffZZTWQqIjbHbDazZ88e3njjDQ4cOEB8fDzFihXD39+fhx9+mMaNG9O4cWMefvhhLfd2H1EAFJv2448/MnjwYAYPHszYsWNxc3MjKiqKs2fPcuzYMTZs2MCaNWuIiIigVatWTJgwgaCgIN32FRGbsWLFCgYOHEh8fDyPP/44RqPR8ozfwYMHSUtLo27duvTt25f+/fvj4uJi7ZIlGxQAxaa1aNGClJQUfv75ZypUqGB5CzjdpUuX2Lt3L7Nnz2b+/Pk0bNiQlStXau1fEbEZzZo148qVK3z11Ve0bt0agCtXrnD16lVCQ0NZvnw5S5cu5dSpU3Tu3JnPPvuMKlWqWLlquRsFQLFZcXFxNG/eHA8Pj0zLFN16hc9kMjF58mTee+89Xn/9daZOnVrQ5YqIFLjIyEgqVKjA22+/zUcffQSQ6e7H9evX2bdvH9OnT2fBggU88cQTLF68OMOPaSl8NBG02CSz2YybmxvVqlXj4MGDHDp0yNJuMpksJ7j0dS6NRiPDhg2jdu3a/Pvvv8TGxlqzfBGRAnH8+HEcHR2xs7PL8rEXFxcXmjRpwg8//MCQIUNYunQpy5cvL+BKJacUAMUmGQwGjEaj5dbGW2+9xYkTJyztQIZFzuHGOpcBAQFERkbi5ORkrdJFRApMtWrV8PHxYenSpURERFiWv7x1XV+TyYSbmxuDBw/GxcWFLVu2WKliyS4FQLFpgwcP5p133mHNmjXUrVuXd955h23btpGYmGgJgzdPf3DkyBGqVKmiKWFExCaULFmSxx57jAMHDjBy5EjOnTuH0Wi0/FC+dQ3gxMREvLy8uHz5srVKlmyyt3YBItaS/pzf8OHDKVKkCJMmTWLy5Mn88ssvNGrUiAYNGtCwYUOqVKnCjh07+Pzzzzl+/DiTJk2ydukiIgVm/PjxJCQk8MMPP7BkyRIGDBhA9+7dadKkSabn/NauXUt4eDidOnWyUrWSXXoJRGzWrS96nD17llmzZvHbb7+xf//+TP2LFSvGW2+9xciRIwuyTBERqzGZTBiNRs6cOcM333zDF198QVJSEs7OztSrV4/GjRvTsmVLEhMT2bx5MzNmzKB69ers2rXL2qXLXSgAitzEZDIRHR1NSEgIO3bsYOfOnbi6ulK5cmUaN25Mq1atrF2iiIjVXLp0iVmzZjF//nz27duXaXvXrl156623aNq0acEXJzmiACg2af/+/YSGhnLs2DHLyyABAQF4eXlletMtKSlJL32IiE1Jv0OSfgXwdo4fP86GDRsIDw/H398fLy8vHn30UU0EfZ9QABSbkpqayg8//MBHH33EhQsXMmwrXbo07du35+mnn6Zdu3YZtt3pJCgi8qBJS0tj7ty5/Pfffxw/fpyHHnqI+vXrU7lyZfz8/ChevPht5/nTKkn3DwVAsSkLFy5kwIABBAQE8NJLL1G7dm327t3Lvn37+Pfffzlw4AAmk4nGjRszatQoHn30UQU/EbEpe/bs4aOPPmLZsmU4OTmRlJRk2ebl5UXLli3p0aMHXbp0wdHREVDwux8pAIpNadiwISaTifnz5xMQEJBh28mTJ9m8eTO//vorK1aswMPDgxkzZtC9e3crVSsiUvC6dOnC1q1befnll+nXrx9paWkcOHCA//77j+DgYHbu3ElcXBytWrVi7NixNGvWTAHwPqQAKDbjwoULVK1alb59+/Lll18CN25z3Dz5c3rb0qVLef311zGZTCxZskQPNIuITYiIiMDf35/33nuP8ePHZ9oeHh7Ozp07Wbx4MYsXL8bLy4tFixbRvHlzK1Qr90L3tsRmxMbG4ubmxtmzZ4EbQe/mCU3Tl4Gzs7OjW7dufP7551y4cIG///7bsl1E5EG2fv16nJycqFevHnDj+eebV0Xy8/Oje/fuzJ49m1mzZpGUlMQrr7zC+fPnrVm25IICoNiMgIAA/Pz8WLt2LRs3brzt2pZGo9FyouvRowcVK1Zk586dpKam6vaGiDzwSpQogdls5uTJk8D/BcBb10d3cXGhX79+DB06lCNHjnD48GFrli25oAAoNmXSpEkYjUY6dOjAJ598wtGjR0lJSQGwnODSP4eEhGBnZ4ezszP29lo0R0QefA0bNqRIkSLMmjWLw4cPY29vn+EuCdw4V6ampgLQokULXF1dNfHzfUgBUGxKUFAQH3/8MW5ubowdO5ZXXnmFadOmsXXrViIiIkhLS8PR0ZGUlBR++uknwsLC6NOnj7XLFhHJdyaTCS8vL6ZNm0ZISAiNGjXi448/5uDBg5a7ILfeCTl58iTx8fHUrFnTSlVLbuklELFJR44cYerUqSxfvpxz585RunRpatSogYeHB66urpw+fZrNmzfTsWNHli9fbu1yRUQKzNWrV/n666/55JNPiI+Pp379+rRt25YGDRpQvXp1qlSpAsCWLVsYMmQIkZGRlmer5f6hACg25eZnWaKioti3bx/bt29nx44dHDlyhPDwcAB8fX3p2bMn77zzDt7e3tYsWUTEKkJCQvj222/5448/OH36NEWLFsXb2xsnJyc8PDz4999/KV68OKNGjWLQoEHWLldySAFQHmjpgS8lJQWj0Uh0dDTJycn4+flZ+iQnJxMZGWm5xREeHk79+vVxc3OzYuUiIgUnq9WOLl26RFhYGLt377bMAXj69GkqVqyIr68vY8eOJSgo6LargkjhpgAoD7yjR4/y7bffsnz5cpycnDCbzZQpU4bWrVvTu3dvKlWqZO0SRUSsLiYmhvj4eE6dOoWfnx8VKlSwbEtOTiY5ORk3NzcuXLhAcnIyZcuWtWK1cq8UAOWBtnHjRt58800OHTrEQw89ROXKlTlw4ECG51U6dOjAq6++yqOPPoqTk5PW/RURm3Lx4kWWLFnC559/zpkzZ0hLSyMtLY2HHnqI7t2706dPH6pVq2btMiWPKQDKA61FixaEhYUxc+ZMWrZsiZ2dHQ4ODhw8eJDFixezYMECjh8/jouLC++++y4ffvihtUsWESlQQ4cO5dtvv8XX15dHHnkER0dHduzYQVhYGNevXwegVatWvPvuu7Rt29YyX6rmRr2/KQDKA+vMmTNUqFCBMWPGMHLkSAwGw21PWkuWLGHSpEns2rWLd955h7Fjx+Lk5GSlqkVECs7p06cJCAjgqaeeYv78+QCWOyD79+9n1apVLF26lJ07d+Ls7Mynn37KG2+8Yc2SJY/oPpc8sPbu3YvBYKBYsWIYDAaSk5Mt4c9kMpGWlgZAt27d+N///kfdunWZNm0a//33nzXLFhEpMAsWLMDNzY2BAwdagl/6JM+1a9fmvffe459//uGXX36hUqVKDBkyhK+//tqaJUseUQCUB9bDDz8MwIEDBwBwdHS0bDMajZa31sxmM1WqVOHbb78lISGBLVu2FHyxIiJWcP78eUwmE8WLFwdurJGevvKRyWTCZDLh4OBAr169mDt3LmXKlOG7777j2rVr1ixb8oACoDywfH196datGzNmzGDkyJFERETctl/6r12j0UixYsU4ffp0QZYpImI1zZs3Jy4uju3btwPg4OBg2WY0GjNcFQwMDGTw4MGcOnWKnTt3WqVeyTsKgPLAcnR05O233+ahhx5i0qRJDBkyhNWrV5OUlJShX/oJb+/evcTFxdGiRQtrlCsiUuCaNm1KnTp1GDx4MGPHjuXkyZPc+mrAzZ+LFi1KQkJChjsqcn/SSyDywDtx4gRjx45l4cKFJCcnU6dOHZ544gkaN26Mq6srjo6OhIWFMWTIEDw8PDh69Ki1SxYRKTB//vknAwYMIDo6mq5du/L000/TqFEjSpYsibOzs+XZ6ejoaN544w1Wr17NpUuXrFy13CsFQHlgpb/o4eDgwJkzZyxvs23dupW4uDiMRiMeHh5cvnwZuPHA84QJE+jQoYOVKxcRKVhhYWGMGzeO33//natXr1KzZk1atmxJ9erVcXV1xcXFhXnz5rFixQqGDx/O+PHjrV2y3CMFQLEpKSkplrV/z549y9WrV7l06RKdO3emffv2+Pr6WrtEEZECk5qaip2dnWUZzE2bNrF27VqCg4OJiIggOTk5Q/9Ro0bx2muvUbJkSStVLHlFAVAeOKmpqYSEhLBmzRpcXV1xcHCgRIkS1KlTJ8MawElJSZrvT0RsXnJycoZn+q5fv87BgwcJCwsjPj6eyMhIXF1d6dChAzVq1LBipZKXFADlgXLy5EmmTJnCN998k6G9SJEiBAQE0LJlSzp27EiTJk1wc3PL8OtXRMRWnDhxgpUrV3L48GEcHR1xcXGhRo0atGrVSndCbIQCoDxQevTowdKlSxkwYAANGzbE3t6e2NhYNm/ezJo1a7hy5QplypThhRde4I033sDLy8vaJYuIFKiFCxfyzjvvEBERgcFgwMXFhfj4eABKly7NY489Rq9evWjZsiWOjo6kpKRkmB5GHgwKgPLAOHXqFJUqVWLo0KFMmjQp01W9c+fOsWzZMmbNmsXu3btp1aoV33//PZUqVbJSxSIiBSsiIoK6devi6enJ1KlTcXV1pWjRopw+fZrffvuNJUuWkJCQgKenJ4MGDeLdd9/Fw8PD2mVLPtA8gPLAWLFiBY6OjrRq1cqy9NvNfHx8ePnll5k3bx6vvPIKGzduZMKECZYl4UREHnQzZszAaDTyxRdf8Nhjj9G8eXMCAwN54okn+N///seVK1eYNWsW/v7+TJw4kRdffJHo6Ghrly35QAFQHhgODg4kJibi4uJi+Xw7lStXZsqUKbz00kvMnj2bsLCwgixTRMRqtm3bRpkyZQgMDAT+byWkm6fN6tevH7/99hvPPPMMv/32Gz/99JM1S5Z8ogAoD4xGjRpRpEgRRo0axfHjxzEYDJjN5kxX+FJSUnB2dqZdu3YYjUaCg4OtVLGISMFJSUmhYsWKhIWFWdb+TV/39+b10QHKly/Pt99+S+3atfnf//5HXFycVWqW/KMAKA+MgIAAnn32WbZs2cK7777Lvn37MBgMlpOayWTCbDZbrgzGx8djMBj0xpuI2AQHBweaN29OfHw8AwcOtKx7fusPZbPZjMlkwtXVlYYNG3LmzBmioqKsVbbkEwVAeWAUKVKE6dOn8/rrr/P7779Tt25dOnbsyIIFC7h69SpGo9HyYsj58+eZPXs2xYsXp23btlauXESkYHTo0IE2bdowb9483nnnHf79998MP5QBDAYDRqORK1eukJSUhIODA5UrV7Zi1ZIf9BawPDBMJhNGo5ELFy7wyy+/8NVXX3Hy5EkAXFxcaNKkCfXr1ycsLIwtW7YQGxvLuHHjGDp0qJUrFxEpOFevXmXo0KHMmjULgBYtWvDSSy/RoUMH3NzcuH79Op6ennz33Xe8++67PPPMM5nmVpX7nwKgPBDMZvNtJ3P+448/mDNnDlu2bOHy5cs4OTmRkJBAvXr1ePvtt+ncubPlpRERkQddamoq9vb2nDlzhsWLFzN37lwOHDgA3HgeMCgoCE9PT44ePUpYWBhNmzZlzpw5PPTQQ1auXPKaAqA8MM6ePYuvry8JCQmkpKTg7u5u2Xbt2jX27NkDgK+vL25ubnh7e1urVBGRQiEpKYm//vqLP//8k/379xMXF8fVq1dxdHTkmWee4ZVXXqFs2bLWLlPygQKg3NfMZjPLly/nxx9/5ODBg1y7do1atWpRq1YtAgMDqVmzJpUqVcLV1dXapYqIWNWFCxeIjo6mRIkSxMbGUrJkSUqUKGHZfvnyZc6dO2cJfO7u7lom8wGmACj3tVGjRjF58mRcXFwoV64cKSkpJCcnExERgdlspnbt2nTv3p3nnnuO0qVLW7tcEZECFxkZyfvvv8/atWs5e/YsRYsWpUKFClStWpWgoCCaNGlCrVq1LI/DZPVIjTxYFADlvnXq1Clq1KhBy5YtmTJlClWrViUmJoaIiAjCwsLYvHkzq1evJjQ0lNq1azN+/Hgee+wxy8siIiIPuqioKJ588kl27NhhecnDaDRy+vRpDhw4QEJCAtWrV6dnz5689NJL+Pj4WLtkKSAKgHLfGjduHF9++SWLFi2iTZs2loeb08XFxXH48GEWLVrE1KlT8fb2ZtWqVdSpU8d6RYuIFKDRo0czdepUxo4dy5tvvgnAlStXuHbtGidPnmTNmjX89ttvHD16lIYNG/LZZ5/RtGlTXQW0AQqAct96/vnnWbt2LXv37sXb29tywrrdiWvhwoUMGjSIatWqaeUPEbEZNWrUoGLFisyaNYtSpUplOj8mJSUREhLC3Llz+eKLL6hSpQqbNm3Cy8vLilVLQdB9MLlv1apVi6ioKP755x/gxuSlJpMpw8kt/fdNr169eOqppzh+/DghISFWqVdEpCCdP38es9lMUlISpUqVAsj049jJyYlatWoxceJEpk6dSkhICJ9//rk1ypUCpgAo962goCBcXV358MMP2b17N4Dl2b70pYzSQyHcWCouISFBa1qKyAPPbDZTqlQpatSowY4dO9i5c6el/db10eHGHICvv/46Dz/8MLt27eLatWsFXbIUMAVAuS+ZzWYeeeQRvvjiC0JDQwkKCmLQoEGsX7+eq1evWpYyghuhMCEhgYMHD+Ls7EyDBg2sXL2ISP5KPwe2a9eOq1ev8tZbb3H48OFM66OnpaVZ7pTExcVRrlw5Lly4gJubmzXLlwJgf/cuIoVP+m2Mp59+mtTUVEaPHs2MGTNYunQpjRs3pmHDhgQFBVG3bl1CQ0OZNWsWS5Ys4fXXX7dy5SIiBWfAgAFcunSJkSNHUrNmTfr27UufPn1o3rw5zs7OwP89KrNr1y72799Px44drVmyFBC9BCL3pVsfZI6Pj2fmzJksXLiQXbt2WW5xGAwG7O3tSUlJoV+/fowbNw5fX19rlS0iUmDSz5NXrlxh1qxZTJw4kejoaOzs7KhXrx5NmzalVatWeHh4sGvXLqZPn87Vq1fZsGEDNWvWtHb5ks8UAOWBEhMTw7Fjx9i+fTv//PMPaWlpVK5cmWrVqvHiiy9auzwRkQJz6w/lxMRE5s6dy//+97/bzoZQvXp1RowYwTPPPFOQZYqVKADKfefChQscPHiQY8eOce3aNYKCgqhatSolS5a0PNuSLikpCScnJ8tnzW0lIgLh4eGsW7eOQ4cOUbp0aby8vGjWrBmVKlWydmlSQBQA5b6yatUqPv7440y/XosXL06bNm3o1asXXbp0wcHBwbJNK3+IiK3566+/OHToEPv27cPb25v69etTqVIlypUrR4kSJTKcI8U2KQDKfSMiIoKWLVsSHx9Pv379aNWqFSdOnGDv3r3s37+fAwcOkJSURPXq1Rk5ciTdu3fH0dFRV/1ExGZcuXKFCRMm8Nlnn2FnZ5dhypfixYvTtGlTnnzySR5//HGKFy9u2abzpO3RW8By3/j++++5fPkyM2fO5Kmnnsqw7cyZM2zbto1ly5Yxf/58nn32Wc6cOcM777yjk5qI2IwZM2Ywffp0nnjiCd544w18fHzYu3cvISEh7Nq1i+DgYP78808CAwP58MMPeeKJJ4DME0TLg09XAOW+0ahRI4oUKcLixYspWbIkqampGea0Srdx40aGDx/Of//9xzfffEP//v2tVLGISMEqX748Dz/8MHPnzqVEiRIZtp07d469e/eybNkyZs2aRVpaGj/88AMvvfSSlaoVa9KDUXJfuHbtGkWLFiUqKgoXFxfgxgTP6eEvfeUPgFatWvHjjz/i4uLCH3/8YdkuIvIgO3r0KBcvXqR27dqW8GcymSznRh8fHzp16sS0adP4448/qFChAu+++67WR7dRCoByX3Bzc6NevXqEhISwYMECgEwvdqR/NplMBAYG0rx5c44ePcrp06d1e0NEHnhms5lixYoRFhYGQGpqKpBxiUyz2YyjoyMdO3bk888/5/Lly5b11MW2KADKfSN9ncqXXnqJN954gz179pCYmAj83/MrqampGI1G4uLicHR0JDExEX9/f2uWLSJSIKpVq4avry8rV65k1apV2NvbZ/qhfPP66I888gjly5dn165d1ihXrEwBUO4bvr6+fPTRR5QvX57p06czaNAgJk+ezN9//83p06dJTEzE3v7Ge01//vknf//9N4899piVqxYRyX/pj7l89dVXuLu706lTJ4YOHcrOnTsz/VBOSUkBICQkhKSkJHx8fKxTtFiVXgKRQu/W6QkuXbrEhAkTWLRoEREREZQqVYqHH34YHx8fXFxcSEhIYNGiRVSoUIGlS5dSpUoVK1YvIlJw0tLSmDdvHiNGjCAqKorq1avTrl07mjRpQvXq1alatSpGo5GzZ8/y9ttvs3jxYnbs2EHdunWtXboUMAVAuS+kh8AzZ87g4+OD0Wjk0KFDLF++nL///psjR44QEREBgKenJ3Xq1OGrr76iRo0aVq5cRKTgRUdHM336dBYtWsSxY8dwcXHB19cXNzc3ihcvztGjR4mOjuaFF17gm2++sXa5YgUKgFKopaamsnXrVmbNmsWxY8cwGAy4uLjQoEEDevbsSWBgIGazmYiICBISEjhx4gRVq1alXLly2Nvba3JTEbEp6TMi2NnZkZCQQGhoKLt27WLr1q3s2LGDo0ePUqpUKcqVK8dLL73Es88+i6urq7XLFitQAJRCbfLkyYwbN46rV69SqVIl7OzsCAkJsWyvXr06r776Kt27d8fLy8uKlYqIFE4mk4nExEQcHR2JjY0lKipKd0dEAVAKr5MnT1KzZk3q1q3L3LlzcXR0xNvbm6ioKP78808WL17M33//DdyY+2/ixInUr1/fukWLiBSghIQEwsPD8fPzo0iRIhm2mUwmDAaD5S7IrXdEtE66bVMAlEJr1KhRfP/998yfP582bdoAmU9gBw8eZPLkySxatAh/f39+/vln6tWrZ62SRUQK1KeffsqSJUt46qmnaNSoEVWqVMHb2zvDCknp/2c+/dwZHR2Np6enZdYEsU0KgFJodevWjX379rFx40b8/PxITU21PNeX/oxLuqlTpzJ06FCef/55Zs+ebcWqRUQKTtmyZTl37hx2dnZ4eHjQpEkT2rVrR8OGDalYsWKm5eDi4+MZM2YMFy9eZObMmboCaMMU/6XQCgwM5Pfff+fatWsAll+rN6//m35F8M033+Sff/5hw4YNnDhxgooVK1qtbhGRgnDs2DFiY2Np3Lgxffr0Ye3atQQHB7N8+XL8/Pxo2bIlbdu2JTAwEF9fX4oVK8ahQ4eYMWMGLVu2VPizcQqAUmi1atUKgGeeeYYpU6bQrFkzHB0dM/VLS0vDzs6OKlWqsGrVKktgFBF5kB07dozExETatWvH4MGD6dy5MyEhIQQHB7NhwwaWLFnCzz//TPXq1WndujUdOnRg/fr1xMXFMWDAAGuXL1amW8BSaKWlpfHuu+/y+eefU7VqVQYPHkz37t3x9vbO1Pfy5csMGTKEVatWceHCBStUKyJSsH799Vd69uzJggUL6Nmzp6U9JSWF06dPs3//fv755x/LXKkODg6YzWacnJy4dOmSFSuXwkABUAq977//ns8++4wTJ07g4+PDk08+yWOPPUa5cuWws7OjWLFiTJs2jS+//JJXX32VKVOmWLtkEZF8ZzabOXr0KM7OzlSoUOG2857Gx8dz7NgxQkJCmD17NmvXruW1117jq6++slLVUlgoAEqhZzabOX78ODNmzGDBggWcOXMGAC8vLxwcHIiMjMRkMvH0008zceJEypYta+WKRUSs63Zh8I033mD69On8+++/BAYGWqkyKSwUAOW+Eh8fz86dO1m2bBnnzp3jwoULuLu707NnT7p164azs7O1SxQRKTTS5/o7deoUXbt25fLly4SHh1u7LCkE9BKI3FdcXV1p1aoVrVq1IiUlBQcHB2uXJCJSaKW/6Xv27FlSUlJ49dVXrVyRFBa6AigiIvKAM5vNnDlzhuLFi2vtXwEUAEVERERsjmaBFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMf8PHaurYWWri3wAAAAASUVORK5CYII=" }, - "execution_count": 6, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -300,8 +534,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:58.093487Z", - "start_time": "2023-11-09T23:56:51.061766Z" + "end_time": "2023-11-10T01:53:08.520972Z", + "start_time": "2023-11-10T01:53:04.549457Z" } }, "id": "352129ef4f8f6cff" @@ -320,12 +554,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 46, "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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" 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" }, "metadata": {}, "output_type": "display_data" @@ -373,8 +607,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:58.267794Z", - "start_time": "2023-11-09T23:56:58.102515Z" + "end_time": "2023-11-10T01:53:08.594859Z", + "start_time": "2023-11-10T01:53:08.521355Z" } }, "id": "44baa6f9eaf8b320" @@ -391,25 +625,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 13, 13, 14]\n" - ] - }, - { - "data": { - "text/plain": "
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- }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], + "execution_count": 47, + "outputs": [], "source": [ "# Initialize register with A=0, B=1, C=2, ...\n", "qr = [QuantumRegister(1, name=str(i)) for i in range(15)]\n", @@ -443,8 +660,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:56:58.687930Z", - "start_time": "2023-11-09T23:56:58.269737Z" + "end_time": "2023-11-10T01:53:08.598697Z", + "start_time": "2023-11-10T01:53:08.596920Z" } }, "id": "7000db4359eed86a" @@ -461,13 +678,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 48, "outputs": [ { "data": { - "text/plain": "0.12777000000000002" + "text/plain": "
", + "image/png": 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WYy89JRD6QbPPRWgDgPnM7gfMXn5uBEIfYBiGqfvg4MGDstvtpi0/twKhDcDcfshut+vw4cOmLT+3AuE9cOLECZ0/f9605fvzcVCSoqOjFR4eLklq0aKFQkIC8yfAr7/+2q3pvvrqKw8nsZZg2f8SbeBqgqUNJCcn6+eff3ZrWn99tKKzgqUN/Pjjj25dEHfkyBG/rAsJMzuAN506dUpjxoyRJI0fP1558+bNMTw+Pl67d+/OVcV33bp1lZSUlKucAIKLu1+ONW7c+JpV51WrVlV2dra7sa6pYsWKPjnwnzhx4qrD1q5dq9jY2KsOvzQsNjb2uj9GJSUlqV69epe93rVrV+XPn9/JtM7x1JehZu7/K/FWm7hWQY2n2sDV9r8kVa5c2SfPk3WnXQRDHwAEu+v1Dd7uB9PS0hQXF+dkWvdxLnR113oc9PX2v5T7NrBixQrawFVwLISvHDt27KrDfPGZqHXr1sqXL5+Tad3jj33AJd7uC653pbkvPhPdeOONstlsTqR1nz+2AY4DvnOt79p90Q82bNhQefLkcTKtc/huyHlZWVnXHO7tfvDYsWOWPh++FsMw9Mgjj+jChQuqWrWqXnjhBbVr107ly5f3yPyt1A+6eyHM8ePHfbJ/neHpNuDt/S9Zqw24+7vsl19+SRvIBau0gesdK65lxIgRmjRpkgfTuM/f2oBV9r+kXN3dunnz5o6iJ1+KjY3VunXr3Jo2oAt6nn/+eZ0+fVo333yz2rVrd9nw+Ph4LV68OFeVWElJSTp06FBuYgKA5R05csTsCIqNjXXqZDssLMztk3Iz74rgb8xoE75oAxTpXpkV+gAAvukH+WxzZVboB53d/5L7beDChQu0gauwQhsAfHEcOHnypFvTBQuz+wJftAF/vjuJN5m973GRL94D1yqsRE6B+N2QYRh+ez48efJkrVy5UmPHjtX999+vxMREde/eXStXrvRIoWag9IP+un+vx9v7XwqMNpCRkUEbyIVAaAPnzp3z67v0XwvHAedc68YCVhWwBT27du3SlClTJEm//fbbNRvq1q1b3V7O9a6QBIB/s9vtfnfgK1GihE8qb0+dOnXVK9OvV2gRGxursLAwZWVlXXfcqw0vUqSIxytz/XF/O8NbbSIpKemqV5N5qg1ca1jJkiW9fjWq5H/twld9ABDsDMPQkSNHrnrVrbf7wdDQUJ98vvG3PlDyXT944cIFHT9+/IrDnCk6zW0byJ8/v2JiYpwLmwu0AeDqTp48edVHjfjiM1GxYsU8fmeKf/PHPuASX/QFR44cuerVut4+F7DZbCpZsqTzYd3kj22A44DvHDt2TJmZmVcc5ot+MDY21uN37vXHNu8Mb7wvDMO4ZmGht/vBsLAwFS9e3LmwueDpNrFz504NGTJE9erV0+DBgxUaGqpRo0Zp6NChmjx5sp544olcL8NK/WBqaqrOnDnj8nTh4eEqUqSI5wO5wZNtwBf7X7JWGzh9+rRbd+goWLCgChQo4IVErqMNuM8wDB09etStu9J54zcgd/lbG7DK/pcu3qXp6NGjLk9ns9kUGxtrynrk6jtXI0A9+OCDhiSjQIECRvHixa/4V7RoUUOSIck4cOCA2ZEBBImUlBRH35OSkmJ2nKsyI+drr73mWKarf5f68QMHDrg1fUhIiJGamurxdfKX/e0MX6xLmzZtTGsDN998s1fW6Ur8oV34Q0YgEDVo0MC0fvD+++/3yTr6S/9iRs709HQjLCzMtDYwadIkn6wnbQC4ujFjxpjWB0RERBiZmZleX0d/e2/5Ou9//vMf09rAnXfe6fX1Mwz/aQP+kjPQ9O3b17T3QNmyZb2yToHUlnyxLtWrVzetDXTu3Nkr6/RvntyO2dnZRoMGDYzw8HDj999/d7yelZVl1K1b14iIiDB27dplek5PSk1NNaKjo13ev5999pnZ0R08tW29uf89mdPTfv31V5f3f548eYwjR46YHd2BNpA7kyZNcrkNxMfHG3a73ezoDv7QBqy6/w3DMFq1auVyG+jdu7fZsd1ijTIqD/vhhx/06aefKiwsTL/++quSkpKu+Hf48GHlzZtXknL12C0AgGfUqVPHtGVXq1ZNERERpi0fF5nZBsxcNgBcQj8Y3PLly6fq1aubtnzaAGA+M9+HtWrVUlhYwN7M229wLoBgx3sAtAHXvPzyy1qzZo3GjBmjqlWrOl4PDQ3Vu+++q6ysLHXv3v2qd4L1RxEREerVq5dL05QvX1733nuvlxKZJxj3vyTVq1dPt956q0vTdOzYMSCfuhKsbeCRRx5RwYIFXZrmqaee8snd+X0tWNvAk08+6dL4oaGh6tevn5fSeFfAFfQYhqGnn35aktS7d+8cDfffwsLCVKlSJUkU9ACAFSQmJpp2y8smTZqYslzkZOZ+oA0AsAL6QZi1HyIjI1W3bl1Tlg3g/916662m3QKe44A1cC6AYNe4cWPTls17wBroB523Y8cODR8+XPXr13f8LvZP8fHxGjVqlH744QdNnjzZhITe8/zzz6tZs2ZOjXvDDTdo8eLFAVe4HMz732az6aOPPlJcXJxT49euXVtvvvmml1P5XjC3gZiYGC1atMhx447r6d69ux599FEvp/K9YG4DTZs21dixY50ef8aMGaZeRJcbAVfQ8/7772vdunW64YYbNGrUqOuOHx8fL4mCHgCwgoiICHXt2tWUZbt6VQe845ZbblFCQoLPl1u8eHHdf//9Pl8uAPxby5YtVbJkSZ8vNz4+XrfddpvPl4vLmXVO0rlzZ0VFRZmybAD/74YbblD79u19vlybzaYePXr4fLm43J133qny5cv7fLk33XST/vOf//h8ucC/lStXTnfddZfPlxsREaFOnTr5fLm4XNu2bXXDDTf4fLm33nqratas6fPl5kbVqlV1/vx5/fzzzwoNDb3iOEOGDJFhGHriiSd8nM678ubNqyVLllz3fVulShX99NNPqlatmo+S+U4w739JiouL05o1a1SvXr1rjnfvvfdqxYoVpl1I7E3B3gaaNWumb7/9ViVKlLjqOGFhYRo0aJBmzpwZkHfnCfY2MHToUL3xxhvXfPpGdHS0PvjgA3Xv3t2HyTwroAp60tPTNXToUEnSiBEjVLhw4etOQ0EPAFhL3759fb7Mxo0bO44HMJfNZjPltoc9e/Z0upofALwpT548phR09OvXLyC/2PBHlStXdvpKU08y4xwMwJWZcT7csmVLlSlTxufLxeVCQkLUp08fny+3T58+CgkJqK+K4cfMOC/p1KmToqOjfb5cXC4iIsKUH904H/Y/+fPn13vvvaedO3fq6aefVqVKlRzHsnz58unbb7/V9u3br/kkD/i3G2+8Ub/++qt+/PFHdezY0VHQEBoaqj59+mjLli364osv6N8D2B133KF9+/bpo48+0p133uloA2FhYRozZoz279+vl156ifPcAPb444/r0KFDev3111WnTh3Hvs6bN69mzZqlQ4cOqWPHjianzJ2Aar358+fXgQMHZBiGnnrqKaemGT58uAzD0LZt27wbDgDglKpVq/r8itQRI0b4dHm4tocfftinV6TGxMT47bNTAQSmvn37qkiRIj5bXtmyZdWlSxefLQ/X5+tzk9atW6tGjRo+XSaAq6tXr57uueceny0vJCREzz33nM+Wh+t77LHHfHrHvhIlSnCHJljKvffeqzp16vhsefnz59czzzzjs+Xh+p566ikVLFjQZ8urWrWq2rZt67PlwbMqVKigSZMm6c8//3TcqaNw4cL6z3/+w4/4QcBms+m2227TBx98oNjYWElSbGyspk6dyufcIJEnTx61bdtW3333naMNFC9eXMOHD7/m3XsQOAoVKqQnnnhC69atc+zzokWL6tFHH1VkZKTJ6XKPIxkAWMDOnTvVoEEDVapUSfXq1dP27duvON7s2bNVsWJFlS9fXj169FBmZqYk6eeff1atWrVUq1YtxcfHq1evXsrIyJAk7d27V40bN1Z0dLRq1ap12Ty3bt2qxo0bq2rVqqpataoWLVrktfV01uTJk1W0aFGfLKtPnz5+93zsQBcREaG3337bZ8t78803Vbx4cZ8tz1VPPPGEypYtK5vNpk2bNl1xnGv1AcuXL9fNN9+satWqKT4+XoMGDZLdbvfhGgBwVZEiRTR16lSfLe/tt98OiA+3geT2229X//79fbKswoUL+7S9OcuZ8+OVK1cqf/78jmNgrVq1lJ6e7hh+tfNcu92ugQMHqnr16qpSpYoeffRRXbhwwWfrBlyPzWbTjBkzfPZD5sCBA3XzzTf7ZFlwTnR0tGbOnOmz5c2YMUOFChXy2fKuJrffjVxiGIaaNm161XXq1q2bbDabzpw5I+ni8eKfx5KyZcsqJibGk6sGF4WFhemdd95Rnjx5fLK8cePGqUKFCj5ZFpwTFxenV155xSfLCgkJ0bvvvqvw8HCfLA8AAMAVFPQAgAX06tVLPXv21F9//aXBgwerW7dul42zZ88eDR8+XKtXr9auXbt09OhRzZgxQ5KUkJCgtWvXatOmTdq6dauOHTvm+GGmYMGCeuGFF/TBBx9cNs+0tDTdf//9euGFF7Rjxw5t27ZNjRo18uq6OqNo0aJ66623XJomKSlJBw8eVFJSktPT3HTTTZowYYKr8XzC2S8yrzfeXXfdpZo1a6pWrVpq1KiRNm7c6Bh2rUKRjIwM9e/fXxUrVlSNGjV8/hz522+/3em77V3iThto3bq1OnTo4GI633rooYf0448/XvMRCNfqA2644QZ9+OGH+v3337V+/XqtWbNGc+fO9VV8AG5q27aty3esc6cf7Nevn18WtjpT7Chd+zh4/vx5PfDAA6pUqZISEhL0n//8R7t27fJBeue8+OKLLv+w5E4bmDJliiULW505P5YuPqJs06ZNjr/8+fNLuvZ57uzZs7VhwwZt2LBBO3bsUEhIiF5//XVfrRrglLi4OJfbpTt9QLVq1TR69GhX4/mcs5+PypYtq8qVKzsKMxY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}, - "execution_count": 9, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -483,8 +701,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-09T23:57:36.205130Z", - "start_time": "2023-11-09T23:56:58.737324Z" + "end_time": "2023-11-10T01:53:08.982734Z", + "start_time": "2023-11-10T01:53:08.604771Z" } }, "id": "f3ae346612ee10d" diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index aca45bbdc..62d2e7d56 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -157,7 +157,6 @@ def power_grover( qc_measure.measure([q for q in evidence_qubits], measurement_ecr) # Run the circuit with the Grover operator and measurements e_samples = self.run_circuit(qc_measure, shots=1024*self.circ.num_qubits) - print(e_samples) e_count = {self.label2qubit[e]: 0 for e in evidence} for e_sample_key, e_sample_val in e_samples.items(): # Go through reverse binary that matches order of qubits @@ -267,7 +266,6 @@ def inference( query_indices_rev = [ (self.circ.num_qubits-self.label2qidx[q_key]-1, q_val) for q_key, q_val in query.items() ] - print([(key, val) for key, val in self.samples.items() if val>0.05]) # Get probability of query res = 0 for sample_key, sample_val in self.samples.items(): From fc09532ccb88b03002669ad77a980e1ba5d5b536 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 04:11:55 +0100 Subject: [PATCH 15/48] Bug with 13 tut jupyter file --- .../14_quantum_bayesian_inference.ipynb | 565 ++++++++++++++++++ 1 file changed, 565 insertions(+) create mode 100644 docs/tutorials/14_quantum_bayesian_inference.ipynb diff --git a/docs/tutorials/14_quantum_bayesian_inference.ipynb b/docs/tutorials/14_quantum_bayesian_inference.ipynb new file mode 100644 index 000000000..66b7a6202 --- /dev/null +++ b/docs/tutorials/14_quantum_bayesian_inference.ipynb @@ -0,0 +1,565 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Quantum Bayesian Inference with Qiskit\n", + "\n", + "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions.\n", + "\n", + "##### This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", + "\n" + ], + "metadata": { + "collapsed": false + }, + "id": "4f1ee7dfd66dd6ac" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 1: Creating Rotations for Bayesian Network\n", + "\n", + "In the first example we consider a simple Bayesian network that is only based on two nodes." + ], + "metadata": { + "collapsed": false + }, + "id": "6adf88f1d249b336" + }, + { + "cell_type": "code", + "execution_count": 9, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:06.237273Z", + "start_time": "2023-11-10T03:10:06.234362Z" + } + }, + "id": "e66a76d3f4afc0f7" + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "initial_id", + "metadata": { + "collapsed": true, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:06.512307Z", + "start_time": "2023-11-10T03:10:06.456456Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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+ }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "# Create a directed graph\n", + "G = nx.DiGraph()\n", + "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", + "G.add_node('A', pos=(0, 0))\n", + "G.add_node('B', pos=(1, 0))\n", + "# Add a directed edge from A to B\n", + "G.add_edge('A', 'B')\n", + "# Get the positions of each node\n", + "pos = nx.get_node_attributes(G, 'pos')\n", + "# Draw the graph\n", + "nx.draw(G, pos, with_labels=True, node_size=2000, node_color='skyblue', arrowstyle='->', arrowsize=20)\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "source": [ + "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", + "$$P(A)=0.2$$\n", + "$$P(B|A)=0.9$$\n", + "$$P(B|-A)=0.3$$" + ], + "metadata": { + "collapsed": false + }, + "id": "19b5a6da03a35a85" + }, + { + "cell_type": "code", + "execution_count": 11, + "outputs": [], + "source": [ + "# Include libraries\n", + "import numpy as np\n", + "# Define rotation angles\n", + "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", + "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_B_nA = 2 * np.arcsin(np.sqrt(0.3))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:06.848751Z", + "start_time": "2023-11-10T03:10:06.845522Z" + } + }, + "id": "326c1d2e72f41202" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 2: Create a Quantum Circuit for Bayesian Network\n", + "\n", + "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." + ], + "metadata": { + "collapsed": false + }, + "id": "33797564f68ae67" + }, + { + "cell_type": "code", + "execution_count": 12, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import QuantumRegister\n", + "from qiskit import QuantumCircuit\n", + "# Define quantum registers \n", + "qrA = QuantumRegister(1, name='A')\n", + "qrB = QuantumRegister(1, name='B')\n", + "# Define a 2-qubit quantum circuit\n", + "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", + "#Apply the R_Y_theta rotation gate on the first qubit\n", + "qc.ry(theta_A, 0)\n", + "# Apply the controlled-R_Y_theta rotation gate\n", + "qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB)\n", + "# Apply the X gate on the first qubit\n", + "qc.x(0)\n", + "# Apply the controlled-R_Y_theta rotation gate\n", + "qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB)\n", + "# Apply another X gate on the first qubit\n", + "qc.x(0)\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:07.780289Z", + "start_time": "2023-11-10T03:10:07.719567Z" + } + }, + "id": "4f99dbe56bc6910a" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 3: Perform Inference\n", + "\n", + "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the `inference` method to estimate probabilities given evidence." + ], + "metadata": { + "collapsed": false + }, + "id": "5d22c72ca6352a56" + }, + { + "cell_type": "code", + "execution_count": 13, + "outputs": [ + { + "data": { + "text/plain": "0.11865" + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit_machine_learning.algorithms .inference import QBayesian\n", + "\n", + "query = {'B': 0}\n", + "evidence = {'A': 1}\n", + "# Initialize quantum bayesian inference framework\n", + "qbayesian = QBayesian(circuit=qc)\n", + "# Inference\n", + "qbayesian.inference(query=query, evidence=evidence)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:08.571707Z", + "start_time": "2023-11-10T03:10:08.432543Z" + } + }, + "id": "841bce19ea097bf1" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 4: Generalize the approach for n nodes\n", + "\n", + "Now we generalize the approach for n nodes in a chain with random probabilities." + ], + "metadata": { + "collapsed": false + }, + "id": "79a2c40d290870" + }, + { + "cell_type": "code", + "execution_count": 14, + "outputs": [ + { + "data": { + "text/plain": "
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+ }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Choose the number of nodes\n", + "n = 10 \n", + "# Generate probabilities\n", + "prob = np.random.random_sample(2*(n-1)+1)\n", + "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", + "# Define quantum registers \n", + "qr = [QuantumRegister(1, name=i) for i in range(n)]\n", + "# Generate circuit\n", + "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", + "#Apply the R_Y_theta rotation gate on the first qubit\n", + "qc.ry(theta[0], 0)\n", + "# Apply the controlled-R_Y_theta rotations\n", + "for i in range(1, n, 1):\n", + " qc.cry(theta_B_A, control_qubit=i-1, target_qubit=i)\n", + " qc.x(i-1)\n", + " qc.cry(theta_B_nA, control_qubit=i-1, target_qubit=i)\n", + " qc.x(i-1)\n", + "# Draw circuit\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:09.555012Z", + "start_time": "2023-11-10T03:10:09.304520Z" + } + }, + "id": "3764be5e0ce2db02" + }, + { + "cell_type": "markdown", + "source": [ + "We could also do inference with this model, but the chosen probabilities are random, as is the result." + ], + "metadata": { + "collapsed": false + }, + "id": "9ded5b8b18eb4256" + }, + { + "cell_type": "code", + "execution_count": 15, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'1000000000': 0.3803, '0000000000': 0.6197}\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "evidence = {str(i): 0 for i in range(n-1)}\n", + "# Initialize quantum bayesian\n", + "qbayesian = QBayesian(circuit=qc)\n", + "# Inference\n", + "samples = qbayesian.rejection_sampling(evidence=evidence)\n", + "print(samples)\n", + "plot_histogram(samples)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:17.943025Z", + "start_time": "2023-11-10T03:10:10.706205Z" + } + }, + "id": "cbb3c2d9a11b43ac" + }, + { + "cell_type": "markdown", + "source": [ + "# Step 5: Burglary Alarm Example: \n", + "\n", + "Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." + ], + "metadata": { + "collapsed": false + }, + "id": "72989e15f2fdd872" + }, + { + "cell_type": "code", + "execution_count": 16, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Create a directed graph\n", + "G = nx.DiGraph()\n", + "# Add nodes\n", + "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", + "# Add edges\n", + "G.add_edges_from([(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"),\n", + " (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")])\n", + "# Manually set positions\n", + "pos = {\"Burglary\": (0, 1), \"Earthquake\": (1, 1),\n", + " \"Alarm\": (0.5, 0.5),\n", + " \"JohnCalls\": (0, 0), \"MaryCalls\": (1, 0)}\n", + "# Draw the network\n", + "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", + "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", + "plt.show()\n", + " " + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:18.025012Z", + "start_time": "2023-11-10T03:10:17.953579Z" + } + }, + "id": "16f5ec62b6f90570" + }, + { + "cell_type": "markdown", + "source": [ + "The Bayesian Network for this scenario involves the following variables:\n", + "\n", + "Burglary (B): Whether a burglary has occurred.\n", + "Earthquake (E): Whether an earthquake has occurred.\n", + "Alarm (A): Whether the alarm goes off.\n", + "John Calls (J): Whether John calls you.\n", + "Mary Calls (M): Whether Mary calls you." + ], + "metadata": { + "collapsed": false + }, + "id": "85ffd7ab1e8316e4" + }, + { + "cell_type": "code", + "execution_count": 17, + "outputs": [], + "source": [ + "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_E = 2 * np.arcsin(np.sqrt(0.002))\n", + "theta_A_nBnE = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_A_nBE = 2 * np.arcsin(np.sqrt(0.29))\n", + "theta_A_BnE = 2 * np.arcsin(np.sqrt(0.94))\n", + "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", + "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", + "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_M_nA = 2 * np.arcsin(np.sqrt(0.01))\n", + "theta_M_A = 2 * np.arcsin(np.sqrt(0.7))\n", + " " + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:21.228824Z", + "start_time": "2023-11-10T03:10:21.206538Z" + } + }, + "id": "f79d7c9a5cca338" + }, + { + "cell_type": "markdown", + "source": [ + "The Bayesian network can be represented by the following quantum circuit:" + ], + "metadata": { + "collapsed": false + }, + "id": "d2693a276552450f" + }, + { + "cell_type": "code", + "execution_count": 18, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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+ }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize register\n", + "var = ['B','E','A','J','M']\n", + "qr = [QuantumRegister(1, name=v) for v in var]\n", + "qc = QuantumCircuit(*qr, name='Pachinko')\n", + "# Specify control qubits\n", + "# P(B)\n", + "qc.ry(theta_B, qr[0])\n", + "# P(E)\n", + "qc.ry(theta_E, qr[1])\n", + "# P(A|-B,-E)\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", + "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", + "# P(A|-B,E)\n", + "qc.x(qr[0])\n", + "qc.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[0])\n", + "# P(A|B,-E)\n", + "qc.x(qr[1])\n", + "qc.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[1])\n", + "# P(A|B,E)\n", + "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", + "# P(J|-A)\n", + "qc.x(qr[2])\n", + "qc.cry(theta_J_nA, qr[2], qr[3])\n", + "qc.x(qr[2])\n", + "# P(J|A)\n", + "qc.cry(theta_J_A, qr[2], qr[3])\n", + "# P(M|-A)\n", + "qc.x(qr[2])\n", + "qc.cry(theta_M_nA, qr[2], qr[4])\n", + "qc.x(qr[2])\n", + "# P(M|A)\n", + "qc.cry(theta_M_A, qr[2], qr[4])\n", + "# Draw circuit\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)\n" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:22.846088Z", + "start_time": "2023-11-10T03:10:22.535173Z" + } + }, + "id": "85bb861283b06275" + }, + { + "cell_type": "markdown", + "source": [ + "Using this network, you can perform various probabilistic inferences. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." + ], + "metadata": { + "collapsed": false + }, + "id": "bb0e805d2f7fb30c" + }, + { + "cell_type": "code", + "execution_count": 19, + "outputs": [ + { + "data": { + "text/plain": "0.004829999999999999" + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "query = {'B': 1}\n", + "evidence = {'J': 1}\n", + "# Initialize quantum bayesian inference framework\n", + "qbayesian = QBayesian(circuit=qc)\n", + "# Inference\n", + "qbayesian.inference(query=query, evidence=evidence)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:59.887367Z", + "start_time": "2023-11-10T03:10:59.526529Z" + } + }, + "id": "5468619791203a79" + }, + { + "cell_type": "code", + "execution_count": null, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false + }, + "id": "72a1d1076dd05cb0" + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From b3fb76cecbf518b740ff81f461a26379168fdd3a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 04:29:49 +0100 Subject: [PATCH 16/48] Bug fix with 13 tut jupyter file --- .../13_quantum_bayesian_inference.ipynb | 560 ++++++----------- .../14_quantum_bayesian_inference.ipynb | 565 ------------------ 2 files changed, 182 insertions(+), 943 deletions(-) delete mode 100644 docs/tutorials/14_quantum_bayesian_inference.ipynb diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index bddba2ee8..e3489b483 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -5,7 +5,7 @@ "source": [ "# Quantum Bayesian Inference with Qiskit\n", "\n", - "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions. \n", + "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions.\n", "\n", "##### This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", "\n" @@ -13,7 +13,7 @@ "metadata": { "collapsed": false }, - "id": "64eb0ac8be046640" + "id": "4f1ee7dfd66dd6ac" }, { "cell_type": "markdown", @@ -25,11 +25,19 @@ "metadata": { "collapsed": false }, - "id": "cafd433bf5016f60" + "id": "6adf88f1d249b336" }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 10, + "id": "initial_id", + "metadata": { + "collapsed": true, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:06.512307Z", + "start_time": "2023-11-10T03:10:06.456456Z" + } + }, "outputs": [ { "data": { @@ -56,15 +64,7 @@ "nx.draw(G, pos, with_labels=True, node_size=2000, node_color='skyblue', arrowstyle='->', arrowsize=20)\n", "# Show the plot\n", "plt.show()" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T01:53:06.075105Z", - "start_time": "2023-11-10T01:53:03.964957Z" - } - }, - "id": "925af2a5fe37bf8c" + ] }, { "cell_type": "markdown", @@ -77,19 +77,11 @@ "metadata": { "collapsed": false }, - "id": "c2fedc900c1152d3" + "id": "19b5a6da03a35a85" }, { "cell_type": "code", - "execution_count": 41, - "id": "initial_id", - "metadata": { - "collapsed": true, - "ExecuteTime": { - "end_time": "2023-11-10T01:53:06.075307Z", - "start_time": "2023-11-10T01:53:04.049355Z" - } - }, + "execution_count": 11, "outputs": [], "source": [ "# Include libraries\n", @@ -98,7 +90,15 @@ "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", "theta_B_nA = 2 * np.arcsin(np.sqrt(0.3))" - ] + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:06.848751Z", + "start_time": "2023-11-10T03:10:06.845522Z" + } + }, + "id": "326c1d2e72f41202" }, { "cell_type": "markdown", @@ -110,18 +110,18 @@ "metadata": { "collapsed": false }, - "id": "5cd1787e381e1030" + "id": "33797564f68ae67" }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 12, "outputs": [ { "data": { "text/plain": "
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" }, - "execution_count": 42, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -149,11 +149,11 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:06.075447Z", - "start_time": "2023-11-10T01:53:04.056015Z" + "end_time": "2023-11-10T03:10:07.780289Z", + "start_time": "2023-11-10T03:10:07.719567Z" } }, - "id": "c4984e988c8ededd" + "id": "4f99dbe56bc6910a" }, { "cell_type": "markdown", @@ -165,97 +165,17 @@ "metadata": { "collapsed": false }, - "id": "644fd909109b2e64" + "id": "5d22c72ca6352a56" }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 13, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00906 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.02694 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 5.19609 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.001s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.001s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.002s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 5.42998 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.01788 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.04697 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.01574 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.04101 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00381 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 2.39205 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.06199 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09704 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.03028 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01574 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00715 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.39403 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03767 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.08988 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02670 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.02003 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.01693 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.26696 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03886 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09084 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02623 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01693 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.01788 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 37.86802 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00477 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00072 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.00811 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 3.83615 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.001s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.001s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 4.67014 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.01431 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.10109 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.05722 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.98174 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.13614 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09704 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02813 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01597 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.59574 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.07105 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.10395 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02694 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.01812 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00405 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 1.44100 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 0.03791 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 0.09394 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.02599 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.02408 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.01812 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 32.92513 (ms)\n" - ] - }, { "data": { - "text/plain": "0.11922" + "text/plain": "0.11865" }, - "execution_count": 43, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -273,11 +193,11 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:06.077940Z", - "start_time": "2023-11-10T01:53:04.128656Z" + "end_time": "2023-11-10T03:10:08.571707Z", + "start_time": "2023-11-10T03:10:08.432543Z" } }, - "id": "8d7a132268680e61" + "id": "841bce19ea097bf1" }, { "cell_type": "markdown", @@ -289,18 +209,18 @@ "metadata": { "collapsed": false }, - "id": "fb1ef1a3c7e0ac9f" + "id": "79a2c40d290870" }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 14, "outputs": [ { "data": { "text/plain": "
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}, - "execution_count": 44, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -329,11 +249,11 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:06.093229Z", - "start_time": "2023-11-10T01:53:04.244818Z" + "end_time": "2023-11-10T03:10:09.555012Z", + "start_time": "2023-11-10T03:10:09.304520Z" } }, - "id": "9021e193f69b0392" + "id": "3764be5e0ce2db02" }, { "cell_type": "markdown", @@ -343,179 +263,25 @@ "metadata": { "collapsed": false }, - "id": "6180fa5c5fae8d" + "id": "9ded5b8b18eb4256" }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 15, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00620 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01907 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 281.26693 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.002s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.010s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 17.19189 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.35095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.86808 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.34261 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 33.26821 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 1.72710 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 3.97491 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.87595 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.35095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 34.79385 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 1.88112 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 4.23598 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.85235 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.34213 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 36.93390 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 2.03085 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 4.22120 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 0.88501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00811 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.40007 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.39315 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 450.05584 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01407 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 232.22804 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.003s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.017s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 27.04120 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 0.66090 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.60432 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.66400 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 64.04185 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.42512 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.89809 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.58596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.68402 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 63.49897 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.40509 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.62796 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.61505 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.65899 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 63.62295 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 3.32594 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 7.77507 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 1.68180 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 0.67306 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00477 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.67830 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 515.87081 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00095 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01717 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 587.18991 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.005s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.033s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 51.32413 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 1.31083 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.22413 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.31989 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 133.64792 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.69782 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.83910 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.23009 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00620 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.36399 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 129.71878 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 6.80709 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.44499 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.13973 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.35517 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00501 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 127.05207 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.74693 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.60783 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.17287 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00525 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.28102 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00381 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 1.26791 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 1234.83801 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 0.00525 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnitarySynthesis - 0.00119 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: HighLevelSynthesis - 0.01001 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: UnrollCustomDefinitions - 762.33602 (ms)\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Begin BasisTranslator from source basis {('mcx_gray', 10), ('ry', 1), ('x', 1), ('cry', 2), ('h', 1), ('rz', 1), ('measure', 1), ('cx', 2)} to target basis {'save_density_matrix', 'cx', 'set_statevector', 'measure', 'cp', 'sdg', 'tdg', 'mcphase', 'save_expval', 'p', 'set_unitary', 'cu3', 'cy', 'id', 'mcx', 'save_amplitudes', 'barrier', 'u3', 'rz', 'cu1', 'pauli', 'rx', 'set_superop', 'mcswap', 'rzx', 'u', 'mcsx', 'ecr', 'save_statevector', 'ry', 'mcu1', 'set_density_matrix', 'save_superop', 'if_else', 'save_clifford', 'mcu', 'cswap', 'break_loop', 'u1', 'mcrz', 'save_statevector_dict', 'ccx', 'save_probabilities', 'rzz', 'sx', 'r', 'switch_case', 'mcy', 'swap', 'mcz', 'delay', 'u2', 'save_amplitudes_sq', 'unitary', 'save_matrix_product_state', 'mcu3', 'roerror', 'save_state', 'snapshot', 'set_matrix_product_state', 'initialize', 'diagonal', 'while_loop', 'h', 'cz', 'kraus', 's', 'continue_loop', 'mcu2', 'mcry', 'save_probabilities_dict', 'mcp', 'x', 'csx', 'superop', 'cu2', 'mcrx', 'sxdg', 'cu', 'qerror_loc', 'ryy', 'y', 'for_loop', 'save_stabilizer', 'save_unitary', 'mcx_gray', 'rxx', 'multiplexer', 'reset', 'mcr', 'quantum_channel', 't', 'set_stabilizer', 'save_expval_var', 'z'}.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation path search completed in 0.000s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation paths composed in 0.006s.\n", - "INFO:qiskit.transpiler.passes.basis.basis_translator:Basis translation instructions replaced in 0.033s.\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: BasisTranslator - 55.11713 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: RemoveResetInZeroState - 1.33991 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.41511 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.39093 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00572 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 125.62895 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.15208 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.98597 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.48496 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00787 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.52016 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 150.48409 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 7.29823 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 16.40582 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.73816 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00906 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.53112 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Optimize1qGatesDecomposition - 132.76291 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: CXCancellation - 6.85596 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: GatesInBasis - 15.81717 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Depth - 3.26610 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00691 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: Size - 1.41692 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: FixedPoint - 0.00739 (ms)\n", - "INFO:qiskit.transpiler.runningpassmanager:Pass: ContainsInstruction - 1.53494 (ms)\n", - "INFO:qiskit.compiler.transpiler:Total Transpile Time - 1358.55627 (ms)\n" - ] - }, { "name": "stdout", "output_type": "stream", "text": [ - "{'1000000000': 0.40371, '0000000000': 0.59629}\n" + "{'1000000000': 0.3803, '0000000000': 0.6197}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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iRYtyvb/Lly/j6+uLwWCgQ4cOt+1jMBiy/Kdfv365PraIiIhIYWKf2y9GRUXx888/M3PmTBYuXMiiRYuoUKECL730Ev369aN06dK5Lmrjxo20b98eZ2dnevfuTdGiRVmyZAm9evUiIiKC4cOH53ifr732GrGxsXft5+/vf9uwV6dOnRwfU0RERKQwMpjNZvO97uTgwYP88MMPzJ8/n8uXL2Nvb0/nzp0ZMGAAHTp0wGAwZHtfqampVK1alTNnzrB9+3ZL8IqNjSUoKIhTp05x7Ngx/P39s73PJUuW0L17d6ZPn85rr71G+/bt+euvvzL1MxgMtGjRgr///jvb+76TuLg4PDw8iI2Nxd3dPU/2easBX+bLbkVybcYQa1cgImKbcpI78uQlkJo1azJt2jTOnTvHTz/9RLNmzfjjjz/o3Lkz/v7+jB07lrNnz2ZrXxs2bCAsLIw+ffpkuOrm4eHByJEjSU5OZu7cudmuLTo6mldeeYXnnnuOTp065XRoIiIiIg+cPH0L2MnJifbt29OxY0dKly6N2WzmzJkzjB07looVKzJ48GCuX79+x32kX31r165dpm3t27cHYNOmTdmu6eWXX8bOzo6pU6dmq/+VK1f44YcfGD9+PN999x0HDx7M9rFERERE7ge5fgbwVmvWrGHmzJksW7aMlJQUypQpw4cffsjzzz/Pnj17mDJlCt999x3Xr19n9uzZWe4nNDQUgICAgEzbSpcujZubm6XP3cybN4/ffvuNpUuX4unpma1nAPfv38+gQYMytHXo0IG5c+fi5eV1x+8mJSWRlJRk+RwXFwdASkoKKSkpABiNRuzs7EhLS8NkMln6prenpqZy8115Ozs7jEZjlu0ihU36f+vp7O1vnGZSU1MztDs4OGAymUhLS7O0GQwG7O3ts2zP6u8mr/6eslu7xqQxaUwaU2EcU07cUwA8e/Yss2bNYvbs2Zw+fRq4ceVu0KBBdOnSBTs7OwAqVqxI9+7d6dKlC3/88ccd95ke0jw8PG673d3dPVtB7ty5c7zxxhs8/fTTdO3aNVvjGT58ON26daNy5co4Ojpy6NAhxo0bx6pVq+jcuTPBwcGWMd3OhAkTGDt2bKb2NWvW4OLiAoCfnx+BgYEcOHCA8PBwS58qVapQtWpVdu7cSXR0tKW9Tp06+Pv7s3nzZq5evWppb9y48V0DqYg1rFy5MsPnjh07kpCQwMaNGy1t9vb2dOrUiZiYGIKDgy3tRYsWpXXr1kRERLBv3z5Le6lSpWjSpAmhoaGEhIRY2vP672nNmjUZTtitWrWiSJEiGpPGpDFpTPfFmHx8fMiuXL8E0rlzZ1avXk1aWhre3t688MILDBw4kPLly2f5nQkTJvDBBx9kSLi3ateuHWvXriU0NJRKlSpl2u7r68u1a9fuGgI7duzIv//+y+HDhylZsiQAp06dokKFClm+BHI7JpOJ1q1bs2nTJpYsWcJTTz2VZd/bXQEsV64cMTExlocx8/rXiF4CkcLmm8G6AqgxaUwak8ZkjTHFx8dn+yWQXF8BXLlyJa1bt2bQoEE8+eSTlsHeSZcuXe6aTtOv/GUV8OLi4vD09LzjPubOncuqVatYvHixJfzlltFoZMCAAWzatImtW7feMQA6OTnh5OSUqd3BwQEHB4cMbXZ2dre9mpjV/47Z+d9XpDC49b/1O7Ubjcbb3rbIqj2rv5u8+nvKSe1ZtWtMGhNoTFnVmNN2jSnnY8quXD9EduzYMdatW0ePHj2yHU4efvhhnn/++Tv2SX/273bP+UVFRXHt2rXbPh94s7179wLQo0ePDJM5V6hQAYDVq1djMBiyPbdfeoiMj4/PVn8REZHC4uuvv6Z8+fI4OzvTsGFDdu7cma3vLViwAIPBwBNPPJGh3Ww2M2rUKMqUKUORIkVo27Ztls/mJyUlUadOHQwGQ4bbm2J9uQ6A48ePZ9myZXfss3z5cvr375+j/bZo0QK48dzcrVavXp2hT1YaN27Miy++mOmfXr16AVC2bFlefPHFO17Nu9mOHTsA7nh7W0REpLBZuHAhw4YNY/To0ezZs4fatWvTvn17Lly4cMfvnTp1irfeeotHHnkk07ZJkybx1Vdf8d1337Fjxw5cXV1p3749iYmJmfq+8847OXouTQpOrp8BNBqNjBkzhlGjRmXZ55NPPmHUqFF3fObvVqmpqVSpUoWzZ89mORF0SEiIJYxFRkYSGxtLmTJlsnxxJN2dngE8ePAgVatWzXS5dtu2bTz66KOkpKRw5MgRHnrooWyPRRNBiy3SRNAihUfDhg1p0KAB06dPB248116uXDlef/113nvvvdt+Jy0tjebNm9O/f3/++ecfrly5wtKlS4EbV/98fHwYPnw4b731FnDj/z57e3szZ84cevfubdnPqlWrGDZsGEuWLKFGjRrs3btXq2rlswKfCDoriYmJOX52zd7enpkzZ2IymWjevDkDBw5k+PDh1K5dm2PHjjF+/PgMV+JGjBhBtWrV+P333++p1ilTpuDj48OTTz7JG2+8wfDhw+nQoQPNmjUjMTGRr776KkfhT0RExJqSk5P5999/adu2raXNaDTStm3bDG+h3uqjjz7Cy8uLF198MdO2kydPEhUVlWGfHh4eNGzYMMM+z58/z4ABA/jpp58ss2BI4XJPbxZktcSb2WwmIiKCVatW5erSb6tWrdiyZQujR49m4cKFpKSkULNmTSZOnGi5jZvXunbtypUrV9i/fz9r164lOTmZ0qVL07t3b4YMGUJQUFC+HFdERCQ/xMTEWGbquJm3tzdHjx697Xe2bNnCjz/+mOXzelFRUZZ93LrP9G1ms5l+/frx8ssvU79+fU6dOnVvA5F8kaMAaDQaM4S+MWPGMGbMmCz7m81m3n333VwVFhQUxKpVq+7ab86cOcyZMydb+yxfvjxZ3fF+8sknefLJJ3NSooiIyAPj6tWrPPfcc8yYMeOeZtCYNm0aV69eZcSIEXlYneS1HAXA5s2bWwLg5s2b8fPzu+2LEXZ2dhQvXpzWrVszYMCAPClUREREsq9kyZLY2dlx/vz5DO3nz5+ndOnSmfqHhYVx6tQpunTpYmlLn2fO3t6ekJAQy/fOnz9PmTJlMuwz/fm+DRs2EBwcnGlatPr16/PMM88wd+7cPBmf3JscBcD0dXrhxtXAF1544Y4vgYiIiIh1ODo6Uq9ePdavX2+ZysVkMrF+/Xpee+21TP2rVq3KwYMHM7R98MEHXL16lalTp1KuXDkcHBwoXbo069evtwS+uLg4duzYwSuvvALAV199xccff2zZx7lz52jfvj0LFy6kYcOG+TNYybFcPwN48+zTIiIiUvgMGzaM559/nvr16xMUFMSXX35JfHw8L7zwAgB9+/bF19eXCRMm4OzszMMPP5zh+8WKFQPI0D5kyBA+/vhjAgICqFChAh9++CE+Pj6WkOnn55dhH25ubgA89NBDlC1bNp9GKjml5SVEREQeUL169SI6OppRo0YRFRVFnTp1+OuvvywvcYSHh9929Yk7eeedd4iPj2fgwIFcuXKFZs2a8ddff+Hs7JwfQ5B8ku15APv374/BYGD8+PF4e3tne4Jng8HAjz/+eE9F3q80D6DYIs0DKCJiHTnJHdkOgOlvAB85coTKlStn+xeDwWDI0UTQDxIFQLFFCoAiItaRk9yR7VvAJ0+eBMDX1zfDZxERERG5v2Q7APr7+9/xs4iIiIjcH/J1KTgRERERKXyyfQUwPDw81we59ZVwEREREbGebAfA8uXLZ7n2750YDAZSU1Nz/D0RERERyR/ZDoB9+/bNVQAUERERkcIl2wFwzpw5+ViGiIiIiBQUvQQiIiIiYmMUAEVERERsTLZvAWspOBEREZEHg5aCy0daCk5skZaCExGxDi0FJyIiIiJZ0lJwIiIiIjYm2wFQRETkfqPHZKQwKUyPyNzzW8C///47Xbt2xc/PDw8PD/z8/HjiiSdYunRpHpQnIiIiInkt11cAU1NT6dOnD0uWLMFsNmNvb0+JEiWIiopi2bJl/Pnnn3Tr1o358+djb68LjSIiIiKFRa6vAE6YMIFff/2VRx55hH/++YfExEQiIyNJTExk8+bNNGvWjCVLlvDpp5/mZb0iIiIico9yHQBnz55N1apVWbduHU2bNrVMC2M0GmnWrBnr1q2jcuXKzJo1K8+KFREREZF7l+sAGBkZSZcuXbK8vevg4ECXLl2IjIzMdXEiIiIikvdyHQDLlSvHtWvX7tgnPj4ePz+/3B5CRERERPJBrgPgSy+9xKJFi7K8wnf27FkWLlzISy+9lOviRERERCTvZfv13PDw8Ayfe/bsydatWwkMDGTIkCE0a9YMb29vzp8/zz///MPUqVNp1qwZPXr0yPOiRURERCT3sh0Ay5cvj8FgyNRuNpt5//33b9u+bNkyli9fTmpq6r1VKSIiIiJ5JtsBsG/fvrcNgCIiIiJyf8l2AJwzZ04+liEiIiIiBeWel4ITERERkfuLAqCIiIiIjbmnRXqvXr3K9OnTWbduHefOnSMpKSlTH4PBQFhY2L0cRkRERETyUK4DYHR0NE2aNCEsLAx3d3fi4uLw8PAgOTmZhIQEAHx8fHBwcMizYkVERETk3uX6FvCYMWMICwvjf//7H5cvXwZg6NChxMfHs2PHDoKCgihfvjyHDx/Os2JFRERE5N7lOgCuXLmSNm3a8Oyzz2aaHqZBgwasWrWKU6dOMXbs2HsuUkRERETyTq4DYGRkJIGBgZbPdnZ2llu/AJ6enjz22GMsWrTo3ioUERERkTyV6wDo4eFBSkqK5bOnpydnzpzJ0Mfd3Z3z58/nvjoRERERyXO5DoAVK1bk1KlTls+BgYGsXbuWixcvApCQkMCff/6Jn5/fPRcpIiIiInkn1wGwXbt2rF+/nuvXrwMwaNAgLly4QO3atenRowcPP/wwYWFh9OvXL69qFREREZE8kOsA+PLLLzNjxgxLAHzqqaf47LPPiI+PZ8mSJURFRTFs2DDefvvtPCtWRERERO5drucBLFOmDL169crQNnz4cIYMGUJMTAxeXl6Z3g4WEREREeu7p5VAbsfOzg5vb++83q2IiIiI5JF7DoCRkZEsWLCAvXv3Ehsbi4eHB4GBgfTu3ZsyZcrkRY0iIiIikofuKQB+/fXXvP322yQlJWE2my3t8+bN4/3332fy5Mm8+uqr91ykiIiIiOSdXAfABQsW8Prrr1OyZEnef/99HnnkEby9vTl//jybN29m6tSplu09e/bMy5pFRERE5B7kOgBOmjSJkiVLsm/fPnx8fCztVapUoXnz5vTr14/AwEAmTpyoACgiIiJSiOR6GpgjR47Qs2fPDOHvZmXLlqVHjx4cOXIk18WJiIiISN7LdQAsVqwYrq6ud+zj5uZGsWLFcnsIEREREckHuQ6Ajz/+OH/++Sepqam33Z6SksKff/5J165dc12ciIiIiOS9XAfASZMm4erqSrt27di+fXuGbcHBwbRr146iRYvy6aef3nORIiIiIpJ3sv0SSMWKFTO1JScns2fPHpo2bYq9vT0lS5YkJibGclWwTJky1K1bl7CwsLyrWERERETuSbYDoMlkyrS0m4ODA35+fhnabn0pxGQy3UN5IiIiIpLXsh0AT506lY9liIiIiEhByfUzgCIiIiJyf7rntYABUlNTCQkJIS4uDnd3d6pUqYK9fZ7sWkRERETy2D1dAbx06RIDBgzAw8ODWrVq0axZM2rVqkWxYsUYOHAgFy9ezKs6RURERCSP5Poy3aVLl2jUqBHHjx+nePHiPPLII5QpU4aoqCh2797NzJkz2bRpE8HBwRQvXjwvaxYRERGRe5DrK4Djxo3j+PHjvP3225w+fZq//vqL2bNns2rVKk6fPs27775LaGgon3zySV7WKyIiIiL3KNcB8I8//qBly5ZMnDgx05JwLi4uTJgwgZYtW/L777/fc5EiIiIikndyHQDPnTtH48aN79incePGnDt3LreHEBEREZF8kOsA6OHhwenTp+/Y5/Tp03h4eOT2ECIiIiKSD3IdAFu0aMHixYtZt27dbbevX7+exYsX07Jly9weQkRERETyQa7fAh49ejQrVqygffv2dOzYkRYtWuDt7c358+f5+++/WbVqFS4uLowaNSov6xURERGRe5TrAFijRg1Wr15Nv379WLFiBStWrMBgMGA2mwF46KGHmDNnDjVq1MizYkVERETk3t3Tch3NmjUjNDSUrVu3snfvXstKIIGBgTRt2hSDwZBXdYqIiIhIHsl1AOzfvz81a9Zk6NChNGvWjGbNmuVlXSIiIiKST3L9Esj8+fO5cOFCXtYiIiIiIgUg1wHwoYceIjIyMi9rEREREZECkOsA2L9/f1asWMHZs2fzsh4RERERyWe5fgawW7dubNy4kSZNmvDOO+/QoEEDvL29b/vih5+f3z0VKSIiIiJ5J9cBsGLFipZpX954440s+xkMBlJTU3N7GBERERHJY7kOgH379s3XaV527drF6NGj2bZtGykpKdSsWZNhw4bRs2fPbH1/1apVzJ07l3379hEVFUVycjJ+fn40bdqUd999l8qVK9/2e6tXr2b8+PHs2bMHg8FAvXr1+OCDD2jTpk1eDk9ERETEanIdAOfMmZOHZWS0ceNG2rdvj7OzM71796Zo0aIsWbKEXr16ERERwfDhw++6j5UrV7J9+3YaNmzIY489hoODA0eOHGHu3Ln8/PPPrFy5ktatW2f4zrx583juuecoVaoU/fr1A2DhwoU8+uijLFq0iO7du+fHcEVEREQKlMGcvnRHIZGamkrVqlU5c+YM27dvp06dOgDExsYSFBTEqVOnOHbsGP7+/nfcT2JiIs7Ozpna169fT9u2balfvz67du2ytF++fJmKFStib2/P3r17KVu2LABnzpwhMDAQgBMnTlC0aNFsjyUuLg4PDw9iY2Nxd3fP9vdyYsCX+bJbkVybMcTaFYj8H50jpTDJ7/NjTnJHrt8CTpeUlMTvv//OqFGjePPNNxk1ahS///47SUlJudrfhg0bCAsLo0+fPpbwB+Dh4cHIkSNJTk5m7ty5d93P7cIfQJs2bfD09OT48eMZ2hcvXsyVK1d4/fXXLeEPoGzZsrz22mvExMTw+++/52pMIiIiIoXJPS0Ft2zZMgYOHEh0dDQ3X0g0GAx4eXnxww8/0KVLlxzt8++//wagXbt2mba1b98egE2bNuW65uDgYC5fvpxp5ZK7HXfMmDFs2rSJvn375vrYIiIiIoVBrgPg+vXr6datG3Z2dvTv359HHnkEb29vzp8/z+bNm5k3bx5PPfUUq1evzvSs3Z2EhoYCEBAQkGlb6dKlcXNzs/TJjjVr1rBt2zaSkpIIDQ1l+fLllCxZki+++CLbx01vu9txk5KSMlz5jIuLAyAlJYWUlBQAjEYjdnZ2pKWlYTKZLH3T21NTUzOEaTs7O4xGY5btIoVN+n/r6eztb5xmbp0NwMHBAZPJRFpamqXNYDBgb2+fZXtWfzd59feU3do1pvtpTFqTXgqX/Px7yolcB8DRo0dTpEgRtm3bxsMPP5xhW9++fXnjjTdo2rQpo0ePzlEAjI2NBW7c8r0dd3d3S5/sWLNmDVOmTLF8rlSpEgsWLKBevXrZPm76ffS7HXfChAmMHTv2tjW4uLgAN+ZEDAwM5MCBA4SHh1v6VKlShapVq7Jz506io6Mt7XXq1MHf35/Nmzdz9epVS3vjxo3x8vK6Yz0i1rBy5coMnzt27EhCQgIbN260tNnb29OpUydiYmIIDg62tBctWpTWrVsTERHBvn37LO2lSpWiSZMmhIaGEhISYmnP67+nNWvWZAgRrVq1okiRIhrTfTwmcECkMMnPvycfH59s15Hrl0BcXV3p06cPM2bMyLLPiy++yIIFC4iPj8/2ftu1a8fatWsJDQ2lUqVKmbb7+vpy7dq1HIVAgGvXrvHff//x0UcfsW7dOmbNmkWfPn0s2ytXrkxoaCgpKSmWX5PpUlJScHR0pFatWuzfvz/LY9zuCmC5cuWIiYmxhMi8/iWsB5ylsPlmsK4AakyFZ0wDp+oKoBQeM4bk7xXA+Pj4bL8EkusrgC4uLpQqVeqOfby8vCxXvrIr/QpcVgEvLi4OT0/PHO0TwM3NjaCgIJYuXUr9+vUZOHAgjz76qGUMNx+3RIkSmY55c5+sODk54eTklKndwcEBB4eMv0Lt7Oyws7PL1PfW8Hm3dpHC5tb/1u/UbjQab3vbIqv2rP5u8urvKSe1Z9WuMRW+MYkUJvn995TtOnL7xbZt27Ju3bo79lm3bh2PPvpojvZ7p+ftoqKiuHbt2m2f08sue3t7WrVqRXx8PLt3787Wce/0fKCIiIjI/SbXAXDy5MlcuHCBvn37EhERkWFbREQEzz33HDExMUyePDlH+23RogVw47m5W61evTpDn9w6d+4ckPHXYkEcV0RERKQwyPUzgK1bt+by5cscOHAAOzs7/Pz8LG8Bh4eHk5aWRq1atTLdrjUYDKxfvz7L/aamplKlShXOnj2b5UTQISEhlC9fHoDIyEhiY2MpU6ZMhlu0u3fvpn79+pn2v3r1arp06YKrqytnzpzB1dUVuDERdIUKFXBwcNBE0CL3QBNBS2Gic6QUJoVpIuhcP1iWPm8e3AhtJ06c4MSJExn63O6FibutH2xvb8/MmTNp3749zZs3z7AU3OnTp5k8ebIl/AGMGDGCuXPnMnv2bMvybQANGjTg4YcfplatWpQtW5b4+HgOHDjAP//8g4ODA7NmzbKEPwBPT0+mT5/Oc889R926denVqxdwYym4ixcvsnDhwhyFPxEREZHCKtcB8OY3T/Jaq1at2LJlC6NHj2bhwoWkpKRQs2ZNJk6caAlmdzN+/Hg2btzIpk2biI6Oxmg04ufnx8CBAxkyZAjVqlXL9J1nn32WkiVLMn78eGbPno3BYKBevXp88MEHtG3bNq+HKSIiImIVhW4t4AeJbgGLLdItYClMdI6UwqQw3QLOs6UkwsPD2bx5c17tTkRERETySZ4FwNmzZ9OqVau82p2IiIiI5BMtJisiIiJiYxQARURERGyMAqCIiIiIjcmzAOjh4YGfn19e7U5ERERE8kmeBcAhQ4Zw8uTJvNqdiIiIiOQT3QIWERERsTHZXgkkfY6/oKAgnJ2dczTnX/PmzXNemYiIiIjki2wHwJYtW2IwGDhy5AiVK1e2fM6OtLS0XBcoIiIiInkr2wFw1KhRGAwGSpYsmeGziIiIiNxfsh0Ax4wZc8fPIiIiInJ/0EsgIiIiIjYm1wHw6tWrnDhxgpSUlAztCxcu5JlnnuHFF19kz54991ygiIiIiOStbN8CvtU777zDvHnzOH/+PA4ODgB8++23vPbaa5jNZgAWLFjAv//+S9WqVfOmWhERERG5Z7m+Arhp0ybatm2Li4uLpe3TTz/F19eXzZs3s2jRIsxmM5999lmeFCoiIiIieSPXVwAjIyPp0KGD5fORI0eIiIhg0qRJNGvWDIBff/01R/MFioiIiEj+y/UVwKSkJBwdHS2fN23ahMFgoF27dpa2ihUrcvbs2XurUERERETyVK4DYNmyZTlw4IDl8/LlyylevDi1atWytF28eBE3N7d7q1BERERE8lSubwE/9thjfP3117z11ls4Ozvz119/0bdv3wx9jh07hp+f3z0XKSIiIiJ5J9cBcMSIEfz55598/vnnAJQpU4aPPvrIsv3ChQts3bqV11577d6rFBEREZE8k+sAWLp0aQ4fPsz69esBaN68Oe7u7pbtMTExfPbZZ7Rv3/7eqxQRERGRPJPrAAhQpEgROnfufNtt1atXp3r16veyexERERHJB1oKTkRERMTG3NMVwLS0NBYtWsS6des4d+4cSUlJmfoYDAbLbWIRERERsb5cB8D4+HjatWvH9u3bMZvNGAwGyxJwgOWzwWDIk0JFREREJG/k+hbwxx9/THBwMGPHjiUmJgaz2cyYMWOIjIxk4cKFVKxYkR49etz2qqCIiIiIWE+uA+Bvv/1Go0aN+OCDDyhevLil3dvbmx49erBx40bWrVuntYBFRERECplcB8Dw8HAaNWr0fzsyGjNc7StbtiydOnVi7ty591ahiIiIiOSpXAdAV1dXjMb/+7qHhweRkZEZ+pQuXZrw8PDcVyciIiIieS7XAdDf3z9DuHv44YfZsGGD5Sqg2Wxm/fr1lClT5t6rFBEREZE8k+sA2KZNGzZu3EhqaioAzz//POHh4TRu3Ji3336bZs2asW/fPrp165ZnxYqIiIjIvcv1NDADBgygRIkSREdHU6ZMGfr378/evXv55ptv2LdvHwDdunVjzJgxeVSqiIiIiOSFXAfAgIAA3n333Qxt06ZNY9SoUZw4cQJ/f39Kly59zwWKiIiISN66p5VAbqdUqVKUKlUqr3crIiIiInlEawGLiIiI2JhcXwGsWLFitvoZDAbCwsJyexgRERERyWO5DoAmk+m26/zGxsZy5coVAMqUKYOjo2OuixMRERGRvJfrAHjq1Kk7bhs2bBjnz59n7dq1uT2EiIiIiOSDfHkGsHz58ixcuJDLly/z/vvv58chRERERCSX8u0lEAcHBx599FEWLVqUX4cQERERkVzI17eAr1+/zqVLl/LzECIiIiKSQ/kWAP/55x9++eUXqlSpkl+HEBEREZFcyPVLIK1bt75te2pqKmfPnrW8JDJq1KjcHkJERERE8kGuA+Dff/9923aDwYCnpyft2rVj2LBhPProo7k9hIiIiIjkg3uaB1BERERE7j/3vBbwhQsXOHv2LCaTCV9fX0qXLp0XdYmIiIhIPsnVSyBJSUlMmjSJgIAAypQpQ/369QkKCsLX15eSJUsydOjQO04ULSIiIiLWk+MAGBERQYMGDRgxYgRhYWGUKVOGoKAggoKCKFOmDJcuXWLq1KnUr1+fdevWWb4XGRmpOQFFRERECoEcBcCUlBQ6duzIoUOHePrppzly5AhnzpwhODiY4OBgzpw5w5EjR3jmmWe4dOkSTzzxBKdOnSIsLIxmzZpx9OjR/BqHiIiIiGRTjp4B/P777zl8+DCjR49m9OjRt+1TpUoVfvrpJypXrszo0aN55plnOHXqFDExMdSrVy9PihYRERGR3MvRFcBFixZRqVKlbM3t98EHHxAQEEBwcDCJiYmsXr2aTp065bpQEREREckbOQqA//33H+3atcNgMNy1r8FgsPTdsWMHLVu2zG2NIiIiIpKHchQAr127hoeHR7b7u7u7Y29vT6VKlXJcmIiIiIjkjxwFQC8vL44fP57t/mFhYXh5eeW4KBERERHJPzkKgI0bN2bVqlVERUXdtW9UVBQrVqygWbNmuS5ORERERPJejgLgyy+/zLVr13jyySeJiYnJst/Fixd58sknuX79OoMGDbrnIkVEREQk7+RoGphWrVoxYMAAZsyYQbVq1Rg0aBCtW7emXLlywI1JotevX8+MGTOIiYlh4MCBevlDREREpJDJ8VrA33zzDe7u7nzxxRdMmDCBCRMmZNhuNpsxGo289dZbmbaJiIiIiPXlOADa2dnx2WefMXDgQObMmUNwcLDlmcDSpUvTpEkTnn/+eQICAvK8WBERERG5dzkOgOkCAgL45JNP8rIWERERESkAOXoJRERERETufwqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYmEIbAHft2kXHjh0pVqwYrq6uNGrUiEWLFmX7+2FhYYwZM4bHH38cX19fDAYD5cuXv+N3DAZDlv/069fv3gYkIiIiUkjYW7uA29m4cSPt27fH2dmZ3r17U7RoUZYsWUKvXr2IiIhg+PDhd93HP//8w9ixY7Gzs6NatWpERUVl69j+/v63DXt16tTJ4ShERERECqdCFwBTU1MZMGAARqORzZs3W4LXqFGjCAoKYuTIkXTv3h1/f/877qd58+YEBwdTu3ZtihQpgrOzc7aOX758ecaMGXOPoxAREREpvArdLeANGzYQFhZGnz59Mlx18/DwYOTIkSQnJzN37ty77qdixYo0atSIIkWK5GO1IiIiIvefQncF8O+//wagXbt2mba1b98egE2bNuXb8a9cucIPP/xATEwMxYsXp2nTptSsWTPfjiciIiJS0ApdAAwNDQUgICAg07bSpUvj5uZm6ZMf9u/fz6BBgzK0dejQgblz5+Ll5ZVvxxUREREpKIUuAMbGxgI3bvnejru7u6VPXhs+fDjdunWjcuXKODo6cujQIcaNG8eqVavo3LkzwcHB2NnZZfn9pKQkkpKSLJ/j4uIASElJISUlBQCj0YidnR1paWmYTCZL3/T21NRUzGazpd3Ozg6j0Zhlu0hhk/7fejp7+xunmdTU1AztDg4OmEwm0tLSLG0GgwF7e/ss27P6u8mrv6fs1q4x3U9jMiBSmOTn31NOFLoAaE2TJ0/O8Llx48YsX76c1q1bs2nTJv744w+eeuqpLL8/YcIExo4dm6l9zZo1uLi4AODn50dgYCAHDhwgPDzc0qdKlSpUrVqVnTt3Eh0dbWmvU6cO/v7+bN68matXr2aoTVckpTBauXJlhs8dO3YkISGBjRs3Wtrs7e3p1KkTMTExBAcHW9qLFi1K69atiYiIYN++fZb2UqVK0aRJE0JDQwkJCbG05/Xf05o1azKEiFatWlGkSBGN6T4eEzggUpjk59+Tj49PtuswmG/+eVUI9OjRg19//ZXdu3dTr169TNuLFi2Kp6dnhkFnh7OzM6VLl+bUqVM5runnn3/m2WefZdiwYUyZMiXLfre7AliuXDliYmJwd3cH8v6X8IAvczwckXz1zWBdAdSYCs+YBk7VFUApPGYMyd8rgPHx8Xh4eBAbG2vJHVkpdFcA05/9Cw0NzRQAo6KiuHbtGkFBQQVaU8mSJQGIj4+/Yz8nJyecnJwytTs4OODgkPFXqJ2d3W1vJ6efyLLbLlLY3Prf+p3ajUbjbW9bZNWe1d9NXv095aT2rNo1psI3JpHCJL//nrJdR66/mU9atGgB3LhteqvVq1dn6FNQduzYAXDXlURERERE7geFLgC2adOGihUrMn/+/Az3wmNjYxk/fjyOjo707dvX0h4ZGcnRo0fv+cWQgwcPZrqtALBt2zYmTpyIg4MDPXr0uKdjiIiIiBQGhe6+or29PTNnzqR9+/Y0b948w1Jwp0+fZvLkyRmuxI0YMYK5c+cye/bsDEu4xcTE8NZbb1k+p6SkEBMTk6HP5MmTLbd3p0yZwooVK2jWrBnlypXDwcGBw4cPs2bNGgwGA19//TUPPfRQfg9fREREJN8VugAIN97o2rJlC6NHj2bhwoWkpKRQs2ZNJk6cSK9evbK1j2vXrmVaMSQ+Pj5D25gxYywBsGvXrly5coX9+/ezdu1akpOTKV26NL1792bIkCEF/tyhiIiISH4pdG8BP0ji4uKy/TZObuktYClsZgyxdgUi/0fnSClM8vv8mJPcUeieARQRERGR/KUAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG1NoA+CuXbvo2LEjxYoVw9XVlUaNGrFo0aIc7SMpKYmPPvqIgIAAnJ2d8fHxYeDAgVy4cCHL7/z8888EBQXh6uqKp6cnnTt3Zs+ePfc6HBEREZFCo1AGwI0bN9K0aVO2bNlCz549efnll4mKiqJXr15MmTIlW/swmUx07dqV0aNHU7JkSYYMGULjxo2ZOXMmjRs3Jjo6OtN3PvnkE5599lkuXLjAyy+/TI8ePdi8eTNNmjRh69ateT1MEREREaswmM1ms7WLuFlqaipVq1blzJkzbN++nTp16gAQGxtLUFAQp06d4tixY/j7+99xP7Nnz6Z///48/fTT/PzzzxgMBgC+++47XnnlFQYOHMj3339v6R8aGkr16tWpWLEiO3fuxMPDA4B9+/bRqFEjKlasyKFDhzAas5+Z4+Li8PDwIDY2Fnd39xz+L5E9A77Ml92K5NqMIdauQOT/6BwphUl+nx9zkjsK3RXADRs2EBYWRp8+fSzhD8DDw4ORI0eSnJzM3Llz77qfGTNmADBhwgRL+AMYNGgQFStW5OeffyYhIcHSPnv2bFJTU3n//fct4Q+gTp06PP300xw5coQtW7bkwQhFRERErKvQBcC///4bgHbt2mXa1r59ewA2bdp0x30kJiayY8cOqlSpkulKocFg4NFHHyU+Pp7du3fn6XFFRERE7geFLgCGhoYCEBAQkGlb6dKlcXNzs/TJSlhYGCaT6bb7uHnfN+8nNDQUNzc3Spcuna3+IiIiIvcre2sXcKvY2FiADLdhb+bu7m7pcy/7uLlf+r97eXllu//tJCUlkZSUlKmOS5cukZKSAoDRaMTOzo60tDRMJpOlb3p7amoqNz+WaWdnh9FozLI9OfGOJYkUuIsXUzJ8tre/cZpJTU3N0O7g4IDJZCItLc3SZjAYsLe3z7I9q7+bvPp7Sv87vVvtGtP9M6bkRAMihUVcHPn69xQfHw9Adl7vKHQB8H42YcIExo4dm6m9QoUKVqhGxDr+N8LaFYiIFE4FdX68evVqlhfB0hW6AJhecFZX2+Li4vD09LznfdzcL/3fc9L/dkaMGMGwYcMsn00mE5cuXaJEiRIZXkSRwicuLo5y5coRERGRb29si4jcj3R+vH+YzWauXr2Kj4/PXfsWugB48/N29erVy7AtKiqKa9euERQUdMd9VKxYEaPRmOUze7d7zjAgIIDg4GCioqIyPQd4p+cSb+bk5ISTk1OGtmLFit3xO1K4uLu76wQnInIbOj/eH+52sSpdoXsJpEWLFgCsWbMm07bVq1dn6JOVIkWKEBQUREhICKdPn86wzWw2s3btWlxdXalfv36eHldERETkflDoAmCbNm2oWLEi8+fPZ9++fZb22NhYxo8fj6OjI3379rW0R0ZGcvTo0Uy3bwcOHAjcuC1788OQ33//PSdOnOCZZ56hSJEilvYXXngBe3t7Pvnkkwz72rdvH7/88gvVqlWjWbNmeT1cERERkQJX6G4B29vbM3PmTNq3b0/z5s3p3bs3RYsWZcmSJZw+fZrJkydTvnx5S/8RI0Ywd+5cZs+eTb9+/Sztzz//PAsXLuSXX37h5MmTtGjRguPHj/Pbb79RoUIFPv744wzHrVy5MmPGjOGDDz6gdu3adOvWjatXr7JgwQLgxsTSOVkFRO4vTk5OjB49OtMtfBERW6fz44Op0C0Fl27nzp2MHj2abdu2kZKSQs2aNRk2bBi9evXK0K9fv363DYBwY1qWTz/9lJ9++omIiAiKFy9O586d+fjjj/H29r7tcX/++We+/PJLDh8+jKOjI02bNmXcuHHUrVs3v4YqIiIiUqAKbQAUERERkfyhe5oiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEXuQfpL9GazGb1QLyIi9wsFQJFcSA97BoPB8v+m/7uIiNxw8w/jtLQ0K1Yit9I8gCK5tHr1ak6dOkVYWBjFixenefPmVKpUiZIlS1pWjTGbzQqGImLTEhMTcXZ2tnYZcotCtxScSGEXHh7OF198wVdffZXptq+/vz+dO3emT58+NG7cWOFPRGzWyZMnWbRoEYcOHSI6OppatWpRr149qlatir+/P8WKFQPAZDJpqVUr0BVAkRwaPHgws2bNomvXrjz77LN4eXmxY8cO9uzZw65du/jvv/8A6NSpEx9++CFBQUE6wYmITfnll18YN24cR48epUiRIiQkJFi2lS1blrZt2/L000/z6KOPWrFK26YAKJIDSUlJFC9enF69ejFr1qxM248ePcrGjRuZP38+W7dupVq1asydO5f69etboVoRkYKXlJRElSpVcHJy4v3336dTp06cO3eOQ4cOcejQIbZs2cLu3btJTEykW7dujBkzhurVq+uHcgHTLWCRHFi7di1paWk0b94cyPj2r9FopGrVqlStWpV+/foxe/Zshg0bxsCBA1m+fDk+Pj7WLF1EpED88ssvREZGMnv2bPr06QNAiRIlqFmzJiaTiRMnTrB161bmzZvHr7/+yunTp1myZAlly5a1cuW2RVFbJAfs7Owwm81ER0cDN95qMxgMll+tJpMJk8lEkSJFePXVVxk2bBj79u3jwIED1ixbRKTAbN26FS8vLxo0aADcOC+m/1g2Go1UqlSJ559/nl9//ZWPPvqIPXv28Oqrr1q5atujACiSA40aNcLR0ZFffvmF0NBQ7O3tM7zokR4G06c76NmzJy4uLmzfvt1aJYuIFCh/f3+io6M5c+YMkHnarPQw6OHhwQcffECnTp3YtWsX4eHhVqvZFikAimST2WzG09OTqVOnsm/fPlq2bMl3333HyZMnLYEv/QSX/vn06dOkpqbq1oaI2IzGjRuTnJzMpEmTiI6Oxs7OLkP4gxvnyvTzZNOmTbl27RrHjx+3Ws22SAFQJJvST2Ddu3dn5MiRXLp0ibfeeovXXnuN77//nuDgYMsvXkdHR06dOsWsWbOws7OjR48e1ixdRKRAmEwm2rRpw/vvv8/q1atp2LAh06dP59ixY5Z5UdPPpXZ2dgBERUWRkpKil+UKmN4CFsmlzZs3891337F27VouXbpE2bJlqVy5Mo6Ojri5ubFr1y6ioqIYOnQon3zyibXLFREpMOfOnWPSpElMnz4do9FI48aNad26NXXr1qVatWpUqlSJxMREfvrpJ95//30aN27MH3/8Ye2ybYoCoEg23G5FD7PZTEREBHv37mXHjh38+++/HDlyhDNnzuDq6oqfnx/vv/8+TzzxBC4uLlaqXETEerZv384PP/zAX3/9RVRUFEWLFqV48eI4ODjg5OTE4cOHqV+/PtOnTycoKMja5doUBUCRbLp+/Tr29vacPn2aIkWKZHiuLyEhgQsXLuDg4EBSUhKXLl2iXr16VqxWRKRg3e6HsslkIiYmhtDQUP7991+2b9/Orl27uHjxIjVq1CAgIIAJEybg7e1tpaptlwKgyF0kJSWxadMmpk+fzvbt23Fzc8NoNFK+fHkee+wxevfuja+vr7XLFBGxKpPJxLlz57h06RJRUVFUr149ww/lpKQkAJycnIiKisLNzQ03NzdA66ZbgwKgyF18+eWXjB07lqSkJOrUqWNZ+u38+fPAjQmge/TowSuvvEKzZs0sJzGdzETEVhw/fpxvvvmGuXPnEh8fT3JyMgaDgZo1a9KrVy+eeeYZ/Pz8MnxHoc+6FABF7iAxMREfHx9q1KjBokWLcHd3x9XVFYAdO3awePFiy6z3Pj4+TJgwgeeee87KVYuIFJzk5GQ6derEhg0baNKkCU2bNiUmJoZdu3YREhJCcnIyAN26dWP48OE0atTIyhULKACK3NG8efMYOHAg8+bN46mnngIy/2pNS0tj1qxZTJ48mdDQUGbOnEn//v2tVbKISIH68ccfefXVVxkzZgwjRozIsG3nzp2sWLGCJUuW8N9//+Hr68v06dPp2rWrlaqVdJoHUOQOQkJCMBqNlnV8U1JSLOHPZDKRlpaGnZ0dAwYM4Ntvv7VMFH358mVrli0iUmAWLVpEnTp16N27NwCpqamWSZ6DgoIYO3YsO3bsYNq0aaSlpdG/f3/++usva5YsKACK3FGTJk24fv06hw8fBsDBwcGyzWg0WiYyNZvNtG7dmlGjRnHkyBH27dtnjXJFRApUYmIiKSkpJCQkULp0aeDG88/p58b09dFdXV0ZPHgw06ZN4/Lly8ybNw/4v5VBpOApAIrcQd26dalevTqvvvoqX3/9NRcvXrxtv9TUVAA8PDwwmUzExsYWZJkiIlbh7OxM3bp1OXTokGXN8/TwBzd+KBuNRsv6v926daNjx47s3buXU6dO6SUQK1IAFLkDb29vxo4dS9GiRXnvvfd499132bZtm+X2Rrr0+f/279+P0WikdevWVqpYRKRgPffcc3h4eNCrVy++//57oqKiMvUxmUwYDAaSk5MpVaoUMTExeHl5WaFaSaeXQESyITg4mI8//phVq1YB0KhRIx5//HHq1q1rmdH+zz//5IsvvqB79+6W2xsiIrZg6tSpjBw5EqPRyJNPPknv3r0JDAykWLFiFClSxNJv+/btDBgwAB8fH1avXm3FikUBUOQOUlNTLbcwjh07xooVK1i2bBm7du3i+vXr2NnZ4ezsTHx8PADPPvssH374IQEBAVauXESkYAUHBzN+/HjWrl1Lamoq9erV45FHHqFChQo4OzsDMGXKFM6dO8fChQtp3769lSu2bQqAIjl0/fp1tm3bxt69e4mJiSEuLo60tDS6d+9O8+bNLSc6ERFbkJKSgoODA2azmdDQUDZu3Mj69evZtWsXUVFRlhVAADw9Pfnmm2/o1auXFSsWUAAUua1Lly6xe/dugoOD8fT0xMnJCV9fX+rVq0eZMmUs/ZKSknBycrJipSIi1nf9+nVcXFwsn2NjYzl8+DAREREkJSVx9uxZKlWqRJMmTbR0ZiGhAChyiy1btvDuu+8SHBwM3JjSwGw24+LiQvXq1Wnbti0dO3YkKCgIR0dHkpOTcXR0tHLVIiIFKzg4mN9++42YmBgcHR3x9PSkbt26tGnThhIlSli7PLkLBUCRmyQmJlKnTh2io6MZO3YsXl5e2NnZERUVxbp161i7di3Xr18nICCAV199lcGDB2Nvb2/tskVECkxqaiqffvopo0aNAqBYsWIkJSWRkJAAgL+/P507d+bpp5+mUaNGGI1Gy21iKTwUAEVuMnPmTN58802mT5/OCy+8kGn7yZMnWbx4MbNnzyYkJIQ+ffowbdo0PD09rVCtiEjB+/nnn3nhhRfo2LEjo0aNwmQyUaRIEY4cOcKCBQtYunQpJpMJf39/hgwZwptvvmntkuU2FABFbtKrVy/27t3LihUrCAgIuO2vVpPJxL///su4ceNYvnw5X375JW+88YaVKhYRKVhNmjTB3t6eH374gapVq2baHhcXx6xZs/j66685deoUb775JuPGjcswHYxYnyaCFvn/UlNTKVmyJOfOnbMsaXS7WxZGo5EGDRowZ84c6tWrx7Rp07h+/XpBlysiUuAuXbrEyZMn8ff3p3LlypYVPuD/1kd3d3dnyJAhLFy4kIYNG/L555+zadMmK1cut1IAFOHGepT29vY0bdqU69evM2zYMC5fvgz830ntZqmpqRQvXpzmzZsTHR1NSEiINcoWESlQZrOZMmXKcOLECYxGIwaDwbKc283ro8ONpTTnzZuHg4OD5bawFB4KgCJgOYG1aNGC5s2b8+OPPzJixAhOnTqV4aSWlpZmCYtJSUkYDAZMJpMmfhYRm1CiRAlat25NcHAwY8aM4dKlS0DmH8rp/+7r60vt2rXZt2+fZc10KRwUAEVu4uvry4IFC+jatSs//PADFStWpFevXixbtozk5GTs7Owstzs2btzIwoULad68OW5ublauXESkYPTv3x9/f38mTpzIhx9+yPHjxzNd/Uv/99DQUFJSUvD29tZ0WYWMXgIRuUlaWhp2dnacPHmSOXPm8O233xITEwNA0aJFadq0KQEBAezfv5+tW7dSvnx55syZQ9OmTa1cuYhIwQkNDWXo0KGsXLkSgE6dOtG/f39atGiBo6MjCQkJeHp68vLLLzNnzhyWLFlC165drVy13EwBUOT/M5vNllvB6VJSUli0aBE///wzu3btIj4+Hnt7e1JSUujSpQtvv/02DRo0sFLFIiIFLzU1FXt7e0JCQpg/fz7z588nLCwMABcXFwIDAzGZTPz333/ExsbSv39/Zs6caeWq5VYKgCL/n8lkIiIiAn9/f65cuYLRaMTd3d2y/dKlSxw6dAhPT0/LP66urrcNjiIitiI2NpaVK1eyatUqQkJCiI+P59KlSzz00EO88MIL9OzZU4/JFEIKgGLzEhIS+Pzzz1m9ejUHDx7E0dGR2rVrU6dOHerVq0fNmjWpWLEizs7O1i5VRKTA3fwj9/Dhw5hMJlxdXUlISMDX15dixYpZ+sbExHDlyhUqVKhAYmIirq6uVqpa7kYBUGxacnIyffr04bfffqN69eq4urpiMpm4cuUK4eHh2Nvb06BBA5555hmeffZZTWQqIjbHbDazZ88e3njjDQ4cOEB8fDzFihXD39+fhx9+mMaNG9O4cWMefvhhLfd2H1EAFJv2448/MnjwYAYPHszYsWNxc3MjKiqKs2fPcuzYMTZs2MCaNWuIiIigVatWTJgwgaCgIN32FRGbsWLFCgYOHEh8fDyPP/44RqPR8ozfwYMHSUtLo27duvTt25f+/fvj4uJi7ZIlGxQAxaa1aNGClJQUfv75ZypUqGB5CzjdpUuX2Lt3L7Nnz2b+/Pk0bNiQlStXau1fEbEZzZo148qVK3z11Ve0bt0agCtXrnD16lVCQ0NZvnw5S5cu5dSpU3Tu3JnPPvuMKlWqWLlquRsFQLFZcXFxNG/eHA8Pj0zLFN16hc9kMjF58mTee+89Xn/9daZOnVrQ5YqIFLjIyEgqVKjA22+/zUcffQSQ6e7H9evX2bdvH9OnT2fBggU88cQTLF68OMOPaSl8NBG02CSz2YybmxvVqlXj4MGDHDp0yNJuMpksJ7j0dS6NRiPDhg2jdu3a/Pvvv8TGxlqzfBGRAnH8+HEcHR2xs7PL8rEXFxcXmjRpwg8//MCQIUNYunQpy5cvL+BKJacUAMUmGQwGjEaj5dbGW2+9xYkTJyztQIZFzuHGOpcBAQFERkbi5ORkrdJFRApMtWrV8PHxYenSpURERFiWv7x1XV+TyYSbmxuDBw/GxcWFLVu2WKliyS4FQLFpgwcP5p133mHNmjXUrVuXd955h23btpGYmGgJgzdPf3DkyBGqVKmiKWFExCaULFmSxx57jAMHDjBy5EjOnTuH0Wi0/FC+dQ3gxMREvLy8uHz5srVKlmyyt3YBItaS/pzf8OHDKVKkCJMmTWLy5Mn88ssvNGrUiAYNGtCwYUOqVKnCjh07+Pzzzzl+/DiTJk2ydukiIgVm/PjxJCQk8MMPP7BkyRIGDBhA9+7dadKkSabn/NauXUt4eDidOnWyUrWSXXoJRGzWrS96nD17llmzZvHbb7+xf//+TP2LFSvGW2+9xciRIwuyTBERqzGZTBiNRs6cOcM333zDF198QVJSEs7OztSrV4/GjRvTsmVLEhMT2bx5MzNmzKB69ers2rXL2qXLXSgAitzEZDIRHR1NSEgIO3bsYOfOnbi6ulK5cmUaN25Mq1atrF2iiIjVXLp0iVmzZjF//nz27duXaXvXrl156623aNq0acEXJzmiACg2af/+/YSGhnLs2DHLyyABAQF4eXlletMtKSlJL32IiE1Jv0OSfgXwdo4fP86GDRsIDw/H398fLy8vHn30UU0EfZ9QABSbkpqayg8//MBHH33EhQsXMmwrXbo07du35+mnn6Zdu3YZtt3pJCgi8qBJS0tj7ty5/Pfffxw/fpyHHnqI+vXrU7lyZfz8/ChevPht5/nTKkn3DwVAsSkLFy5kwIABBAQE8NJLL1G7dm327t3Lvn37+Pfffzlw4AAmk4nGjRszatQoHn30UQU/EbEpe/bs4aOPPmLZsmU4OTmRlJRk2ebl5UXLli3p0aMHXbp0wdHREVDwux8pAIpNadiwISaTifnz5xMQEJBh28mTJ9m8eTO//vorK1aswMPDgxkzZtC9e3crVSsiUvC6dOnC1q1befnll+nXrx9paWkcOHCA//77j+DgYHbu3ElcXBytWrVi7NixNGvWTAHwPqQAKDbjwoULVK1alb59+/Lll18CN25z3Dz5c3rb0qVLef311zGZTCxZskQPNIuITYiIiMDf35/33nuP8ePHZ9oeHh7Ozp07Wbx4MYsXL8bLy4tFixbRvHlzK1Qr90L3tsRmxMbG4ubmxtmzZ4EbQe/mCU3Tl4Gzs7OjW7dufP7551y4cIG///7bsl1E5EG2fv16nJycqFevHnDj+eebV0Xy8/Oje/fuzJ49m1mzZpGUlMQrr7zC+fPnrVm25IICoNiMgIAA/Pz8WLt2LRs3brzt2pZGo9FyouvRowcVK1Zk586dpKam6vaGiDzwSpQogdls5uTJk8D/BcBb10d3cXGhX79+DB06lCNHjnD48GFrli25oAAoNmXSpEkYjUY6dOjAJ598wtGjR0lJSQGwnODSP4eEhGBnZ4ezszP29lo0R0QefA0bNqRIkSLMmjWLw4cPY29vn+EuCdw4V6ampgLQokULXF1dNfHzfUgBUGxKUFAQH3/8MW5ubowdO5ZXXnmFadOmsXXrViIiIkhLS8PR0ZGUlBR++uknwsLC6NOnj7XLFhHJdyaTCS8vL6ZNm0ZISAiNGjXi448/5uDBg5a7ILfeCTl58iTx8fHUrFnTSlVLbuklELFJR44cYerUqSxfvpxz585RunRpatSogYeHB66urpw+fZrNmzfTsWNHli9fbu1yRUQKzNWrV/n666/55JNPiI+Pp379+rRt25YGDRpQvXp1qlSpAsCWLVsYMmQIkZGRlmer5f6hACg25eZnWaKioti3bx/bt29nx44dHDlyhPDwcAB8fX3p2bMn77zzDt7e3tYsWUTEKkJCQvj222/5448/OH36NEWLFsXb2xsnJyc8PDz4999/KV68OKNGjWLQoEHWLldySAFQHmjpgS8lJQWj0Uh0dDTJycn4+flZ+iQnJxMZGWm5xREeHk79+vVxc3OzYuUiIgUnq9WOLl26RFhYGLt377bMAXj69GkqVqyIr68vY8eOJSgo6LargkjhpgAoD7yjR4/y7bffsnz5cpycnDCbzZQpU4bWrVvTu3dvKlWqZO0SRUSsLiYmhvj4eE6dOoWfnx8VKlSwbEtOTiY5ORk3NzcuXLhAcnIyZcuWtWK1cq8UAOWBtnHjRt58800OHTrEQw89ROXKlTlw4ECG51U6dOjAq6++yqOPPoqTk5PW/RURm3Lx4kWWLFnC559/zpkzZ0hLSyMtLY2HHnqI7t2706dPH6pVq2btMiWPKQDKA61FixaEhYUxc+ZMWrZsiZ2dHQ4ODhw8eJDFixezYMECjh8/jouLC++++y4ffvihtUsWESlQQ4cO5dtvv8XX15dHHnkER0dHduzYQVhYGNevXwegVatWvPvuu7Rt29YyX6rmRr2/KQDKA+vMmTNUqFCBMWPGMHLkSAwGw21PWkuWLGHSpEns2rWLd955h7Fjx+Lk5GSlqkVECs7p06cJCAjgqaeeYv78+QCWOyD79+9n1apVLF26lJ07d+Ls7Mynn37KG2+8Yc2SJY/oPpc8sPbu3YvBYKBYsWIYDAaSk5Mt4c9kMpGWlgZAt27d+N///kfdunWZNm0a//33nzXLFhEpMAsWLMDNzY2BAwdagl/6JM+1a9fmvffe459//uGXX36hUqVKDBkyhK+//tqaJUseUQCUB9bDDz8MwIEDBwBwdHS0bDMajZa31sxmM1WqVOHbb78lISGBLVu2FHyxIiJWcP78eUwmE8WLFwdurJGevvKRyWTCZDLh4OBAr169mDt3LmXKlOG7777j2rVr1ixb8oACoDywfH196datGzNmzGDkyJFERETctl/6r12j0UixYsU4ffp0QZYpImI1zZs3Jy4uju3btwPg4OBg2WY0GjNcFQwMDGTw4MGcOnWKnTt3WqVeyTsKgPLAcnR05O233+ahhx5i0qRJDBkyhNWrV5OUlJShX/oJb+/evcTFxdGiRQtrlCsiUuCaNm1KnTp1GDx4MGPHjuXkyZPc+mrAzZ+LFi1KQkJChjsqcn/SSyDywDtx4gRjx45l4cKFJCcnU6dOHZ544gkaN26Mq6srjo6OhIWFMWTIEDw8PDh69Ki1SxYRKTB//vknAwYMIDo6mq5du/L000/TqFEjSpYsibOzs+XZ6ejoaN544w1Wr17NpUuXrFy13CsFQHlgpb/o4eDgwJkzZyxvs23dupW4uDiMRiMeHh5cvnwZuPHA84QJE+jQoYOVKxcRKVhhYWGMGzeO33//natXr1KzZk1atmxJ9erVcXV1xcXFhXnz5rFixQqGDx/O+PHjrV2y3CMFQLEpKSkplrV/z549y9WrV7l06RKdO3emffv2+Pr6WrtEEZECk5qaip2dnWUZzE2bNrF27VqCg4OJiIggOTk5Q/9Ro0bx2muvUbJkSStVLHlFAVAeOKmpqYSEhLBmzRpcXV1xcHCgRIkS1KlTJ8MawElJSZrvT0RsXnJycoZn+q5fv87BgwcJCwsjPj6eyMhIXF1d6dChAzVq1LBipZKXFADlgXLy5EmmTJnCN998k6G9SJEiBAQE0LJlSzp27EiTJk1wc3PL8OtXRMRWnDhxgpUrV3L48GEcHR1xcXGhRo0atGrVSndCbIQCoDxQevTowdKlSxkwYAANGzbE3t6e2NhYNm/ezJo1a7hy5QplypThhRde4I033sDLy8vaJYuIFKiFCxfyzjvvEBERgcFgwMXFhfj4eABKly7NY489Rq9evWjZsiWOjo6kpKRkmB5GHgwKgPLAOHXqFJUqVWLo0KFMmjQp01W9c+fOsWzZMmbNmsXu3btp1aoV33//PZUqVbJSxSIiBSsiIoK6devi6enJ1KlTcXV1pWjRopw+fZrffvuNJUuWkJCQgKenJ4MGDeLdd9/Fw8PD2mVLPtA8gPLAWLFiBY6OjrRq1cqy9NvNfHx8ePnll5k3bx6vvPIKGzduZMKECZYl4UREHnQzZszAaDTyxRdf8Nhjj9G8eXMCAwN54okn+N///seVK1eYNWsW/v7+TJw4kRdffJHo6Ghrly35QAFQHhgODg4kJibi4uJi+Xw7lStXZsqUKbz00kvMnj2bsLCwgixTRMRqtm3bRpkyZQgMDAT+byWkm6fN6tevH7/99hvPPPMMv/32Gz/99JM1S5Z8ogAoD4xGjRpRpEgRRo0axfHjxzEYDJjN5kxX+FJSUnB2dqZdu3YYjUaCg4OtVLGISMFJSUmhYsWKhIWFWdb+TV/39+b10QHKly/Pt99+S+3atfnf//5HXFycVWqW/KMAKA+MgIAAnn32WbZs2cK7777Lvn37MBgMlpOayWTCbDZbrgzGx8djMBj0xpuI2AQHBweaN29OfHw8AwcOtKx7fusPZbPZjMlkwtXVlYYNG3LmzBmioqKsVbbkEwVAeWAUKVKE6dOn8/rrr/P7779Tt25dOnbsyIIFC7h69SpGo9HyYsj58+eZPXs2xYsXp23btlauXESkYHTo0IE2bdowb9483nnnHf79998MP5QBDAYDRqORK1eukJSUhIODA5UrV7Zi1ZIf9BawPDBMJhNGo5ELFy7wyy+/8NVXX3Hy5EkAXFxcaNKkCfXr1ycsLIwtW7YQGxvLuHHjGDp0qJUrFxEpOFevXmXo0KHMmjULgBYtWvDSSy/RoUMH3NzcuH79Op6ennz33Xe8++67PPPMM5nmVpX7nwKgPBDMZvNtJ3P+448/mDNnDlu2bOHy5cs4OTmRkJBAvXr1ePvtt+ncubPlpRERkQddamoq9vb2nDlzhsWLFzN37lwOHDgA3HgeMCgoCE9PT44ePUpYWBhNmzZlzpw5PPTQQ1auXPKaAqA8MM6ePYuvry8JCQmkpKTg7u5u2Xbt2jX27NkDgK+vL25ubnh7e1urVBGRQiEpKYm//vqLP//8k/379xMXF8fVq1dxdHTkmWee4ZVXXqFs2bLWLlPygQKg3NfMZjPLly/nxx9/5ODBg1y7do1atWpRq1YtAgMDqVmzJpUqVcLV1dXapYqIWNWFCxeIjo6mRIkSxMbGUrJkSUqUKGHZfvnyZc6dO2cJfO7u7lom8wGmACj3tVGjRjF58mRcXFwoV64cKSkpJCcnExERgdlspnbt2nTv3p3nnnuO0qVLW7tcEZECFxkZyfvvv8/atWs5e/YsRYsWpUKFClStWpWgoCCaNGlCrVq1LI/DZPVIjTxYFADlvnXq1Clq1KhBy5YtmTJlClWrViUmJoaIiAjCwsLYvHkzq1evJjQ0lNq1azN+/Hgee+wxy8siIiIPuqioKJ588kl27NhhecnDaDRy+vRpDhw4QEJCAtWrV6dnz5689NJL+Pj4WLtkKSAKgHLfGjduHF9++SWLFi2iTZs2loeb08XFxXH48GEWLVrE1KlT8fb2ZtWqVdSpU8d6RYuIFKDRo0czdepUxo4dy5tvvgnAlStXuHbtGidPnmTNmjX89ttvHD16lIYNG/LZZ5/RtGlTXQW0AQqAct96/vnnWbt2LXv37sXb29tywrrdiWvhwoUMGjSIatWqaeUPEbEZNWrUoGLFisyaNYtSpUplOj8mJSUREhLC3Llz+eKLL6hSpQqbNm3Cy8vLilVLQdB9MLlv1apVi6ioKP755x/gxuSlJpMpw8kt/fdNr169eOqppzh+/DghISFWqVdEpCCdP38es9lMUlISpUqVAsj049jJyYlatWoxceJEpk6dSkhICJ9//rk1ypUCpgAo962goCBcXV358MMP2b17N4Dl2b70pYzSQyHcWCouISFBa1qKyAPPbDZTqlQpatSowY4dO9i5c6el/db10eHGHICvv/46Dz/8MLt27eLatWsFXbIUMAVAuS+ZzWYeeeQRvvjiC0JDQwkKCmLQoEGsX7+eq1evWpYyghuhMCEhgYMHD+Ls7EyDBg2sXL2ISP5KPwe2a9eOq1ev8tZbb3H48OFM66OnpaVZ7pTExcVRrlw5Lly4gJubmzXLlwJgf/cuIoVP+m2Mp59+mtTUVEaPHs2MGTNYunQpjRs3pmHDhgQFBVG3bl1CQ0OZNWsWS5Ys4fXXX7dy5SIiBWfAgAFcunSJkSNHUrNmTfr27UufPn1o3rw5zs7OwP89KrNr1y72799Px44drVmyFBC9BCL3pVsfZI6Pj2fmzJksXLiQXbt2WW5xGAwG7O3tSUlJoV+/fowbNw5fX19rlS0iUmDSz5NXrlxh1qxZTJw4kejoaOzs7KhXrx5NmzalVatWeHh4sGvXLqZPn87Vq1fZsGEDNWvWtHb5ks8UAOWBEhMTw7Fjx9i+fTv//PMPaWlpVK5cmWrVqvHiiy9auzwRkQJz6w/lxMRE5s6dy//+97/bzoZQvXp1RowYwTPPPFOQZYqVKADKfefChQscPHiQY8eOce3aNYKCgqhatSolS5a0PNuSLikpCScnJ8tnzW0lIgLh4eGsW7eOQ4cOUbp0aby8vGjWrBmVKlWydmlSQBQA5b6yatUqPv7440y/XosXL06bNm3o1asXXbp0wcHBwbJNK3+IiK3566+/OHToEPv27cPb25v69etTqVIlypUrR4kSJTKcI8U2KQDKfSMiIoKWLVsSHx9Pv379aNWqFSdOnGDv3r3s37+fAwcOkJSURPXq1Rk5ciTdu3fH0dFRV/1ExGZcuXKFCRMm8Nlnn2FnZ5dhypfixYvTtGlTnnzySR5//HGKFy9u2abzpO3RW8By3/j++++5fPkyM2fO5Kmnnsqw7cyZM2zbto1ly5Yxf/58nn32Wc6cOcM777yjk5qI2IwZM2Ywffp0nnjiCd544w18fHzYu3cvISEh7Nq1i+DgYP78808CAwP58MMPeeKJJ4DME0TLg09XAOW+0ahRI4oUKcLixYspWbIkqampGea0Srdx40aGDx/Of//9xzfffEP//v2tVLGISMEqX748Dz/8MHPnzqVEiRIZtp07d469e/eybNkyZs2aRVpaGj/88AMvvfSSlaoVa9KDUXJfuHbtGkWLFiUqKgoXFxfgxgTP6eEvfeUPgFatWvHjjz/i4uLCH3/8YdkuIvIgO3r0KBcvXqR27dqW8GcymSznRh8fHzp16sS0adP4448/qFChAu+++67WR7dRCoByX3Bzc6NevXqEhISwYMECgEwvdqR/NplMBAYG0rx5c44ePcrp06d1e0NEHnhms5lixYoRFhYGQGpqKpBxiUyz2YyjoyMdO3bk888/5/Lly5b11MW2KADKfSN9ncqXXnqJN954gz179pCYmAj83/MrqampGI1G4uLicHR0JDExEX9/f2uWLSJSIKpVq4avry8rV65k1apV2NvbZ/qhfPP66I888gjly5dn165d1ihXrEwBUO4bvr6+fPTRR5QvX57p06czaNAgJk+ezN9//83p06dJTEzE3v7Ge01//vknf//9N4899piVqxYRyX/pj7l89dVXuLu706lTJ4YOHcrOnTsz/VBOSUkBICQkhKSkJHx8fKxTtFiVXgKRQu/W6QkuXbrEhAkTWLRoEREREZQqVYqHH34YHx8fXFxcSEhIYNGiRVSoUIGlS5dSpUoVK1YvIlJw0tLSmDdvHiNGjCAqKorq1avTrl07mjRpQvXq1alatSpGo5GzZ8/y9ttvs3jxYnbs2EHdunWtXboUMAVAuS+kh8AzZ87g4+OD0Wjk0KFDLF++nL///psjR44QEREBgKenJ3Xq1OGrr76iRo0aVq5cRKTgRUdHM336dBYtWsSxY8dwcXHB19cXNzc3ihcvztGjR4mOjuaFF17gm2++sXa5YgUKgFKopaamsnXrVmbNmsWxY8cwGAy4uLjQoEEDevbsSWBgIGazmYiICBISEjhx4gRVq1alXLly2Nvba3JTEbEp6TMi2NnZkZCQQGhoKLt27WLr1q3s2LGDo0ePUqpUKcqVK8dLL73Es88+i6urq7XLFitQAJRCbfLkyYwbN46rV69SqVIl7OzsCAkJsWyvXr06r776Kt27d8fLy8uKlYqIFE4mk4nExEQcHR2JjY0lKipKd0dEAVAKr5MnT1KzZk3q1q3L3LlzcXR0xNvbm6ioKP78808WL17M33//DdyY+2/ixInUr1/fukWLiBSghIQEwsPD8fPzo0iRIhm2mUwmDAaD5S7IrXdEtE66bVMAlEJr1KhRfP/998yfP582bdoAmU9gBw8eZPLkySxatAh/f39+/vln6tWrZ62SRUQK1KeffsqSJUt46qmnaNSoEVWqVMHb2zvDCknp/2c+/dwZHR2Np6enZdYEsU0KgFJodevWjX379rFx40b8/PxITU21PNeX/oxLuqlTpzJ06FCef/55Zs+ebcWqRUQKTtmyZTl37hx2dnZ4eHjQpEkT2rVrR8OGDalYsWKm5eDi4+MZM2YMFy9eZObMmboCaMMU/6XQCgwM5Pfff+fatWsAll+rN6//m35F8M033+Sff/5hw4YNnDhxgooVK1qtbhGRgnDs2DFiY2Np3Lgxffr0Ye3atQQHB7N8+XL8/Pxo2bIlbdu2JTAwEF9fX4oVK8ahQ4eYMWMGLVu2VPizcQqAUmi1atUKgGeeeYYpU6bQrFkzHB0dM/VLS0vDzs6OKlWqsGrVKktgFBF5kB07dozExETatWvH4MGD6dy5MyEhIQQHB7NhwwaWLFnCzz//TPXq1WndujUdOnRg/fr1xMXFMWDAAGuXL1amW8BSaKWlpfHuu+/y+eefU7VqVQYPHkz37t3x9vbO1Pfy5csMGTKEVatWceHCBStUKyJSsH799Vd69uzJggUL6Nmzp6U9JSWF06dPs3//fv755x/LXKkODg6YzWacnJy4dOmSFSuXwkABUAq977//ns8++4wTJ07g4+PDk08+yWOPPUa5cuWws7OjWLFiTJs2jS+//JJXX32VKVOmWLtkEZF8ZzabOXr0KM7OzlSoUOG2857Gx8dz7NgxQkJCmD17NmvXruW1117jq6++slLVUlgoAEqhZzabOX78ODNmzGDBggWcOXMGAC8vLxwcHIiMjMRkMvH0008zceJEypYta+WKRUSs63Zh8I033mD69On8+++/BAYGWqkyKSwUAOW+Eh8fz86dO1m2bBnnzp3jwoULuLu707NnT7p164azs7O1SxQRKTTS5/o7deoUXbt25fLly4SHh1u7LCkE9BKI3FdcXV1p1aoVrVq1IiUlBQcHB2uXJCJSaKW/6Xv27FlSUlJ49dVXrVyRFBa6AigiIvKAM5vNnDlzhuLFi2vtXwEUAEVERERsjmaBFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMf8PHaurYWWri3wAAAAASUVORK5CYII=" 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" }, - "execution_count": 45, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -534,27 +300,27 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:08.520972Z", - "start_time": "2023-11-10T01:53:04.549457Z" + "end_time": "2023-11-10T03:10:17.943025Z", + "start_time": "2023-11-10T03:10:10.706205Z" } }, - "id": "352129ef4f8f6cff" + "id": "cbb3c2d9a11b43ac" }, { "cell_type": "markdown", "source": [ - "# Step 5: Pachinko \n", + "# Step 5: Burglary Alarm Example: \n", "\n", - "Pachinko is a popular Japanese game that combines elements of pinball and slot machines. Players purchase steel balls, launch them into a playfield filled with pins, and aim to land them in specific pockets. Let us now consider a pachinko game for 15 pins, in which a ball goes to the left or right of the pin with a probability of 0.5 in each case. You can use the following code to plot the Pachinko game." + "Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." ], "metadata": { "collapsed": false }, - "id": "438ad95c79da22d9" + "id": "72989e15f2fdd872" }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 16, "outputs": [ { "data": { @@ -567,159 +333,197 @@ ], "source": [ "import matplotlib.pyplot as plt\n", - "import networkx as nx\n", "\n", - "# Create a new graph\n", + "# Create a directed graph\n", "G = nx.DiGraph()\n", - "\n", - "# Add nodes with their positions\n", - "positions = {'A': (2, -1), 'B': (1, -2.5), 'C': (3, -2.5),\n", - " 'D': (0, -4), 'E': (2, -4), 'F': (4, -4),\n", - " 'G': (-1, -5.5), 'H': (1, -5.5), 'I': (3, -5.5), 'J': (5, -5.5),\n", - " 'K': (-2, -7), 'L': (0, -7), 'M': (2, -7), 'N': (4, -7), 'O': (6, -7)}\n", - "\n", - "for node, pos in positions.items():\n", - " G.add_node(node, pos=pos)\n", - "\n", - "# Add edges with labels\n", - "edges = [('A', 'B', '1/2'), ('A', 'C', '1/2'),\n", - " ('B', 'D', '1/2'), ('B', 'E', '1/2'), \n", - " ('C', 'E', '1/2'), ('C', 'F', '1/2'),\n", - " ('D', 'G', '1/2'), ('D', 'H', '1/2'),\n", - " ('E', 'H', '1/2'), ('E', 'I', '1/2'),\n", - " ('F', 'I', '1/2'), ('F', 'J', '1/2'),\n", - " ('G', 'K', '1/2'), ('G', 'L', '1/2'),\n", - " ('H', 'L', '1/2'), ('H', 'M', '1/2'),\n", - " ('I', 'M', '1/2'), ('I', 'N', '1/2'),\n", - " ('J', 'N', '1/2'), ('J', 'O', '1/2')]\n", - "\n", - "for u, v, weight in edges:\n", - " G.add_edge(u, v, weight=weight)\n", - "\n", - "# Draw the graph\n", - "plt.figure(figsize=(10, 8))\n", - "nx.draw(G, pos=positions, with_labels=True, node_color='skyblue', node_size=2000, edge_color='gray')\n", - "nx.draw_networkx_edge_labels(G, pos=positions, edge_labels={(u, v): d['weight'] for u, v, d in G.edges(data=True)})\n", - "\n", - "plt.title(\"Pachinko\")\n", - "plt.show()\n" + "# Add nodes\n", + "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", + "# Add edges\n", + "G.add_edges_from([(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"),\n", + " (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")])\n", + "# Manually set positions\n", + "pos = {\"Burglary\": (0, 1), \"Earthquake\": (1, 1),\n", + " \"Alarm\": (0.5, 0.5),\n", + " \"JohnCalls\": (0, 0), \"MaryCalls\": (1, 0)}\n", + "# Draw the network\n", + "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", + "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", + "plt.show()\n", + " " ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:08.594859Z", - "start_time": "2023-11-10T01:53:08.521355Z" + "end_time": "2023-11-10T03:10:18.025012Z", + "start_time": "2023-11-10T03:10:17.953579Z" } }, - "id": "44baa6f9eaf8b320" + "id": "16f5ec62b6f90570" }, { "cell_type": "markdown", "source": [ - "To convert the Pachinko game into a quantum circuit, no negation of the variables is required, since: $P(X)=0.5=1-P(X)=P(-X)$." + "The Bayesian Network for this scenario involves the following variables:\n", + "\n", + "Burglary (B): Whether a burglary has occurred.\n", + "Earthquake (E): Whether an earthquake has occurred.\n", + "Alarm (A): Whether the alarm goes off.\n", + "John Calls (J): Whether John calls you.\n", + "Mary Calls (M): Whether Mary calls you." ], "metadata": { "collapsed": false }, - "id": "5a4f56e71f082e28" + "id": "85ffd7ab1e8316e4" }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 17, "outputs": [], "source": [ - "# Initialize register with A=0, B=1, C=2, ...\n", - "qr = [QuantumRegister(1, name=str(i)) for i in range(15)]\n", - "qc_pac = QuantumCircuit(*qr, name='Pachinko')\n", - "# Angle for controlled-rotation gates\n", - "rotation_angle_0 = 2 * np.arcsin(0)\n", - "rotation_angle_1 = 2 * np.arcsin(1/2)\n", - "# Specify control qubits\n", - "c_qubits=list(range(10))+list(range(10))\n", - "c_qubits.sort()\n", - "# Specify target qubits\n", - "offset = 0\n", - "t_qubits = list()\n", - "for d in range(5):\n", - " offset += d\n", - " for i in range(d+1):\n", - " if (i+offset) != 0:\n", - " t_qubits.append(i+offset)\n", - " if (i != 0) and (i != d):\n", - " t_qubits.append(i+offset)\n", - "print(t_qubits)\n", - "# Apply controlled rotation gates with the specified angle\n", - "qc_pac.ry(rotation_angle_1, 0)\n", - "for cq, tq in zip(c_qubits, t_qubits):\n", - " qc_pac.cry(rotation_angle_1, control_qubit=qr[cq], target_qubit=qr[tq])\n", - " qc_pac.cry(rotation_angle_0, control_qubit=qr[cq], target_qubit=qr[tq])\n", - " \n", - "# Draw circuit\n", - "qc_pac.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_E = 2 * np.arcsin(np.sqrt(0.002))\n", + "theta_A_nBnE = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_A_nBE = 2 * np.arcsin(np.sqrt(0.29))\n", + "theta_A_BnE = 2 * np.arcsin(np.sqrt(0.94))\n", + "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", + "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", + "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_M_nA = 2 * np.arcsin(np.sqrt(0.01))\n", + "theta_M_A = 2 * np.arcsin(np.sqrt(0.7))" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:08.598697Z", - "start_time": "2023-11-10T01:53:08.596920Z" + "end_time": "2023-11-10T03:10:21.228824Z", + "start_time": "2023-11-10T03:10:21.206538Z" } }, - "id": "7000db4359eed86a" + "id": "f79d7c9a5cca338" }, { "cell_type": "markdown", "source": [ - "Assume that you have seen the ball at node E. Now inference the probability that the ball will land at node M." + "The Bayesian network can be represented by the following quantum circuit:" ], "metadata": { "collapsed": false }, - "id": "b10379ad3c6087cf" + "id": "d2693a276552450f" }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 18, "outputs": [ { "data": { "text/plain": "
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}, - "execution_count": 48, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "query = {'12': 1}\n", - "evidence = {'4': 1}\n", + "# Initialize register\n", + "var = ['B','E','A','J','M']\n", + "qr = [QuantumRegister(1, name=v) for v in var]\n", + "qc = QuantumCircuit(*qr, name='Pachinko')\n", + "# Specify control qubits\n", + "# P(B)\n", + "qc.ry(theta_B, qr[0])\n", + "# P(E)\n", + "qc.ry(theta_E, qr[1])\n", + "# P(A|-B,-E)\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", + "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", + "# P(A|-B,E)\n", + "qc.x(qr[0])\n", + "qc.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[0])\n", + "# P(A|B,-E)\n", + "qc.x(qr[1])\n", + "qc.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[1])\n", + "# P(A|B,E)\n", + "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", + "# P(J|-A)\n", + "qc.x(qr[2])\n", + "qc.cry(theta_J_nA, qr[2], qr[3])\n", + "qc.x(qr[2])\n", + "# P(J|A)\n", + "qc.cry(theta_J_A, qr[2], qr[3])\n", + "# P(M|-A)\n", + "qc.x(qr[2])\n", + "qc.cry(theta_M_nA, qr[2], qr[4])\n", + "qc.x(qr[2])\n", + "# P(M|A)\n", + "qc.cry(theta_M_A, qr[2], qr[4])\n", + "# Draw circuit\n", + "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)\n" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T03:10:22.846088Z", + "start_time": "2023-11-10T03:10:22.535173Z" + } + }, + "id": "85bb861283b06275" + }, + { + "cell_type": "markdown", + "source": [ + "Using this network, you can perform various probabilistic inferences. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." + ], + "metadata": { + "collapsed": false + }, + "id": "bb0e805d2f7fb30c" + }, + { + "cell_type": "code", + "execution_count": 21, + "outputs": [ + { + "data": { + "text/plain": "0.47266" + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "query = {'M': 1}\n", + "evidence = {'A': 1}\n", "# Initialize quantum bayesian inference framework\n", - "qbayesian = QBayesian(circuit=qc_pac)\n", + "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", "qbayesian.inference(query=query, evidence=evidence)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T01:53:08.982734Z", - "start_time": "2023-11-10T01:53:08.604771Z" + "end_time": "2023-11-10T03:28:03.558287Z", + "start_time": "2023-11-10T03:28:02.746890Z" } }, - "id": "f3ae346612ee10d" + "id": "5468619791203a79" }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "outputs": [], "source": [], "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-09T23:57:36.208046Z", - "start_time": "2023-11-09T23:57:36.205546Z" - } + "collapsed": false }, - "id": "6d2c15ce28c7d74a" + "id": "72a1d1076dd05cb0" } ], "metadata": { diff --git a/docs/tutorials/14_quantum_bayesian_inference.ipynb b/docs/tutorials/14_quantum_bayesian_inference.ipynb deleted file mode 100644 index 66b7a6202..000000000 --- a/docs/tutorials/14_quantum_bayesian_inference.ipynb +++ /dev/null @@ -1,565 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "source": [ - "# Quantum Bayesian Inference with Qiskit\n", - "\n", - "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions.\n", - "\n", - "##### This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", - "\n" - ], - "metadata": { - "collapsed": false - }, - "id": "4f1ee7dfd66dd6ac" - }, - { - "cell_type": "markdown", - "source": [ - "# Step 1: Creating Rotations for Bayesian Network\n", - "\n", - "In the first example we consider a simple Bayesian network that is only based on two nodes." - ], - "metadata": { - "collapsed": false - }, - "id": "6adf88f1d249b336" - }, - { - "cell_type": "code", - "execution_count": 9, - "outputs": [], - "source": [], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:06.237273Z", - "start_time": "2023-11-10T03:10:06.234362Z" - } - }, - "id": "e66a76d3f4afc0f7" - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "initial_id", - "metadata": { - "collapsed": true, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:06.512307Z", - "start_time": "2023-11-10T03:10:06.456456Z" - } - }, - "outputs": [ - { - "data": { - "text/plain": "
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- }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "import networkx as nx\n", - "# Create a directed graph\n", - "G = nx.DiGraph()\n", - "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", - "G.add_node('A', pos=(0, 0))\n", - "G.add_node('B', pos=(1, 0))\n", - "# Add a directed edge from A to B\n", - "G.add_edge('A', 'B')\n", - "# Get the positions of each node\n", - "pos = nx.get_node_attributes(G, 'pos')\n", - "# Draw the graph\n", - "nx.draw(G, pos, with_labels=True, node_size=2000, node_color='skyblue', arrowstyle='->', arrowsize=20)\n", - "# Show the plot\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "source": [ - "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", - "$$P(A)=0.2$$\n", - "$$P(B|A)=0.9$$\n", - "$$P(B|-A)=0.3$$" - ], - "metadata": { - "collapsed": false - }, - "id": "19b5a6da03a35a85" - }, - { - "cell_type": "code", - "execution_count": 11, - "outputs": [], - "source": [ - "# Include libraries\n", - "import numpy as np\n", - "# Define rotation angles\n", - "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", - "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_B_nA = 2 * np.arcsin(np.sqrt(0.3))" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:06.848751Z", - "start_time": "2023-11-10T03:10:06.845522Z" - } - }, - "id": "326c1d2e72f41202" - }, - { - "cell_type": "markdown", - "source": [ - "# Step 2: Create a Quantum Circuit for Bayesian Network\n", - "\n", - "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." - ], - "metadata": { - "collapsed": false - }, - "id": "33797564f68ae67" - }, - { - "cell_type": "code", - "execution_count": 12, - "outputs": [ - { - "data": { - "text/plain": "
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" - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit import QuantumRegister\n", - "from qiskit import QuantumCircuit\n", - "# Define quantum registers \n", - "qrA = QuantumRegister(1, name='A')\n", - "qrB = QuantumRegister(1, name='B')\n", - "# Define a 2-qubit quantum circuit\n", - "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", - "#Apply the R_Y_theta rotation gate on the first qubit\n", - "qc.ry(theta_A, 0)\n", - "# Apply the controlled-R_Y_theta rotation gate\n", - "qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB)\n", - "# Apply the X gate on the first qubit\n", - "qc.x(0)\n", - "# Apply the controlled-R_Y_theta rotation gate\n", - "qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB)\n", - "# Apply another X gate on the first qubit\n", - "qc.x(0)\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:07.780289Z", - "start_time": "2023-11-10T03:10:07.719567Z" - } - }, - "id": "4f99dbe56bc6910a" - }, - { - "cell_type": "markdown", - "source": [ - "# Step 3: Perform Inference\n", - "\n", - "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the `inference` method to estimate probabilities given evidence." - ], - "metadata": { - "collapsed": false - }, - "id": "5d22c72ca6352a56" - }, - { - "cell_type": "code", - "execution_count": 13, - "outputs": [ - { - "data": { - "text/plain": "0.11865" - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit_machine_learning.algorithms .inference import QBayesian\n", - "\n", - "query = {'B': 0}\n", - "evidence = {'A': 1}\n", - "# Initialize quantum bayesian inference framework\n", - "qbayesian = QBayesian(circuit=qc)\n", - "# Inference\n", - "qbayesian.inference(query=query, evidence=evidence)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:08.571707Z", - "start_time": "2023-11-10T03:10:08.432543Z" - } - }, - "id": "841bce19ea097bf1" - }, - { - "cell_type": "markdown", - "source": [ - "# Step 4: Generalize the approach for n nodes\n", - "\n", - "Now we generalize the approach for n nodes in a chain with random probabilities." - ], - "metadata": { - "collapsed": false - }, - "id": "79a2c40d290870" - }, - { - "cell_type": "code", - "execution_count": 14, - "outputs": [ - { - "data": { - "text/plain": "
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- }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Choose the number of nodes\n", - "n = 10 \n", - "# Generate probabilities\n", - "prob = np.random.random_sample(2*(n-1)+1)\n", - "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", - "# Define quantum registers \n", - "qr = [QuantumRegister(1, name=i) for i in range(n)]\n", - "# Generate circuit\n", - "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", - "#Apply the R_Y_theta rotation gate on the first qubit\n", - "qc.ry(theta[0], 0)\n", - "# Apply the controlled-R_Y_theta rotations\n", - "for i in range(1, n, 1):\n", - " qc.cry(theta_B_A, control_qubit=i-1, target_qubit=i)\n", - " qc.x(i-1)\n", - " qc.cry(theta_B_nA, control_qubit=i-1, target_qubit=i)\n", - " qc.x(i-1)\n", - "# Draw circuit\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:09.555012Z", - "start_time": "2023-11-10T03:10:09.304520Z" - } - }, - "id": "3764be5e0ce2db02" - }, - { - "cell_type": "markdown", - "source": [ - "We could also do inference with this model, but the chosen probabilities are random, as is the result." - ], - "metadata": { - "collapsed": false - }, - "id": "9ded5b8b18eb4256" - }, - { - "cell_type": "code", - "execution_count": 15, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'1000000000': 0.3803, '0000000000': 0.6197}\n" - ] - }, - { - "data": { - "text/plain": "
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HjxIeHk6TJk344osvGDlyZFEdUkREREQKwf5OvnzmzBnmzZvH/PnzOXnyJABdunRh+PDhPPLII9jZ2QEQEBBA7969eeSRR/jxxx/vvGoRERERKbRCB8AePXqwdu1asrKy8PHxYezYsQwbNozq1avf9DutWrVi9erVhT2kiIiIiBSBQgfA1atX07FjR4YPH87jjz+Ovf3td/XII49QpUqVwh5SRERERIpAoQPgkSNHqFmzZoG+U79+ferXr1/YQ4qIiIhIESj0SyBTpkxhxYoVt+yzcuVKhgwZUqj97969m27dulG2bFlcXV1p2bIl4eHhhdoXwKVLl/D19cVgMPDQQw/l2cdgMNz0n8GDBxf62CIiIiKlSaGvAC5YsIDq1avz6KOP3rTPvn37CAsLY968eQXa96ZNm+jatSvOzs7069cPd3d3li1bRmhoKDExMbzyyisFrveFF14gMTHxtv38/f3zDHuNGzcu8DFFRERESqM7egv4dq5du5avZwNvlJmZydChQzEajWzdutUSvCZMmEBwcDDjx4+nd+/e+Pv753ufy5YtY9GiRcyePZsXXnjhln2rV6/OpEmTClSziIiIyN3kjuYBNBgMebabzWZOnTrFmjVrCvzSx8aNG4mOjqZ///45rrp5enoyfvx40tPTCQsLy/f+4uLieP7553nqqafo3r17gWoRERERuRcV6PKc0WjMEfomTZp0y6tlZrOZsWPHFqigzZs3A9fnE/ynrl27ArBly5Z87++5557Dzs6OmTNn5usW8OXLl/nqq6+Ij4+nXLlytG7dmgYNGuT7eCIiIiKlXYECYNu2bS0BcOvWrfj5+eU575+dnR3lypWjY8eODB06tEAFRUVFARAYGJhrW6VKlXBzc7P0uZ2FCxfy/fffs3z5cry8vPIVAPft28fw4cNztD300EOEhYXh7e19y++mpaWRlpZm+ZyUlARARkYGGRkZwPUQbWdnR1ZWFiaTydI3uz0zMxOz2Wxpt7Ozw2g03rRdpLTJ/m89W/ZjIJmZmTnaHRwcMJlMZGVlWdoMBgP29vY3bb/Z301R/T3lt3aNSWPSmDSm0jimgihQAMy+Opd9oGeeeYYJEyYU6IC3kx3SPD0989zu4eGRryB39uxZXnrpJZ588kl69uyZr2O/8sor9OrVi1q1auHo6MiBAwd45513WLNmDT169CAiIsKyuklepk6dyuTJk3O1r1u3DhcXFwD8/PwICgpi//79nDp1ytKndu3a1KlTh127dhEXF2dpb9y4Mf7+/mzdupUrV65Y2kNCQm4bSEWs4Z+TvXfr1o3U1FQ2bdpkabO3t6d79+7Ex8cTERFhaXd3d6djx47ExMSwd+9eS3vFihVp1aoVUVFRREZGWtqL+u9p3bp1OU7YHTp0oEyZMhqTxqQxaUx3xZgK8tidwXxjxC0FunTpwvr164mKispznkFfX1+Sk5NvGwK7devGH3/8wcGDB6lQoQIAJ06coEaNGnTt2pWff/45X/WYTCY6duzIli1bWLZsGU888cRN++Z1BbBatWrEx8fj4eEBFP2vkaGf5GsYIiXms5G6AqgxaUwak8ZkjTGlpKTg6elJYmKiJXfcTLG+BVwY2Vf+bhbwkpKS8PLyuuU+wsLCWLNmDUuXLrWEv8IyGo0MHTqULVu2sH379lsGQCcnJ5ycnHK1Ozg44ODgkKPNzs4uz6uJN3truqBvU4tYyz//W79Vu9FozPO2xc3ab/Z3U1R/TwWp/WbtGpPGBBrTzWosaLvGVPAx5Ve+U8WQIUMwGAxMmTIFHx+ffE/wbDAY+M9//pPvgrKf/YuKiqJp06Y5tsXGxpKcnExwcPAt97Fnzx4A+vTpk+f2tWvXYjAYaNSoUY7LrTeTHSJTUlJu21dERESktMt3AFywYAEGg4GxY8fi4+PDggUL8vW9ggbAdu3aMXXqVNatW0e/fv1ybFu7dq2lz62EhISQnJycqz05OZklS5ZQtWpVunbtip+fX75q2rlzJ0CeL7yIiIiI3G3y/QzgyZMngevP4Nnb21s+50dBJm3OzMykdu3anDlzhh07dljmAkxMTCQ4OJgTJ04QGRlpCWPnzp0jMTGRypUr3/TFkWy3egbwr7/+ok6dOrku1/7222907tyZjIwMDh06xH333ZfvsSQlJeX7Xnxh6RlAKW3mjLJ2BSIitqkguSPfVwD/GeIKEuoKwt7enrlz59K1a1fatm2bYym4kydPMmPGjBxX4saNG0dYWBjz58+/o/V6P/zwQ1atWkWbNm2oVq0aDg4OHDx4kHXr1mEwGPj0008LFP5ERERESqtS+WZBhw4d2LZtGxMnTmTJkiVkZGTQoEEDpk2bRmhoaLEcs2fPnly+fJl9+/axfv160tPTqVSpEv369WPUqFG3fe5QRERE5G6R71vAN841U1D5fdbuXqNbwGKLdAtYRMQ6iuUWcPXq1W+69u+tGAyGXPPgiIiIiIj15DsADho0qFABUERERERKlwJNAyMiIiIid7+CrRwsIiIiInc9BUARERERG1PqloITERERkeKV72lgjEYjBoOBQ4cOUatWrTwXLM7zAAYDWVlZd1Tk3UrTwIgt0jQwIiLWUSzTwBw/fhy4vhTcjZ9FRERE5O6S72cA/f398ff3x97ePsfn/PwjIiIipcenn35K9erVcXZ2pkWLFuzateumfb///nuaNWtG2bJlcXV1pXHjxnz99dc5+iQnJ/PCCy9QtWpVypQpQ7169fjiiy+KexhyB0rlUnAiIiJSPJYsWcKYMWP44osvaNGiBZ988gldu3YlMjISb2/vXP3LlSvHG2+8QZ06dXB0dGTlypU888wzeHt707VrVwDGjBnDxo0bWbhwIdWrV2fdunWMGDGCKlWq8Oijj5b0ECUf7vgt4B9++IGePXvi5+eHp6cnfn5+PPbYYyxfvrwIyhMREZGi9NFHHzF06FCeeeYZy5U6FxcX5s2bl2f/9u3b8/jjj1O3bl3uu+8+Xn75ZRo2bMi2bdssfX777Teefvpp2rdvT/Xq1Rk2bBiNGjW65ZVFsa5CB8DMzEz69u1L7969+emnn4iNjcXFxYXY2FhWrFhBr1696Nu3r5aBExERKSXS09P5448/6NSpk6XNaDTSqVMnIiIibvt9s9nMhg0biIyMpG3btpb2Vq1asWLFCs6cOYPZbGbTpk0cOXKELl26FMs45M4VOgBOnTqV7777jgceeIBff/2Va9euce7cOa5du8bWrVtp06YNy5Yt4/333y/KekVERKSQ4uPjycrKwsfHJ0e7j48PsbGxN/1eYmIibm5uODo60r17d2bNmkXnzp0t22fNmkW9evWoWrUqjo6OPPTQQ3z66ac5QqKULoV+BnD+/PnUqVOHX375xfJiCFz/JdGmTRt++eUXGjZsyLx583jzzTeLpFgREREpee7u7uzdu5fk5GQ2bNjAmDFjCAgIoH379sD1ALhjxw5WrFiBv78/W7duZeTIkVSpUiXH1UYpPQodAM+dO8dLL72UI/zdyMHBgUceeYRZs2YVujgREREpOhUqVMDOzo7z58/naD9//jyVKlW66feMRiM1a9YEoHHjxhw6dIipU6fSvn17UlNTGT9+PD/88APdu3cHoGHDhuzdu5cZM2YoAJZShb4FXK1aNZKTk2/ZJyUlBT8/v8IeQkRERIqQo6MjTZs2ZcOGDZY2k8nEhg0bCAkJyfd+TCYTaWlpAGRkZJCRkZFrgQg7OztMJlPRFC5FrtAB8NlnnyU8PJxz587luf3MmTMsWbKEZ599ttDFiYiISNEaM2YMc+bMISwsjEOHDvH888+TkpLCM888A8CgQYMYN26cpf/UqVNZv349x44d49ChQ3z44Yd8/fXXDBw4EAAPDw/atWvHa6+9xubNmzl+/DgLFizgv//9L48//rhVxii3l+9bwKdOncrxuW/fvmzfvp2goCBGjRpFmzZt8PHx4fz58/z666/MnDmTNm3a0KdPnyIvWkRERAonNDSUuLg4JkyYQGxsLI0bN+bnn3+2vBhy6tSpHFfzUlJSGDFiBKdPn6ZMmTLUqVOHhQsXEhoaaumzePFixo0bx4ABA0hISMDf35/33nuP5557rsTHJ/lT4LWA/8lsNt+0Pft7tjoVjNYCFluktYBFRKyjWNYCHjRoUJ5BT0RERETuLvkOgAsWLCjGMkRERESkpNzxUnAiIiIicndRABQRERGxMYWeCBrgypUrzJ49m19++YWzZ89a5gS6kcFgIDo6+k4OIyIiIiJFqNABMC4ujlatWhEdHY2Hh4flzZP09HRSU1MBqFKlCg4ODkVWrIiIiIjcuULfAp40aRLR0dH897//5dKlSwCMHj2alJQUdu7cSXBwMNWrV+fgwYNFVqyIiIiI3LlCB8DVq1fz4IMPMnDgwFzTwzRv3pw1a9Zw4sQJJk+efMdFioiIiEjRKXQAPHfuHEFBQZbPdnZ2llu/AF5eXjz88MOEh4ffWYUiIiIiUqQKHQA9PT3JyMiwfPby8uL06dM5+nh4eHD+/PnCVyciIiIiRa7QATAgIIATJ05YPgcFBbF+/XouXrwIQGpqKj/99BN+fn53XKSIiIiIFJ1CB8AuXbqwYcMGrl69CsDw4cO5cOECjRo1ok+fPtSvX5/o6GgGDx5cVLWKiIiISBEo9DQwzz33HPXq1ePq1au4uLjwxBNP8MEHH/Duu++ybNkyypQpw5gxY3jttdeKsl4REZF8G/qJtSsQ+Z85o6xdwf8UOgBWrlyZ0NDQHG2vvPIKo0aNIj4+Hm9v71xvB4uIiIiI9d3RSiB5sbOzw8fHp6h3KyIiIiJF5I4D4Llz51i8eDF79uwhMTERT09PgoKC6NevH5UrVy6KGkVERESkCN1RAPz000957bXXSEtLw2w2W9oXLlzIG2+8wYwZMxgxYsQdFykiIiIiRafQAXDx4sW8+OKLVKhQgTfeeIMHHngAHx8fzp8/z9atW5k5c6Zle9++fYuyZhERERG5A4UOgNOnT6dChQrs3buXKlWqWNpr165N27ZtGTx4MEFBQUybNk0BUERERKQUKfQ8gIcOHaJv3745wt+NqlatSp8+fTh06FChixMRERGRolfoAFi2bFlcXV1v2cfNzY2yZcsW9hAiIiIiUgwKHQAfffRRfvrpJzIzM/PcnpGRwU8//UTPnj0LXZyIiIiIFL1CB8Dp06fj6upKly5d2LFjR45tERERdOnSBXd3d95///07LlJEREREik6+XwIJCAjI1Zaens6ff/5J69atsbe3p0KFCsTHx1uuClauXJkmTZoQHR1ddBWLiIiIyB3JdwA0mUy5lnZzcHDAz88vR9s/XwoxmUx3UJ6IiIiIFLV8B8ATJ04UYxkiIiIiUlIK/QygiIiIiNyd7ngtYIDMzEwiIyNJSkrCw8OD2rVrY29fJLsWERERkSJ2R1cAExISGDp0KJ6enjRs2JA2bdrQsGFDypYty7Bhw7h48WJR1SkiIiIiRaTQl+kSEhJo2bIlR48epVy5cjzwwANUrlyZ2NhYfv/9d+bOncuWLVuIiIigXLlyRVmziIiIiNyBQl8BfOeddzh69CivvfYaJ0+e5Oeff2b+/PmsWbOGkydPMnbsWKKionjvvfeKsl4RERERuUOFDoA//vgj7du3Z9q0abmWhHNxcWHq1Km0b9+eH3744Y6LFBEREZGiU+gAePbsWUJCQm7ZJyQkhLNnzxb2ECIiIiJSDAodAD09PTl58uQt+5w8eRJPT8/CHkJEREREikGhA2C7du1YunQpv/zyS57bN2zYwNKlS2nfvn1hDyEiIiIixaDQbwFPnDiRVatW0bVrV7p160a7du3w8fHh/PnzbN68mTVr1uDi4sKECROKsl4RERERuUOFDoD3338/a9euZfDgwaxatYpVq1ZhMBgwm80A3HfffSxYsID777+/yIoVERERkTt3R8t1tGnThqioKLZv386ePXssK4EEBQXRunVrDAZDUdUpIiIiIkWk0AFwyJAhNGjQgNGjR9OmTRvatGlTlHWJiIiISDEp9EsgixYt4sKFC0VZi4iIiIiUgEIHwPvuu49z584VZS0iIiIiUgIKHQCHDBnCqlWrOHPmTFHWIyIiIiLFrNDPAPbq1YtNmzbRqlUrXn/9dZo3b46Pj0+eL374+fndUZEiIiIiUnQKHQADAgIs07689NJLN+1nMBjIzMws7GFEREREpIgVOgAOGjRI07yIiIiI3IUKHQAXLFhQhGWIiIiISEkp9EsgIiIiInJ3uqOVQADS0tJYvXo1e/bsITExEU9PT4KCgujWrRtOTk5FUaOIiIiIFKE7CoArVqxg2LBhxMXFWdYAhusvfnh7e/PVV1/xyCOP3HGRIiIiIlJ0Ch0AN2zYQK9evbCzs2PIkCE88MAD+Pj4cP78ebZu3crChQt54oknWLt2LR07dizKmkVERETkDhQ6AE6cOJEyZcrw22+/Ub9+/RzbBg0axEsvvUTr1q2ZOHGiAqCIiIhIKVLol0D27NlDaGhorvCXrWHDhvTt25c///yzUPvfvXs33bp1o2zZsri6utKyZUvCw8Pz/f01a9bQr18/6tSpQ9myZXFxcaFOnTr83//9H0eOHLnp99auXUu7du1wd3fHw8ODDh06sGHDhkKNQURERKQ0KvQVQBcXFypWrHjLPt7e3ri4uBR435s2baJr1644OzvTr18/3N3dWbZsGaGhocTExPDKK6/cdh+rV69mx44dtGjRgocffhgHBwcOHTpEWFgY33zzDatXr851ZXLhwoU89dRTVKxYkcGDBwOwZMkSOnfuTHh4OL179y7wWERERERKG4P5xrc3CuDJJ58kOjqaXbt23bRP8+bNCQwMZNGiRfneb2ZmJnXq1OH06dPs2LGDxo0bA5CYmEhwcDAnTpzgyJEj+Pv733I/165dw9nZOVf7hg0b6NSpE82aNWP37t2W9kuXLhEQEIC9vT179uyhatWqAJw+fZqgoCAAjh07hru7e77HkpSUhKenJ4mJiXh4eOT7ewUx9JNi2a1Ioc0ZZe0KRP5H50gpTYr7/FiQ3FHoW8AzZszgwoULDBo0iJiYmBzbYmJieOqpp4iPj2fGjBkF2u/GjRuJjo6mf//+lvAH4Onpyfjx40lPTycsLOy2+8kr/AE8+OCDeHl5cfTo0RztS5cu5fLly7z44ouW8AdQtWpVXnjhBeLj4/nhhx8KNBYRERGR0qjQt4CfeuopvLy8+Oabb1i8eDF+fn6Wt4BPnTpFVlYWDRs2ZODAgTm+ZzAYbvlM3ebNmwHo0qVLrm1du3YFYMuWLYUtm4iICC5dukSbNm0KdNxJkyaxZcsWBg0aVOhji4iIiJQGhQ6A2YEJrt+2PXbsGMeOHcvRZ9++fbm+d7v1g6OiogAIDAzMta1SpUq4ublZ+uTHunXr+O2330hLSyMqKoqVK1dSoUIFPv7443wfN7vtdsdNS0sjLS3N8jkpKQmAjIwMMjIyADAajdjZ2ZGVlYXJZLL0zW7PzMzMMaeinZ0dRqPxpu0ipU32f+vZ7O2vn2YyMzNztDs4OGAymcjKyrK0GQwG7O3tb9p+s7+bovp7ym/tGtPdNCatWS+lS3H+PRVEoQPgjQctSomJicD1W7558fDwsPTJj3Xr1vHhhx9aPtesWZPFixfTtGnTfB83+z767Y47depUJk+enGcN2S/D+Pn5ERQUxP79+zl16pSlT+3atalTpw67du0iLi7O0t64cWP8/f3ZunUrV65csbSHhITg7e19y3pErGH16tU5Pnfr1o3U1FQ2bdpkabO3t6d79+7Ex8cTERFhaXd3d6djx47ExMSwd+9eS3vFihVp1aoVUVFRREZGWtqL+u9p3bp1OUJEhw4dKFOmjMZ0F48JHBApTYrz76lKlSr5rqPQL4EUly5durB+/XqioqKoWbNmru2+vr4kJycXKAQCJCcn8/fff/P222/zyy+/MG/ePPr372/ZXqtWLaKiosjIyLD8msyWkZGBo6MjDRs2zPOqZra8rgBWq1aN+Ph4S4gs6l/CesBZSpvPRuoKoMZUesY0bKauAErpMWdU8V4BTElJyfdLIHe8FnC2U6dOceLECdq2bXtH+8m+AnezgJeUlISXl1eB9+vm5kZwcDDLly+nWbNmDBs2jM6dO1umsrnxuOXLl891zBv73IyTk1Oe6x87ODjg4JDzV6idnR12dna5+v4zfN6uXaS0+ed/67dqNxqNed62uFn7zf5uiurvqSC136xdYyp9YxIpTYr77ynfdRT6m/8wf/58OnTocMf7udXzdrGxsSQnJ+f5nF5+2dvb06FDB1JSUvj999/zddxbPR8oIiIicrcpdW8RtGvXDrj+3Nw/rV27Nkefwjp79iyQ89diSRxXREREpDQodQHwwQcfJCAggEWLFuV4GDIxMZEpU6bg6OiYYyqWc+fOcfjw4Vy3jG+8unejtWvX8sMPP1C2bFlCQkIs7X379sXT05NZs2Zx+vRpS/vp06eZPXs2FSpU4PHHHy+iUYqIiIhYT6l7sMze3p65c+fStWtX2rZtm2MpuJMnTzJjxgyqV69u6T9u3DjCwsKYP3++Zfk2uL4KSf369WnYsCFVq1YlJSWF/fv38+uvv+Lg4MC8efNwdXW19Pfy8mL27Nk89dRTNGnShNDQUOD6UnAXL15kyZIlBVoFRERERKS0KrIA6OnpiZ+fX5Hsq0OHDmzbto2JEyeyZMkSMjIyaNCgAdOmTbMEs9uZMmUKmzZtYsuWLcTFxWE0GvHz82PYsGGMGjWKunXr5vrOwIEDqVChAlOmTGH+/PkYDAaaNm3Km2++SadOnYpkbCIiIiLWVuqmgbmXaC1gsUVaC1hKE50jpTS5J9YCFhEREZG7U75vAW/duhWA4OBgnJ2dLZ/z407nBhQRERGRopPvANi+fXsMBgOHDh2iVq1als/5cePM1iIiIiJiXfkOgBMmTMBgMFChQoUcn0VERETk7pLvADhp0qRbfhYRERGRu4NeAhERERGxMYUOgFeuXOHYsWNkZGTkaF+yZAkDBgzg//7v//jzzz/vuEARERERKVqFngj69ddfZ+HChZw/f96ypu7nn3/OCy+8QPbUgosXL+aPP/6gTp06RVOtiIiIiNyxQl8B3LJlC506dcLFxcXS9v777+Pr68vWrVsJDw/HbDbzwQcfFEmhIiIiIlI0Cn0F8Ny5czz00EOWz4cOHSImJobp06fTpk0bAL777rsCzRcoIiIiIsWv0FcA09LScHR0tHzesmULBoOBLl26WNoCAgI4c+bMnVUoIiIiIkWq0AGwatWq7N+/3/J55cqVlCtXjoYNG1raLl68iJub251VKCIiIiJFqtC3gB9++GE+/fRTXn31VZydnfn5558ZNGhQjj5HjhzBz8/vjosUERERkaJT6AA4btw4fvrpJz766CMAKleuzNtvv23ZfuHCBbZv384LL7xw51WKiIiISJEpdACsVKkSBw8eZMOGDQC0bdsWDw8Py/b4+Hg++OADunbteudVioiIiEiRKXQABChTpgw9evTIc1u9evWoV6/enexeRERERIqBloITERERsTF3dAUwKyuL8PBwfvnlF86ePUtaWlquPgaDwXKbWERERESsr9ABMCUlhS5durBjxw7MZjMGg8GyBBxg+WwwGIqkUBEREREpGoW+Bfzuu+8SERHB5MmTiY+Px2w2M2nSJM6dO8eSJUsICAigT58+eV4VFBERERHrKXQA/P7772nZsiVvvvkm5cqVs7T7+PjQp08fNm3axC+//KK1gEVERERKmUIHwFOnTtGyZcv/7chozHG1r2rVqnTv3p2wsLA7q1BEREREilShA6CrqytG4/++7unpyblz53L0qVSpEqdOnSp8dSIiIiJS5AodAP39/XOEu/r167Nx40bLVUCz2cyGDRuoXLnynVcpIiIiIkWm0AHwwQcfZNOmTWRmZgLw9NNPc+rUKUJCQnjttddo06YNe/fupVevXkVWrIiIiIjcuUJPAzN06FDKly9PXFwclStXZsiQIezZs4fPPvuMvXv3AtCrVy8mTZpURKWKiIiISFEodAAMDAxk7NixOdpmzZrFhAkTOHbsGP7+/lSqVOmOCxQRERGRonVHK4HkpWLFilSsWLGodysiIiIiRURrAYuIiIjYmEJfAQwICMhXP4PBQHR0dGEPIyIiIiJFrNAB0GQy5bnOb2JiIpcvXwagcuXKODo6Fro4ERERESl6hQ6AJ06cuOW2MWPGcP78edavX1/YQ4iIiIhIMSiWZwCrV6/OkiVLuHTpEm+88UZxHEJERERECqnYXgJxcHCgc+fOhIeHF9chRERERKQQivUt4KtXr5KQkFCchxARERGRAiq2APjrr7/y7bffUrt27eI6hIiIiIgUQqFfAunYsWOe7ZmZmZw5c8byksiECRMKewgRERERKQaFDoCbN2/Os91gMODl5UWXLl0YM2YMnTt3LuwhRERERKQY3NE8gCIiIiJy97njtYAvXLjAmTNnMJlM+Pr6UqlSpaKoS0RERESKSaFeAklLS2P69OkEBgZSuXJlmjVrRnBwML6+vlSoUIHRo0ffcqJoEREREbGeAgfAmJgYmjdvzrhx44iOjqZy5coEBwcTHBxM5cqVSUhIYObMmTRr1oxffvnF8r1z585pTkARERGRUqBAATAjI4Nu3bpx4MABnnzySQ4dOsTp06eJiIggIiKC06dPc+jQIQYMGEBCQgKPPfYYJ06cIDo6mjZt2nD48OHiGoeIiIiI5FOBngH88ssvOXjwIBMnTmTixIl59qlduzZff/01tWrVYuLEiQwYMIATJ04QHx9P06ZNi6RoERERESm8Al0BDA8Pp2bNmvma2+/NN98kMDCQiIgIrl27xtq1a+nevXuhCxURERGRolGgAPj333/TpUsXDAbDbfsaDAZL3507d9K+ffvC1igiIiIiRahAATA5ORlPT8989/fw8MDe3p6aNWsWuDARERERKR4FCoDe3t4cPXo03/2jo6Px9vYucFEiIiIiUnwKFABDQkJYs2YNsbGxt+0bGxvLqlWraNOmTaGLExEREZGiV6AA+Nxzz5GcnMzjjz9OfHz8TftdvHiRxx9/nKtXrzJ8+PA7LlJEREREik6BpoHp0KEDQ4cOZc6cOdStW5fhw4fTsWNHqlWrBlyfJHrDhg3MmTOH+Ph4hg0bppc/REREREqZAq8F/Nlnn+Hh4cHHH3/M1KlTmTp1ao7tZrMZo9HIq6++mmubiIiIiFhfgQOgnZ0dH3zwAcOGDWPBggVERERYngmsVKkSrVq14umnnyYwMLDIixURERGRO1fgAJgtMDCQ9957ryhrEREREZESUKCXQERERETk7qcAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2JhSGwB3795Nt27dKFu2LK6urrRs2ZLw8PB8fz86OppJkybx6KOP4uvri8FgoHr16rf8jsFguOk/gwcPvrMBiYiIiJQS9tYuIC+bNm2ia9euODs7069fP9zd3Vm2bBmhoaHExMTwyiuv3HYfv/76K5MnT8bOzo66desSGxubr2P7+/vnGfYaN25cwFGIiIiIlE6lLgBmZmYydOhQjEYjW7dutQSvCRMmEBwczPjx4+nduzf+/v633E/btm2JiIigUaNGlClTBmdn53wdv3r16kyaNOkORyEiIiJSepW6W8AbN24kOjqa/v3757jq5unpyfjx40lPTycsLOy2+wkICKBly5aUKVOmGKsVERERufuUuiuAmzdvBqBLly65tnXt2hWALVu2FNvxL1++zFdffUV8fDzlypWjdevWNGjQoNiOJyIiIlLSSl0AjIqKAiAwMDDXtkqVKuHm5mbpUxz27dvH8OHDc7Q99NBDhIWF4e3tfcvvpqWlkZaWZvmclJQEQEZGBhkZGQAYjUbs7OzIysrCZDJZ+ma3Z2ZmYjabLe12dnYYjcabtouUNtn/rWezt79+msnMzMzR7uDggMlkIisry9JmMBiwt7e/afvN/m6K6u8pv7VrTHfTmAyIlCbF+fdUEKUuACYmJgLXb/nmxcPDw9KnqL3yyiv06tWLWrVq4ejoyIEDB3jnnXdYs2YNPXr0ICIiAjs7u5t+f+rUqUyePDlX+7p163BxcQHAz8+PoKAg9u/fz6lTpyx9ateuTZ06ddi1axdxcXGW9saNG+Pv78/WrVu5cuWKpT0kJOS2gVTEGlavXp3jc7du3UhNTWXTpk2WNnt7e7p37058fDwRERGWdnd3dzp27EhMTAx79+61tFesWJFWrVoRFRVFZGSkpb2o/57WrVuXI0R06NCBMmXKaEx38ZjAAZHSpDj/nqpUqZLvOgzmG39elQJdunRh/fr1REVFUbNmzVzbfX19SU5OLnAIdHZ2plKlSpw4caJA3zOZTHTs2JEtW7awbNkynnjiiZv2zesKYLVq1YiPj8fDwwMo+l/CQz8p0HBEit1nI3UFUGMqPWMaNlNXAKX0mDOqeK8ApqSk4OnpSWJioiV33EypuwKYfeXvZgEvKSkJLy+vEqvHaDQydOhQtmzZwvbt228ZAJ2cnHBycsrV7uDggINDzl+hdnZ2eV5NzD6R5bddpLT553/rt2o3Go153ra4WfvN/m6K6u+pILXfrF1jKn1jEilNivvvKd91FPqbxST72b+8nvOLjY0lOTk5z+cDi1OFChUASElJKdHjioiIiBSHUhcA27VrB1x/bu6f1q5dm6NPSdm5cyfAbVcSEREREbkblLoA+OCDDxIQEMCiRYtyPAyZmJjIlClTcHR0ZNCgQZb2c+fOcfjw4Tt+MeSvv/7K9VwJwG+//ca0adNwcHCgT58+d3QMERERkdKg1D1YZm9vz9y5c+natStt27bNsRTcyZMnmTFjRo4rcePGjSMsLIz58+fnWMItPj6eV1991fI5IyOD+Pj4HH1mzJhhub374YcfsmrVKtq0aUO1atVwcHDg4MGDrFu3DoPBwKeffsp9991X3MMXERERKXalLgDC9Vf6t23bxsSJE1myZAkZGRk0aNCAadOmERoamq99JCcn51oxJCUlJUfbpEmTLAGwZ8+eXL58mX379rF+/XrS09OpVKkS/fr1Y9SoUQQHBxfdAEVERESsqNRNA3MvSUpKyvfr2IWlaWCktJkzytoViPyPzpFSmhT3+bEguaPUPQMoIiIiIsVLAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmNKbQDcvXs33bp1o2zZsri6utKyZUvCw8MLtI+0tDTefvttAgMDcXZ2pkqVKgwbNowLFy7c9DvffPMNwcHBuLq64uXlRY8ePfjzzz/vdDgiIiIipUapDICbNm2idevWbNu2jb59+/Lcc88RGxtLaGgoH374Yb72YTKZ6NmzJxMnTqRChQqMGjWKkJAQ5s6dS0hICHFxcbm+89577zFw4EAuXLjAc889R58+fdi6dSutWrVi+/btRT1MEREREaswmM1ms7WLuFFmZiZ16tTh9OnT7Nixg8aNGwOQmJhIcHAwJ06c4MiRI/j7+99yP/Pnz2fIkCE8+eSTfPPNNxgMBgC++OILnn/+eYYNG8aXX35p6R8VFUW9evUICAhg165deHp6ArB3715atmxJQEAABw4cwGjMf2ZOSkrC09OTxMREPDw8Cvi/ifwZ+kmx7Fak0OaMsnYFIv+jc6SUJsV9fixI7ih1VwA3btxIdHQ0/fv3t4Q/AE9PT8aPH096ejphYWG33c+cOXMAmDp1qiX8AQwfPpyAgAC++eYbUlNTLe3z588nMzOTN954wxL+ABo3bsyTTz7JoUOH2LZtWxGMUERERMS6Sl0A3Lx5MwBdunTJta1r164AbNmy5Zb7uHbtGjt37qR27dq5rhQaDAY6d+5MSkoKv//+e5EeV0RERORuUOoCYFRUFACBgYG5tlWqVAk3NzdLn5uJjo7GZDLluY8b933jfqKionBzc6NSpUr56i8iIiJyt7K3dgH/lJiYCJDjNuyNPDw8LH3uZB839sv+d29v73z3z0taWhppaWm56khISCAjIwMAo9GInZ0dWVlZmEwmS9/s9szMTG58LNPOzg6j0XjT9vRrtyxJpMRdvJiR47O9/fXTTGZmZo52BwcHTCYTWVlZljaDwYC9vf1N22/2d1NUf0/Zf6e3q11junvGlH7NgEhpkZREsf49paSkAJCf1ztKXQC8m02dOpXJkyfnaq9Ro4YVqhGxjv+Os3YFIiKlU0mdH69cuXLTi2DZSl0AzC74ZlfbkpKS8PLyuuN93Ngv+98L0j8v48aNY8yYMZbPJpOJhIQEypcvn+NFFCl9kpKSqFatGjExMcX2xraIyN1I58e7h9ls5sqVK1SpUuW2fUtdALzxebumTZvm2BYbG0tycjLBwcG33EdAQABGo/Gmz+zl9ZxhYGAgERERxMbG5noO8FbPJd7IyckJJyenHG1ly5a95XekdPHw8NAJTkQkDzo/3h1ud7EqW6l7CaRdu3YArFu3Lte2tWvX5uhzM2XKlCE4OJjIyEhOnjyZY5vZbGb9+vW4urrSrFmzIj2uiIiIyN2g1AXABx98kICAABYtWsTevXst7YmJiUyZMgVHR0cGDRpkaT937hyHDx/Odft22LBhwPXbsjc+DPnll19y7NgxBgwYQJkyZSztzzzzDPb29rz33ns59rV3716+/fZb6tatS5s2bYp6uCIiIiIlrtTdAra3t2fu3Ll07dqVtm3b0q9fP9zd3Vm2bBknT55kxowZVK9e3dJ/3LhxhIWFMX/+fAYPHmxpf/rpp1myZAnffvstx48fp127dhw9epTvv/+eGjVq8O677+Y4bq1atZg0aRJvvvkmjRo1olevXly5coXFixcD1yeWLsgqIHJ3cXJyYuLEiblu4YuI2DqdH+9NpW4puGy7du1i4sSJ/Pbbb2RkZNCgQQPGjBlDaGhojn6DBw/OMwDC9WlZ3n//fb7++mtiYmIoV64cPXr04N1338XHxyfP437zzTd88sknHDx4EEdHR1q3bs0777xDkyZNimuoIiIiIiWq1AZAERERESkeuqcpIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVDkDmS/RG82m9EL9SIicrdQABQphOywZzAYLP8z+99FROS6G38YZ2VlWbES+SfNAyhSSGvXruXEiRNER0dTrlw52rZtS82aNalQoYJl1Riz2axgKCI27dq1azg7O1u7DPmHUrcUnEhpd+rUKT7++GP+/e9/57rt6+/vT48ePejfvz8hISEKfyJis44fP054eDgHDhwgLi6Ohg0b0rRpU+rUqYO/vz9ly5YFwGQyaalVK9AVQJECGjlyJPPmzaNnz54MHDgQb29vdu7cyZ9//snu3bv5+++/AejevTtvvfUWwcHBOsGJiE359ttveeeddzh8+DBlypQhNTXVsq1q1ap06tSJJ598ks6dO1uxStumAChSAGlpaZQrV47Q0FDmzZuXa/vhw4fZtGkTixYtYvv27dStW5ewsDCaNWtmhWpFREpeWloatWvXxsnJiTfeeIPu3btz9uxZDhw4wIEDB9i2bRu///47165do1evXkyaNIl69erph3IJ0y1gkQJYv349WVlZtG3bFsj59q/RaKROnTrUqVOHwYMHM3/+fMaMGcOwYcNYuXIlVapUsWbpIiIl4ttvv+XcuXPMnz+f/v37A1C+fHkaNGiAyWTi2LFjbN++nYULF/Ldd99x8uRJli1bRtWqVa1cuW1R1BYpADs7O8xmM3FxccD1t9oMBoPlV6vJZMJkMlGmTBlGjBjBmDFj2Lt3L/v377dm2SIiJWb79u14e3vTvHlz4Pp5MfvHstFopGbNmjz99NN89913vP322/z555+MGDHCylXbHgVAkQJo2bIljo6OfPvtt0RFRWFvb5/jRY/sMJg93UHfvn1xcXFhx44d1ipZRKRE+fv7ExcXx+nTp4Hc02Zlh0FPT0/efPNNunfvzu7duzl16pTVarZFCoAi+WQ2m/Hy8mLmzJns3buX9u3b88UXX3D8+HFL4Ms+wWV/PnnyJJmZmbq1ISI2IyQkhPT0dKZPn05cXBx2dnY5wh9cP1dmnydbt25NcnIyR48etVrNtkgBUCSfsk9gvXv3Zvz48SQkJPDqq6/ywgsv8OWXXxIREWH5xevo6MiJEyeYN28ednZ29OnTx5qli4iUCJPJxIMPPsgbb7zB2rVradGiBbNnz+bIkSOWeVGzz6V2dnYAxMbGkpGRoZflSpjeAhYppK1bt/LFF1+wfv16EhISqFq1KrVq1cLR0RE3Nzd2795NbGwso0eP5r333rN2uSIiJebs2bNMnz6d2bNnYzQaCQkJoWPHjjRp0oS6detSs2ZNrl27xtdff80bb7xBSEgIP/74o7XLtikKgCL5kNeKHmazmZiYGPbs2cPOnTv5448/OHToEKdPn8bV1RU/Pz/eeOMNHnvsMVxcXKxUuYiI9ezYsYOvvvqKn3/+mdjYWNzd3SlXrhwODg44OTlx8OBBmjVrxuzZswkODrZ2uTZFAVAkn65evYq9vT0nT56kTJkyOZ7rS01N5cKFCzg4OJCWlkZCQgJNmza1YrUiIiUrrx/KJpOJ+Ph4oqKi+OOPP9ixYwe7d+/m4sWL3H///QQGBjJ16lR8fHysVLXtUgAUuY20tDS2bNnC7Nmz2bFjB25ubhiNRqpXr87DDz9Mv3798PX1tXaZIiJWZTKZOHv2LAkJCcTGxlKvXr0cP5TT0tIAcHJyIjY2Fjc3N9zc3ACtm24NCoAit/HJJ58wefJk0tLSaNy4sWXpt/PnzwPXJ4Du06cPzz//PG3atLGcxHQyExFbcfToUT777DPCwsJISUkhPT0dg8FAgwYNCA0NZcCAAfj5+eX4jkKfdSkAitzCtWvXqFKlCvfffz/h4eF4eHjg6uoKwM6dO1m6dKll1vsqVaowdepUnnrqKStXLSJSctLT0+nevTsbN26kVatWtG7dmvj4eHbv3k1kZCTp6ekA9OrVi1deeYWWLVtauWIBBUCRW1q4cCHDhg1j4cKFPPHEE0DuX61ZWVnMmzePGTNmEBUVxdy5cxkyZIi1ShYRKVH/+c9/GDFiBJMmTWLcuHE5tu3atYtVq1axbNky/v77b3x9fZk9ezY9e/a0UrWSTfMAitxCZGQkRqPRso5vRkaGJfyZTCaysrKws7Nj6NChfP7555aJoi9dumTNskVESkx4eDiNGzemX79+AGRmZlomeQ4ODmby5Mns3LmTWbNmkZWVxZAhQ/j555+tWbKgAChyS61ateLq1ascPHgQAAcHB8s2o9FomcjUbDbTsWNHJkyYwKFDh9i7d681yhURKVHXrl0jIyOD1NRUKlWqBFx//jn73Ji9PrqrqysjR45k1qxZXLp0iYULFwL/WxlESp4CoMgtNGnShHr16jFixAg+/fRTLl68mGe/zMxMADw9PTGZTCQmJpZkmSIiVuHs7EyTJk04cOCAZc3z7PAH138oG41Gy/q/vXr1olu3buzZs4cTJ07oJRArUgAUuQUfHx8mT56Mu7s7//rXvxg7diy//fab5fZGtuz5//bt24fRaKRjx45WqlhEpGQ99dRTeHp6EhoaypdffklsbGyuPiaTCYPBQHp6OhUrViQ+Ph5vb28rVCvZ9BKISD5ERETw7rvvsmbNGgBatmzJo48+SpMmTSwz2v/00098/PHH9O7d23J7Q0TEFsycOZPx48djNBp5/PHH6devH0FBQZQtW5YyZcpY+u3YsYOhQ4dSpUoV1q5da8WKRQFQ5BYyMzMttzCOHDnCqlWrWLFiBbt37+bq1avY2dnh7OxMSkoKAAMHDuStt94iMDDQypWLiJSsiIgIpkyZwvr168nMzKRp06Y88MAD1KhRA2dnZwA+/PBDzp49y5IlS+jatauVK7ZtCoAiBXT16lV+++039uzZQ3x8PElJSWRlZdG7d2/atm1rOdGJiNiCjIwMHBwcMJvNREVFsWnTJjZs2MDu3buJjY21rAAC4OXlxWeffUZoaKgVKxZQABTJU0JCAr///jsRERF4eXnh5OSEr68vTZs2pXLlypZ+aWlpODk5WbFSERHru3r1Ki4uLpbPiYmJHDx4kJiYGNLS0jhz5gw1a9akVatWWjqzlFAAFPmHbdu2MXbsWCIiIoDrUxqYzWZcXFyoV68enTp1olu3bgQHB+Po6Eh6ejqOjo5WrlpEpGRFRETw/fffEx8fj6OjI15eXjRp0oQHH3yQ8uXLW7s8uQ0FQJEbXLt2jcaNGxMXF8fkyZPx9vbGzs6O2NhYfvnlF9avX8/Vq1cJDAxkxIgRjBw5Ent7e2uXLSJSYjIzM3n//feZMGECAGXLliUtLY3U1FQA/P396dGjB08++SQtW7bEaDRabhNL6aEAKHKDuXPn8vLLLzN79myeeeaZXNuPHz/O0qVLmT9/PpGRkfTv359Zs2bh5eVlhWpFREreN998wzPPPEO3bt2YMGECJpOJMmXKcOjQIRYvXszy5csxmUz4+/szatQoXn75ZWuXLHlQABS5QWhoKHv27GHVqlUEBgbm+avVZDLxxx9/8M4777By5Uo++eQTXnrpJStVLCJSslq1aoW9vT1fffUVderUybU9KSmJefPm8emnn3LixAlefvll3nnnnRzTwYj1aSJokf8vMzOTChUqcPbsWcuSRnndsjAajTRv3pwFCxbQtGlTZs2axdWrV0u6XBGREpeQkMDx48fx9/enVq1alhU+4H/ro3t4eDBq1CiWLFlCixYt+Oijj9iyZYuVK5d/UgAU4fp6lPb29rRu3ZqrV68yZswYLl26BPzvpHajzMxMypUrR9u2bYmLiyMyMtIaZYuIlCiz2UzlypU5duwYRqMRg8FgWc7txvXR4fpSmgsXLsTBwcFyW1hKDwVAEbCcwNq1a0fbtm35z3/+w7hx4zhx4kSOk1pWVpYlLKalpWEwGDCZTJr4WURsQvny5enYsSMRERFMmjSJhIQEIPcP5ex/9/X1pVGjRuzdu9eyZrqUDgqAIjfw9fVl8eLF9OzZk6+++oqAgABCQ0NZsWIF6enp2NnZWW53bNq0iSVLltC2bVvc3NysXLmISMkYMmQI/v7+TJs2jbfeeoujR4/muvqX/e9RUVFkZGTg4+Oj6bJKGb0EInKDrKws7OzsOH78OAsWLODzzz8nPj4eAHd3d1q3bk1gYCD79u1j+/btVK9enQULFtC6dWsrVy4iUnKioqIYPXo0q1evBqB79+4MGTKEdu3a4ejoSGpqKl5eXjz33HMsWLCAZcuW0bNnTytXLTdSABT5/8xms+VWcLaMjAzCw8P55ptv2L17NykpKdjb25ORkcEjjzzCa6+9RvPmza1UsYhIycvMzMTe3p7IyEgWLVrEokWLiI6OBsDFxYWgoCBMJhN///03iYmJDBkyhLlz51q5avknBUCR/89kMhETE4O/vz+XL1/GaDTi4eFh2Z6QkMCBAwfw8vKy/OPq6ppncBQRsRWJiYmsXr2aNWvWEBkZSUpKCgkJCdx3330888wz9O3bV4/JlEIKgGLzUlNT+eijj1i7di1//fUXjo6ONGrUiMaNG9O0aVMaNGhAQEAAzs7O1i5VRKTE3fgj9+DBg5hMJlxdXUlNTcXX15eyZcta+sbHx3P58mVq1KjBtWvXcHV1tVLVcjsKgGLT0tPT6d+/P99//z316tXD1dUVk8nE5cuXOXXqFPb29jRv3pwBAwYwcOBATWQqIjbHbDbz559/8tJLL7F//35SUlIoW7Ys/v7+1K9fn5CQEEJCQqhfv76We7uLKACKTfvPf/7DyJEjGTlyJJMnT8bNzY3Y2FjOnDnDkSNH2LhxI+vWrSMmJoYOHTowdepUgoODddtXRGzGqlWrGDZsGCkpKTz66KMYjUbLM35//fUXWVlZNGnShEGDBjFkyBBcXFysXbLkgwKg2LR27dqRkZHBN998Q40aNSxvAWdLSEhgz549zJ8/n0WLFtGiRQtWr16ttX9FxGa0adOGy5cv8+9//5uOHTsCcPnyZa5cuUJUVBQrV65k+fLlnDhxgh49evDBBx9Qu3ZtK1ctt6MAKDYrKSmJtm3b4unpmWuZon9e4TOZTMyYMYN//etfvPjii8ycObOkyxURKXHnzp2jRo0avPbaa7z99tsAue5+XL16lb179zJ79mwWL17MY489xtKlS3P8mJbSRxNBi00ym824ublRt25d/vrrLw4cOGBpN5lMlhNc9jqXRqORMWPG0KhRI/744w8SExOtWb6ISIk4evQojo6O2NnZ3fSxFxcXF1q1asVXX33FqFGjWL58OStXrizhSqWgFADFJhkMBoxGo+XWxquvvsqxY8cs7UCORc7h+jqXgYGBnDt3DicnJ2uVLiJSYurWrUuVKlVYvnw5MTExluUv/7mur8lkws3NjZEjR+Li4sK2bdusVLHklwKg2LSRI0fy+uuvs27dOpo0acLrr7/Ob7/9xrVr1yxh8MbpDw4dOkTt2rU1JYyI2IQKFSrw8MMPs3//fsaPH8/Zs2cxGo2WH8r/XAP42rVreHt7c+nSJWuVLPlkb+0CRKwl+zm/V155hTJlyjB9+nRmzJjBt99+S8uWLWnevDktWrSgdu3a7Ny5k48++oijR48yffp0a5cuIlJipkyZQmpqKl999RXLli1j6NCh9O7dm1atWuV6zm/9+vWcOnWK7t27W6layS+9BCI2658vepw5c4Z58+bx/fffs2/fvlz9y5Yty6uvvsr48eNLskwREasxmUwYjUZOnz7NZ599xscff0xaWhrOzs40bdqUkJAQ2rdvz7Vr19i6dStz5syhXr167N6929qly20oAIrcwGQyERcXR2RkJDt37mTXrl24urpSq1YtQkJC6NChg7VLFBGxmoSEBObNm8eiRYvYu3dvru09e/bk1VdfpXXr1iVfnBSIAqDYpH379hEVFcWRI0csL4MEBgbi7e2d6023tLQ0vfQhIjYl+w5J9hXAvBw9epSNGzdy6tQp/P398fb2pnPnzpoI+i6hACg2JTMzk6+++oq3336bCxcu5NhWqVIlunbtypNPPkmXLl1ybLvVSVBE5F6TlZVFWFgYf//9N0ePHuW+++6jWbNm1KpVCz8/P8qVK5fnPH9aJenuoQAoNmXJkiUMHTqUwMBAnn32WRo1asSePXvYu3cvf/zxB/v378dkMhESEsKECRPo3Lmzgp+I2JQ///yTt99+mxUrVuDk5ERaWpplm7e3N+3bt6dPnz488sgjODo6Agp+dyMFQLEpLVq0wGQysWjRIgIDA3NsO378OFu3buW7775j1apVeHp6MmfOHHr37m2lakVESt4jjzzC9u3bee655xg8eDBZWVns37+fv//+m4iICHbt2kVSUhIdOnRg8uTJtGnTRgHwLqQAKDbjwoUL1KlTh0GDBvHJJ58A129z3Dj5c3bb8uXLefHFFzGZTCxbtkwPNIuITYiJicHf359//etfTJkyJdf2U6dOsWvXLpYuXcrSpUvx9vYmPDyctm3bWqFauRO6tyU2IzExETc3N86cOQNcD3o3TmiavQycnZ0dvXr14qOPPuLChQts3rzZsl1E5F62YcMGnJycaNq0KXD9+ecbV0Xy8/Ojd+/ezJ8/n3nz5pGWlsbzzz/P+fPnrVm2FIICoNiMwMBA/Pz8WL9+PZs2bcpzbUuj0Wg50fXp04eAgAB27dpFZmambm+IyD2vfPnymM1mjh8/DvwvAP5zfXQXFxcGDx7M6NGjOXToEAcPHrRm2VIICoBiU6ZPn47RaOShhx7ivffe4/Dhw2RkZABYTnDZnyMjI7Gzs8PZ2Rl7ey2aIyL3vhYtWlCmTBnmzZvHwYMHsbe3z3GXBK6fKzMzMwFo164drq6umvj5LqQAKDYlODiYd999Fzc3NyZPnszzzz/PrFmz2L59OzExMWRlZeHo6EhGRgZff/010dHR9O/f39pli4gUO5PJhLe3N7NmzSIyMpKWLVvy7rvv8tdff1nugvzzTsjx48dJSUmhQYMGVqpaCksvgYhNOnToEDNnzmTlypWcPXuWSpUqcf/99+Pp6YmrqysnT55k69atdOvWjZUrV1q7XBGREnPlyhU+/fRT3nvvPVJSUmjWrBmdOnWiefPm1KtXj9q1awOwbds2Ro0axblz5yzPVsvdQwFQbMqNz7LExsayd+9eduzYwc6dOzl06BCnTp0CwNfXl759+/L666/j4+NjzZJFRKwiMjKSzz//nB9//JGTJ0/i7u6Oj48PTk5OeHp68scff1CuXDkmTJjA8OHDrV2uFJACoNzTsgNfRkYGRqORuLg40tPT8fPzs/RJT0/n3Llzllscp06dolmzZri5uVmxchGRknOz1Y4SEhKIjo7m999/t8wBePLkSQICAvD19WXy5MkEBwfnuSqIlG4KgHLPO3z4MJ9//jkrV67EyckJs9lM5cqV6dixI/369aNmzZrWLlFExOri4+NJSUnhxIkT+Pn5UaNGDcu29PR00tPTcXNz48KFC6Snp1O1alUrVit3SgFQ7mmbNm3i5Zdf5sCBA9x3333UqlWL/fv353he5aGHHmLEiBF07twZJycnrfsrIjbl4sWLLFu2jI8++ojTp0+TlZVFVlYW9913H71796Z///7UrVvX2mVKEVMAlHtau3btiI6OZu7cubRv3x47OzscHBz466+/WLp0KYsXL+bo0aO4uLgwduxY3nrrLWuXLCJSokaPHs3nn3+Or68vDzzwAI6OjuzcuZPo6GiuXr0KQIcOHRg7diydOnWyzJequVHvbgqAcs86ffo0NWrUYNKkSYwfPx6DwZDnSWvZsmVMnz6d3bt38/rrrzN58mScnJysVLWISMk5efIkgYGBPPHEEyxatAjAcgdk3759rFmzhuXLl7Nr1y6cnZ15//33eemll6xZshQR3eeSe9aePXswGAyULVsWg8FAenq6JfyZTCaysrIA6NWrF//9739p0qQJs2bN4u+//7Zm2SIiJWbx4sW4ubkxbNgwS/DLnuS5UaNG/Otf/+LXX3/l22+/pWbNmowaNYpPP/3UmiVLEVEAlHtW/fr1Adi/fz8Ajo6Olm1Go9Hy1prZbKZ27dp8/vnnpKamsm3btpIvVkTECs6fP4/JZKJcuXLA9TXSs1c+MplMmEwmHBwcCA0NJSwsjMqVK/PFF1+QnJxszbKlCCgAyj3L19eXXr16MWfOHMaPH09MTEye/bJ/7RqNRsqWLcvJkydLskwREatp27YtSUlJ7NixAwAHBwfLNqPRmOOqYFBQECNHjuTEiRPs2rXLKvVK0VEAlHuWo6Mjr732Gvfddx/Tp09n1KhRrF27lrS0tBz9sk94e/bsISkpiXbt2lmjXBGREte6dWsaN27MyJEjmTx5MsePH+efrwbc+Nnd3Z3U1NQcd1Tk7qSXQOSed+zYMSZPnsySJUtIT0+ncePGPPbYY4SEhODq6oqjoyPR0dGMGjUKT09PDh8+bO2SRURKzE8//cTQoUOJi4ujZ8+ePPnkk7Rs2ZIKFSrg7OxseXY6Li6Ol156ibVr15KQkGDlquVOKQDKPSv7RQ8HBwdOnz5teZtt+/btJCUlYTQa8fT05NKlS8D1B56nTp3KQw89ZOXKRURKVnR0NO+88w4//PADV65coUGDBrRv35569erh6uqKi4sLCxcuZNWqVbzyyitMmTLF2iXLHVIAFJuSkZFhWfv3zJkzXLlyhYSEBHr06EHXrl3x9fW1dokiIiUmMzMTOzs7yzKYW7ZsYf369URERBATE0N6enqO/hMmTOCFF16gQoUKVqpYiooCoNxzMjMziYyMZN26dbi6uuLg4ED58uVp3LhxjjWA09LSNN+fiNi89PT0HM/0Xb16lb/++ovo6GhSUlI4d+4crq6uPPTQQ9x///1WrFSKkgKg3FOOHz/Ohx9+yGeffZajvUyZMgQGBtK+fXu6detGq1atcHNzy/HrV0TEVhw7dozVq1dz8OBBHB0dcXFx4f7776dDhw66E2IjFADlntKnTx+WL1/O0KFDadGiBfb29iQmJrJ161bWrVvH5cuXqVy5Ms888wwvvfQS3t7e1i5ZRKRELVmyhNdff52YmBgMBgMuLi6kpKQAUKlSJR5++GFCQ0Np3749jo6OZGRk5JgeRu4NCoByzzhx4gQ1a9Zk9OjRTJ8+PddVvbNnz7JixQrmzZvH77//TocOHfjyyy+pWbOmlSoWESlZMTExNGnSBC8vL2bOnImrqyvu7u6cPHmS77//nmXLlpGamoqXlxfDhw9n7NixeHp6WrtsKQaaB1DuGatWrcLR0ZEOHTpYln67UZUqVXjuuedYuHAhzz//PJs2bWLq1KmWJeFERO51c+bMwWg08vHHH/Pwww/Ttm1bgoKCeOyxx/jvf//L5cuXmTdvHv7+/kybNo3/+7//Iy4uztplSzFQAJR7hoODA9euXcPFxcXyOS+1atXiww8/5Nlnn2X+/PlER0eXZJkiIlbz22+/UblyZYKCgoD/rYR047RZgwcP5vvvv2fAgAF8//33fP3119YsWYqJAqDcM1q2bEmZMmWYMGECR48exWAwYDabc13hy8jIwNnZmS5dumA0GomIiLBSxSIiJScjI4OAgACio6Mta/9mr/t74/roANWrV+fzzz+nUaNG/Pe//yUpKckqNUvxUQCUe0ZgYCADBw5k27ZtjB07lr1792IwGCwnNZPJhNlstlwZTElJwWAw6I03EbEJDg4OtG3blpSUFIYNG2ZZ9/yfP5TNZjMmkwlXV1datGjB6dOniY2NtVbZUkwUAOWeUaZMGWbPns2LL77IDz/8QJMmTejWrRuLFy/mypUrGI1Gy4sh58+fZ/78+ZQrV45OnTpZuXIRkZLx0EMP8eCDD7Jw4UJef/11/vjjjxw/lAEMBgNGo5HLly+TlpaGg4MDtWrVsmLVUhz0FrDcM0wmE0ajkQsXLvDtt9/y73//m+PHjwPg4uJCq1ataNasGdHR0Wzbto3ExETeeecdRo8ebeXKRURKzpUrVxg9ejTz5s0DoF27djz77LM89NBDuLm5cfXqVby8vPjiiy8YO3YsAwYMyDW3qtz9FADlnmA2m/OczPnHH39kwYIFbNu2jUuXLuHk5ERqaipNmzbltddeo0ePHpaXRkRE7nWZmZnY29tz+vRpli5dSlhYGPv37weuPw8YHByMl5cXhw8fJjo6mtatW7NgwQLuu+8+K1cuRU0BUO4ZZ86cwdfXl9TUVDIyMvDw8LBsS05O5s8//wTA19cXNzc3fHx8rFWqiEipkJaWxs8//8xPP/3Evn37SEpK4sqVKzg6OjJgwACef/55qlatau0ypRgoAMpdzWw2s3LlSv7zn//w119/kZycTMOGDWnYsCFBQUE0aNCAmjVr4urqau1SRUSs6sKFC8TFxVG+fHkSExOpUKEC5cuXt2y/dOkSZ8+etQQ+Dw8PLZN5D1MAlLvahAkTmDFjBi4uLlSrVo2MjAzS09OJiYnBbDbTqFEjevfuzVNPPUWlSpWsXa6ISIk7d+4cb7zxBuvXr+fMmTO4u7tTo0YN6tSpQ3BwMK1ataJhw4aWx2Fu9kiN3FsUAOWudeLECe6//37at2/Phx9+SJ06dYiPjycmJobo6Gi2bt3K2rVriYqKolGjRkyZMoWHH37Y8rKIiMi9LjY2lscff5ydO3daXvIwGo2cPHmS/fv3k5qaSr169ejbty/PPvssVapUsXbJUkIUAOWu9c477/DJJ58QHh7Ogw8+aHm4OVtSUhIHDx4kPDycmTNn4uPjw5o1a2jcuLH1ihYRKUETJ05k5syZTJ48mZdffhmAy5cvk5yczPHjx1m3bh3ff/89hw8fpkWLFnzwwQe0bt1aVwFtgAKg3LWefvpp1q9fz549e/Dx8bGcsPI6cS1ZsoThw4dTt25drfwhIjbj/vvvJyAggHnz5lGxYsVc58e0tDQiIyMJCwvj448/pnbt2mzZsgVvb28rVi0lQffB5K7VsGFDYmNj+fXXX4Hrk5eaTKYcJ7fs3zehoaE88cQTHD16lMjISKvUKyJSks6fP4/ZbCYtLY2KFSsC5Ppx7OTkRMOGDZk2bRozZ84kMjKSjz76yBrlSglTAJS7VnBwMK6urrz11lv8/vvvAJZn+7KXMsoOhXB9qbjU1FStaSki9zyz2UzFihW5//772blzJ7t27bK0/3N9dLg+B+CLL75I/fr12b17N8nJySVdspQwBUC5K5nNZh544AE+/vhjoqKiCA4OZvjw4WzYsIErV65YljKC66EwNTWVv/76C2dnZ5o3b27l6kVEilf2ObBLly5cuXKFV199lYMHD+ZaHz0rK8typyQpKYlq1apx4cIF3NzcrFm+lAD723cRKX2yb2M8+eSTZGZmMnHiRObMmcPy5csJCQmhRYsWBAcH06RJE6Kiopg3bx7Lli3jxRdftHLlIiIlZ+jQoSQkJDB+/HgaNGjAoEGD6N+/P23btsXZ2Rn436Myu3fvZt++fXTr1s2aJUsJ0Usgclf654PMKSkpzJ07lyVLlrB7927LLQ6DwYC9vT0ZGRkMHjyYd955B19fX2uVLSJSYrLPk5cvX2bevHlMmzaNuLg47OzsaNq0Ka1bt6ZDhw54enqye/duZs+ezZUrV9i4cSMNGjSwdvlSzBQA5Z4SHx/PkSNH2LFjB7/++itZWVnUqlWLunXr8n//93/WLk9EpMT884fytWvXCAsL47///W+esyHUq1ePcePGMWDAgJIsU6xEAVDuOhcuXOCvv/7iyJEjJCcnExwcTJ06dahQoYLl2ZZsaWlpODk5WT5rbisRETh16hS//PILBw4coFKlSnh7e9OmTRtq1qxp7dKkhCgAyl1lzZo1vPvuu7l+vZYrV44HH3yQ0NBQHnnkERwcHCzbtPKHiNian3/+mQMHDrB37158fHxo1qwZNWvWpFq1apQvXz7HOVJskwKg3DViYmJo3749KSkpDB48mA4dOnDs2DH27NnDvn372L9/P2lpadSrV4/x48fTu3dvHB0dddVPRGzG5cuXmTp1Kh988AF2dnY5pnwpV64crVu35vHHH+fRRx+lXLlylm06T9oevQUsd40vv/ySS5cuMXfuXJ544okc206fPs1vv/3GihUrWLRoEQMHDuT06dO8/vrrOqmJiM2YM2cOs2fP5rHHHuOll16iSpUq7Nmzh8jISHbv3k1ERAQ//fQTQUFBvPXWWzz22GNA7gmi5d6nK4By12jZsiVlypRh6dKlVKhQgczMzBxzWmXbtGkTr7zyCn///TefffYZQ4YMsVLFIiIlq3r16tSvX5+wsDDKly+fY9vZs2fZs2cPK1asYN68eWRlZfHVV1/x7LPPWqlasSY9GCV3heTkZNzd3YmNjcXFxQW4PsFzdvjLXvkDoEOHDvznP//BxcWFH3/80bJdRORedvjwYS5evEijRo0s4c9kMlnOjVWqVKF79+7MmjWLH3/8kRo1ajB27Fitj26jFADlruDm5kbTpk2JjIxk8eLFALle7Mj+bDKZCAoKom3bthw+fJiTJ0/q9oaI3PPMZjNly5YlOjoagMzMTCDnEplmsxlHR0e6devGRx99xKVLlyzrqYttUQCUu0b2OpXPPvssL730En/++SfXrl0D/vf8SmZmJkajkaSkJBwdHbl27Rr+/v7WLFtEpETUrVsXX19fVq9ezZo1a7C3t8/1Q/nG9dEfeOABqlevzu7du61RrliZAqDcNXx9fXn77bepXr06s2fPZvjw4cyYMYPNmzdz8uRJrl27hr399feafvrpJzZv3szDDz9s5apFRIpf9mMu//73v/Hw8KB79+6MHj2aXbt25fqhnJGRAUBkZCRpaWlUqVLFOkWLVeklECn1/jk9QUJCAlOnTiU8PJyYmBgqVqxI/fr1qVKlCi4uLqSmphIeHk6NGjVYvnw5tWvXtmL1IiIlJysri4ULFzJu3DhiY2OpV68eXbp0oVWrVtSrV486depgNBo5c+YMr732GkuXLmXnzp00adLE2qVLCVMAlLtCdgg8ffo0VapUwWg0cuDAAVauXMnmzZs5dOgQMTExAHh5edG4cWP+/e9/c//991u5chGRkhcXF8fs2bMJDw/nyJEjuLi44Ovri5ubG+XKlePw4cPExcXxzDPP8Nlnn1m7XLECBUAp1TIzM9m+fTvz5s3jyJEjGAwGXFxcaN68OX379iUoKAiz2UxMTAypqakcO3aMOnXqUK1aNezt7TW5qYjYlOwZEezs7EhNTSUqKordu3ezfft2du7cyeHDh6lYsSLVqlXj2WefZeDAgbi6ulq7bLECBUAp1WbMmME777zDlStXqFmzJnZ2dkRGRlq216tXjxEjRtC7d2+8vb2tWKmISOlkMpm4du0ajo6OJCYmEhsbq7sjogAopdfx48dp0KABTZo0ISwsDEdHR3x8fIiNjeWnn35i6dKlbN68Gbg+99+0adNo1qyZdYsWESlBqampnDp1Cj8/P8qUKZNjm8lkwmAwWO6C/POOiNZJt20KgFJqTZgwgS+//JJFixbx4IMPArlPYH/99RczZswgPDwcf39/vvnmG5o2bWqtkkVEStT777/PsmXLeOKJJ2jZsiW1a9fGx8cnxwpJ2f9vPvvcGRcXh5eXl2XWBLFNCoBSavXq1Yu9e/eyadMm/Pz8yMzMtDzXl/2MS7aZM2cyevRonn76aebPn2/FqkVESk7VqlU5e/YsdnZ2eHp60qpVK7p06UKLFi0ICAjItRxcSkoKkyZN4uLFi8ydO1dXAG2Y4r+UWkFBQfzwww8kJycDWH6t3rj+b/YVwZdffplff/2VjRs3cuzYMQICAqxWt4hISThy5AiJiYmEhITQv39/1q9fT0REBCtXrsTPz4/27dvTqVMngoKC8PX1pWzZshw4cIA5c+bQvn17hT8bpwAopVaHDh0AGDBgAB9++CFt2rTB0dExV7+srCzs7OyoXbs2a9assQRGEZF72ZEjR7h27RpdunRh5MiR9OjRg8jISCIiIti4cSPLli3jm2++oV69enTs2JGHHnqIDRs2kJSUxNChQ61dvliZbgFLqZWVlcXYsWP56KOPqFOnDiNHjqR37974+Pjk6nvp0iVGjRrFmjVruHDhghWqFREpWd999x19+/Zl8eLF9O3b19KekZHByZMn2bdvH7/++qtlrlQHBwfMZjNOTk4kJCRYsXIpDRQApdT78ssv+eCDDzh27BhVqlTh8ccf5+GHH6ZatWrY2dlRtmxZZs2axSeffMKIESP48MMPrV2yiEixM5vNHD58GGdnZ2rUqJHnvKcpKSkcOXKEyMhI5s+fz/r163nhhRf497//baWqpbRQAJRSz2w2c/ToUebMmcPixYs5ffo0AN7e3jg4OHDu3DlMJhNPPvkk06ZNo2rVqlauWETEuvIKgy+99BKzZ8/mjz/+ICgoyEqVSWmhACh3lZSUFHbt2sWKFSs4e/YsFy5cwMPDg759+9KrVy+cnZ2tXaKISKmRPdffiRMn6NmzJ5cuXeLUqVPWLktKAb0EIncVV1dXOnToQIcOHcjIyMDBwcHaJYmIlFrZb/qeOXOGjIwMRowYYeWKpLTQFUAREZF7nNls5vTp05QrV05r/wqgACgiIiJiczQLpIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjfl/KcsuNuqPl3IAAAAASUVORK5CYII=" - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit.visualization import plot_histogram\n", - "\n", - "evidence = {str(i): 0 for i in range(n-1)}\n", - "# Initialize quantum bayesian\n", - "qbayesian = QBayesian(circuit=qc)\n", - "# Inference\n", - "samples = qbayesian.rejection_sampling(evidence=evidence)\n", - "print(samples)\n", - "plot_histogram(samples)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:17.943025Z", - "start_time": "2023-11-10T03:10:10.706205Z" - } - }, - "id": "cbb3c2d9a11b43ac" - }, - { - "cell_type": "markdown", - "source": [ - "# Step 5: Burglary Alarm Example: \n", - "\n", - "Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." - ], - "metadata": { - "collapsed": false - }, - "id": "72989e15f2fdd872" - }, - { - "cell_type": "code", - "execution_count": 16, - "outputs": [ - { - "data": { - "text/plain": "
", - "image/png": 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" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# Create a directed graph\n", - "G = nx.DiGraph()\n", - "# Add nodes\n", - "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", - "# Add edges\n", - "G.add_edges_from([(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"),\n", - " (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")])\n", - "# Manually set positions\n", - "pos = {\"Burglary\": (0, 1), \"Earthquake\": (1, 1),\n", - " \"Alarm\": (0.5, 0.5),\n", - " \"JohnCalls\": (0, 0), \"MaryCalls\": (1, 0)}\n", - "# Draw the network\n", - "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", - "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", - "plt.show()\n", - " " - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:18.025012Z", - "start_time": "2023-11-10T03:10:17.953579Z" - } - }, - "id": "16f5ec62b6f90570" - }, - { - "cell_type": "markdown", - "source": [ - "The Bayesian Network for this scenario involves the following variables:\n", - "\n", - "Burglary (B): Whether a burglary has occurred.\n", - "Earthquake (E): Whether an earthquake has occurred.\n", - "Alarm (A): Whether the alarm goes off.\n", - "John Calls (J): Whether John calls you.\n", - "Mary Calls (M): Whether Mary calls you." - ], - "metadata": { - "collapsed": false - }, - "id": "85ffd7ab1e8316e4" - }, - { - "cell_type": "code", - "execution_count": 17, - "outputs": [], - "source": [ - "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", - "theta_E = 2 * np.arcsin(np.sqrt(0.002))\n", - "theta_A_nBnE = 2 * np.arcsin(np.sqrt(0.001))\n", - "theta_A_nBE = 2 * np.arcsin(np.sqrt(0.29))\n", - "theta_A_BnE = 2 * np.arcsin(np.sqrt(0.94))\n", - "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", - "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", - "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_M_nA = 2 * np.arcsin(np.sqrt(0.01))\n", - "theta_M_A = 2 * np.arcsin(np.sqrt(0.7))\n", - " " - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:21.228824Z", - "start_time": "2023-11-10T03:10:21.206538Z" - } - }, - "id": "f79d7c9a5cca338" - }, - { - "cell_type": "markdown", - "source": [ - "The Bayesian network can be represented by the following quantum circuit:" - ], - "metadata": { - "collapsed": false - }, - "id": "d2693a276552450f" - }, - { - "cell_type": "code", - "execution_count": 18, - "outputs": [ - { - "data": { - "text/plain": "
", - "image/png": 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- }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize register\n", - "var = ['B','E','A','J','M']\n", - "qr = [QuantumRegister(1, name=v) for v in var]\n", - "qc = QuantumCircuit(*qr, name='Pachinko')\n", - "# Specify control qubits\n", - "# P(B)\n", - "qc.ry(theta_B, qr[0])\n", - "# P(E)\n", - "qc.ry(theta_E, qr[1])\n", - "# P(A|-B,-E)\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", - "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", - "# P(A|-B,E)\n", - "qc.x(qr[0])\n", - "qc.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[0])\n", - "# P(A|B,-E)\n", - "qc.x(qr[1])\n", - "qc.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[1])\n", - "# P(A|B,E)\n", - "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", - "# P(J|-A)\n", - "qc.x(qr[2])\n", - "qc.cry(theta_J_nA, qr[2], qr[3])\n", - "qc.x(qr[2])\n", - "# P(J|A)\n", - "qc.cry(theta_J_A, qr[2], qr[3])\n", - "# P(M|-A)\n", - "qc.x(qr[2])\n", - "qc.cry(theta_M_nA, qr[2], qr[4])\n", - "qc.x(qr[2])\n", - "# P(M|A)\n", - "qc.cry(theta_M_A, qr[2], qr[4])\n", - "# Draw circuit\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)\n" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:22.846088Z", - "start_time": "2023-11-10T03:10:22.535173Z" - } - }, - "id": "85bb861283b06275" - }, - { - "cell_type": "markdown", - "source": [ - "Using this network, you can perform various probabilistic inferences. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." - ], - "metadata": { - "collapsed": false - }, - "id": "bb0e805d2f7fb30c" - }, - { - "cell_type": "code", - "execution_count": 19, - "outputs": [ - { - "data": { - "text/plain": "0.004829999999999999" - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "query = {'B': 1}\n", - "evidence = {'J': 1}\n", - "# Initialize quantum bayesian inference framework\n", - "qbayesian = QBayesian(circuit=qc)\n", - "# Inference\n", - "qbayesian.inference(query=query, evidence=evidence)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T03:10:59.887367Z", - "start_time": "2023-11-10T03:10:59.526529Z" - } - }, - "id": "5468619791203a79" - }, - { - "cell_type": "code", - "execution_count": null, - "outputs": [], - "source": [], - "metadata": { - "collapsed": false - }, - "id": "72a1d1076dd05cb0" - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} From 75e9da37b6783171eb0610028ed3ff31425109ea Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 13:18:35 +0100 Subject: [PATCH 17/48] Bug fix example step 5 tut 13 --- .../13_quantum_bayesian_inference.ipynb | 94 +++++++++---------- 1 file changed, 47 insertions(+), 47 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index e3489b483..1010958ae 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -29,13 +29,13 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 17, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-10T03:10:06.512307Z", - "start_time": "2023-11-10T03:10:06.456456Z" + "end_time": "2023-11-10T12:08:45.299538Z", + "start_time": "2023-11-10T12:08:45.253178Z" } }, "outputs": [ @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 18, "outputs": [], "source": [ "# Include libraries\n", @@ -94,8 +94,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:06.848751Z", - "start_time": "2023-11-10T03:10:06.845522Z" + "end_time": "2023-11-10T12:08:45.305983Z", + "start_time": "2023-11-10T12:08:45.303595Z" } }, "id": "326c1d2e72f41202" @@ -114,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 19, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, - "execution_count": 12, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:07.780289Z", - "start_time": "2023-11-10T03:10:07.719567Z" + "end_time": "2023-11-10T12:08:45.395309Z", + "start_time": "2023-11-10T12:08:45.309905Z" } }, "id": "4f99dbe56bc6910a" @@ -169,13 +169,13 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 20, "outputs": [ { "data": { - "text/plain": "0.11865" + "text/plain": "0.12128" }, - "execution_count": 13, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -193,8 +193,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:08.571707Z", - "start_time": "2023-11-10T03:10:08.432543Z" + "end_time": "2023-11-10T12:08:45.493775Z", + "start_time": "2023-11-10T12:08:45.405510Z" } }, "id": "841bce19ea097bf1" @@ -213,14 +213,14 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 21, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 14, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -249,8 +249,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:09.555012Z", - "start_time": "2023-11-10T03:10:09.304520Z" + "end_time": "2023-11-10T12:08:45.782782Z", + "start_time": "2023-11-10T12:08:45.493232Z" } }, "id": "3764be5e0ce2db02" @@ -267,21 +267,21 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 22, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'1000000000': 0.3803, '0000000000': 0.6197}\n" + "{'0000000000': 0.60154, '1000000000': 0.39846}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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HjxIeHk6TJk344osvGDlyZFEdUkREREQKwf5OvnzmzBnmzZvH/PnzOXnyJABdunRh+PDhPPLII9jZ2QEQEBBA7969eeSRR/jxxx/vvGoRERERKbRCB8AePXqwdu1asrKy8PHxYezYsQwbNozq1avf9DutWrVi9erVhT2kiIiIiBSBQgfA1atX07FjR4YPH87jjz+Ovf3td/XII49QpUqVwh5SRERERIpAoQPgkSNHqFmzZoG+U79+ferXr1/YQ4qIiIhIESj0SyBTpkxhxYoVt+yzcuVKhgwZUqj97969m27dulG2bFlcXV1p2bIl4eHhhdoXwKVLl/D19cVgMPDQQw/l2cdgMNz0n8GDBxf62CIiIiKlSaGvAC5YsIDq1avz6KOP3rTPvn37CAsLY968eQXa96ZNm+jatSvOzs7069cPd3d3li1bRmhoKDExMbzyyisFrveFF14gMTHxtv38/f3zDHuNGzcu8DFFRERESqM7egv4dq5du5avZwNvlJmZydChQzEajWzdutUSvCZMmEBwcDDjx4+nd+/e+Pv753ufy5YtY9GiRcyePZsXXnjhln2rV6/OpEmTClSziIiIyN3kjuYBNBgMebabzWZOnTrFmjVrCvzSx8aNG4mOjqZ///45rrp5enoyfvx40tPTCQsLy/f+4uLieP7553nqqafo3r17gWoRERERuRcV6PKc0WjMEfomTZp0y6tlZrOZsWPHFqigzZs3A9fnE/ynrl27ArBly5Z87++5557Dzs6OmTNn5usW8OXLl/nqq6+Ij4+nXLlytG7dmgYNGuT7eCIiIiKlXYECYNu2bS0BcOvWrfj5+eU575+dnR3lypWjY8eODB06tEAFRUVFARAYGJhrW6VKlXBzc7P0uZ2FCxfy/fffs3z5cry8vPIVAPft28fw4cNztD300EOEhYXh7e19y++mpaWRlpZm+ZyUlARARkYGGRkZwPUQbWdnR1ZWFiaTydI3uz0zMxOz2Wxpt7Ozw2g03rRdpLTJ/m89W/ZjIJmZmTnaHRwcMJlMZGVlWdoMBgP29vY3bb/Z301R/T3lt3aNSWPSmDSm0jimgihQAMy+Opd9oGeeeYYJEyYU6IC3kx3SPD0989zu4eGRryB39uxZXnrpJZ588kl69uyZr2O/8sor9OrVi1q1auHo6MiBAwd45513WLNmDT169CAiIsKyuklepk6dyuTJk3O1r1u3DhcXFwD8/PwICgpi//79nDp1ytKndu3a1KlTh127dhEXF2dpb9y4Mf7+/mzdupUrV65Y2kNCQm4bSEWs4Z+TvXfr1o3U1FQ2bdpkabO3t6d79+7Ex8cTERFhaXd3d6djx47ExMSwd+9eS3vFihVp1aoVUVFRREZGWtqL+u9p3bp1OU7YHTp0oEyZMhqTxqQxaUx3xZgK8tidwXxjxC0FunTpwvr164mKispznkFfX1+Sk5NvGwK7devGH3/8wcGDB6lQoQIAJ06coEaNGnTt2pWff/45X/WYTCY6duzIli1bWLZsGU888cRN++Z1BbBatWrEx8fj4eEBFP2vkaGf5GsYIiXms5G6AqgxaUwak8ZkjTGlpKTg6elJYmKiJXfcTLG+BVwY2Vf+bhbwkpKS8PLyuuU+wsLCWLNmDUuXLrWEv8IyGo0MHTqULVu2sH379lsGQCcnJ5ycnHK1Ozg44ODgkKPNzs4uz6uJN3truqBvU4tYyz//W79Vu9FozPO2xc3ab/Z3U1R/TwWp/WbtGpPGBBrTzWosaLvGVPAx5Ve+U8WQIUMwGAxMmTIFHx+ffE/wbDAY+M9//pPvgrKf/YuKiqJp06Y5tsXGxpKcnExwcPAt97Fnzx4A+vTpk+f2tWvXYjAYaNSoUY7LrTeTHSJTUlJu21dERESktMt3AFywYAEGg4GxY8fi4+PDggUL8vW9ggbAdu3aMXXqVNatW0e/fv1ybFu7dq2lz62EhISQnJycqz05OZklS5ZQtWpVunbtip+fX75q2rlzJ0CeL7yIiIiI3G3y/QzgyZMngevP4Nnb21s+50dBJm3OzMykdu3anDlzhh07dljmAkxMTCQ4OJgTJ04QGRlpCWPnzp0jMTGRypUr3/TFkWy3egbwr7/+ok6dOrku1/7222907tyZjIwMDh06xH333ZfvsSQlJeX7Xnxh6RlAKW3mjLJ2BSIitqkguSPfVwD/GeIKEuoKwt7enrlz59K1a1fatm2bYym4kydPMmPGjBxX4saNG0dYWBjz58+/o/V6P/zwQ1atWkWbNm2oVq0aDg4OHDx4kHXr1mEwGPj0008LFP5ERERESqtS+WZBhw4d2LZtGxMnTmTJkiVkZGTQoEEDpk2bRmhoaLEcs2fPnly+fJl9+/axfv160tPTqVSpEv369WPUqFG3fe5QRERE5G6R71vAN841U1D5fdbuXqNbwGKLdAtYRMQ6iuUWcPXq1W+69u+tGAyGXPPgiIiIiIj15DsADho0qFABUERERERKlwJNAyMiIiIid7+CrRwsIiIiInc9BUARERERG1PqloITERERkeKV72lgjEYjBoOBQ4cOUatWrTwXLM7zAAYDWVlZd1Tk3UrTwIgt0jQwIiLWUSzTwBw/fhy4vhTcjZ9FRERE5O6S72cA/f398ff3x97ePsfn/PwjIiIipcenn35K9erVcXZ2pkWLFuzateumfb///nuaNWtG2bJlcXV1pXHjxnz99dc5+iQnJ/PCCy9QtWpVypQpQ7169fjiiy+KexhyB0rlUnAiIiJSPJYsWcKYMWP44osvaNGiBZ988gldu3YlMjISb2/vXP3LlSvHG2+8QZ06dXB0dGTlypU888wzeHt707VrVwDGjBnDxo0bWbhwIdWrV2fdunWMGDGCKlWq8Oijj5b0ECUf7vgt4B9++IGePXvi5+eHp6cnfn5+PPbYYyxfvrwIyhMREZGi9NFHHzF06FCeeeYZy5U6FxcX5s2bl2f/9u3b8/jjj1O3bl3uu+8+Xn75ZRo2bMi2bdssfX777Teefvpp2rdvT/Xq1Rk2bBiNGjW65ZVFsa5CB8DMzEz69u1L7969+emnn4iNjcXFxYXY2FhWrFhBr1696Nu3r5aBExERKSXS09P5448/6NSpk6XNaDTSqVMnIiIibvt9s9nMhg0biIyMpG3btpb2Vq1asWLFCs6cOYPZbGbTpk0cOXKELl26FMs45M4VOgBOnTqV7777jgceeIBff/2Va9euce7cOa5du8bWrVtp06YNy5Yt4/333y/KekVERKSQ4uPjycrKwsfHJ0e7j48PsbGxN/1eYmIibm5uODo60r17d2bNmkXnzp0t22fNmkW9evWoWrUqjo6OPPTQQ3z66ac5QqKULoV+BnD+/PnUqVOHX375xfJiCFz/JdGmTRt++eUXGjZsyLx583jzzTeLpFgREREpee7u7uzdu5fk5GQ2bNjAmDFjCAgIoH379sD1ALhjxw5WrFiBv78/W7duZeTIkVSpUiXH1UYpPQodAM+dO8dLL72UI/zdyMHBgUceeYRZs2YVujgREREpOhUqVMDOzo7z58/naD9//jyVKlW66feMRiM1a9YEoHHjxhw6dIipU6fSvn17UlNTGT9+PD/88APdu3cHoGHDhuzdu5cZM2YoAJZShb4FXK1aNZKTk2/ZJyUlBT8/v8IeQkRERIqQo6MjTZs2ZcOGDZY2k8nEhg0bCAkJyfd+TCYTaWlpAGRkZJCRkZFrgQg7OztMJlPRFC5FrtAB8NlnnyU8PJxz587luf3MmTMsWbKEZ599ttDFiYiISNEaM2YMc+bMISwsjEOHDvH888+TkpLCM888A8CgQYMYN26cpf/UqVNZv349x44d49ChQ3z44Yd8/fXXDBw4EAAPDw/atWvHa6+9xubNmzl+/DgLFizgv//9L48//rhVxii3l+9bwKdOncrxuW/fvmzfvp2goCBGjRpFmzZt8PHx4fz58/z666/MnDmTNm3a0KdPnyIvWkRERAonNDSUuLg4JkyYQGxsLI0bN+bnn3+2vBhy6tSpHFfzUlJSGDFiBKdPn6ZMmTLUqVOHhQsXEhoaaumzePFixo0bx4ABA0hISMDf35/33nuP5557rsTHJ/lT4LWA/8lsNt+0Pft7tjoVjNYCFluktYBFRKyjWNYCHjRoUJ5BT0RERETuLvkOgAsWLCjGMkRERESkpNzxUnAiIiIicndRABQRERGxMYWeCBrgypUrzJ49m19++YWzZ89a5gS6kcFgIDo6+k4OIyIiIiJFqNABMC4ujlatWhEdHY2Hh4flzZP09HRSU1MBqFKlCg4ODkVWrIiIiIjcuULfAp40aRLR0dH897//5dKlSwCMHj2alJQUdu7cSXBwMNWrV+fgwYNFVqyIiIiI3LlCB8DVq1fz4IMPMnDgwFzTwzRv3pw1a9Zw4sQJJk+efMdFioiIiEjRKXQAPHfuHEFBQZbPdnZ2llu/AF5eXjz88MOEh4ffWYUiIiIiUqQKHQA9PT3JyMiwfPby8uL06dM5+nh4eHD+/PnCVyciIiIiRa7QATAgIIATJ05YPgcFBbF+/XouXrwIQGpqKj/99BN+fn53XKSIiIiIFJ1CB8AuXbqwYcMGrl69CsDw4cO5cOECjRo1ok+fPtSvX5/o6GgGDx5cVLWKiIiISBEo9DQwzz33HPXq1ePq1au4uLjwxBNP8MEHH/Duu++ybNkyypQpw5gxY3jttdeKsl4REZF8G/qJtSsQ+Z85o6xdwf8UOgBWrlyZ0NDQHG2vvPIKo0aNIj4+Hm9v71xvB4uIiIiI9d3RSiB5sbOzw8fHp6h3KyIiIiJF5I4D4Llz51i8eDF79uwhMTERT09PgoKC6NevH5UrVy6KGkVERESkCN1RAPz000957bXXSEtLw2w2W9oXLlzIG2+8wYwZMxgxYsQdFykiIiIiRafQAXDx4sW8+OKLVKhQgTfeeIMHHngAHx8fzp8/z9atW5k5c6Zle9++fYuyZhERERG5A4UOgNOnT6dChQrs3buXKlWqWNpr165N27ZtGTx4MEFBQUybNk0BUERERKQUKfQ8gIcOHaJv3745wt+NqlatSp8+fTh06FChixMRERGRolfoAFi2bFlcXV1v2cfNzY2yZcsW9hAiIiIiUgwKHQAfffRRfvrpJzIzM/PcnpGRwU8//UTPnj0LXZyIiIiIFL1CB8Dp06fj6upKly5d2LFjR45tERERdOnSBXd3d95///07LlJEREREik6+XwIJCAjI1Zaens6ff/5J69atsbe3p0KFCsTHx1uuClauXJkmTZoQHR1ddBWLiIiIyB3JdwA0mUy5lnZzcHDAz88vR9s/XwoxmUx3UJ6IiIiIFLV8B8ATJ04UYxkiIiIiUlIK/QygiIiIiNyd7ngtYIDMzEwiIyNJSkrCw8OD2rVrY29fJLsWERERkSJ2R1cAExISGDp0KJ6enjRs2JA2bdrQsGFDypYty7Bhw7h48WJR1SkiIiIiRaTQl+kSEhJo2bIlR48epVy5cjzwwANUrlyZ2NhYfv/9d+bOncuWLVuIiIigXLlyRVmziIiIiNyBQl8BfOeddzh69CivvfYaJ0+e5Oeff2b+/PmsWbOGkydPMnbsWKKionjvvfeKsl4RERERuUOFDoA//vgj7du3Z9q0abmWhHNxcWHq1Km0b9+eH3744Y6LFBEREZGiU+gAePbsWUJCQm7ZJyQkhLNnzxb2ECIiIiJSDAodAD09PTl58uQt+5w8eRJPT8/CHkJEREREikGhA2C7du1YunQpv/zyS57bN2zYwNKlS2nfvn1hDyEiIiIixaDQbwFPnDiRVatW0bVrV7p160a7du3w8fHh/PnzbN68mTVr1uDi4sKECROKsl4RERERuUOFDoD3338/a9euZfDgwaxatYpVq1ZhMBgwm80A3HfffSxYsID777+/yIoVERERkTt3R8t1tGnThqioKLZv386ePXssK4EEBQXRunVrDAZDUdUpIiIiIkWk0AFwyJAhNGjQgNGjR9OmTRvatGlTlHWJiIiISDEp9EsgixYt4sKFC0VZi4iIiIiUgEIHwPvuu49z584VZS0iIiIiUgIKHQCHDBnCqlWrOHPmTFHWIyIiIiLFrNDPAPbq1YtNmzbRqlUrXn/9dZo3b46Pj0+eL374+fndUZEiIiIiUnQKHQADAgIs07689NJLN+1nMBjIzMws7GFEREREpIgVOgAOGjRI07yIiIiI3IUKHQAXLFhQhGWIiIiISEkp9EsgIiIiInJ3uqOVQADS0tJYvXo1e/bsITExEU9PT4KCgujWrRtOTk5FUaOIiIiIFKE7CoArVqxg2LBhxMXFWdYAhusvfnh7e/PVV1/xyCOP3HGRIiIiIlJ0Ch0AN2zYQK9evbCzs2PIkCE88MAD+Pj4cP78ebZu3crChQt54oknWLt2LR07dizKmkVERETkDhQ6AE6cOJEyZcrw22+/Ub9+/RzbBg0axEsvvUTr1q2ZOHGiAqCIiIhIKVLol0D27NlDaGhorvCXrWHDhvTt25c///yzUPvfvXs33bp1o2zZsri6utKyZUvCw8Pz/f01a9bQr18/6tSpQ9myZXFxcaFOnTr83//9H0eOHLnp99auXUu7du1wd3fHw8ODDh06sGHDhkKNQURERKQ0KvQVQBcXFypWrHjLPt7e3ri4uBR435s2baJr1644OzvTr18/3N3dWbZsGaGhocTExPDKK6/cdh+rV69mx44dtGjRgocffhgHBwcOHTpEWFgY33zzDatXr851ZXLhwoU89dRTVKxYkcGDBwOwZMkSOnfuTHh4OL179y7wWERERERKG4P5xrc3CuDJJ58kOjqaXbt23bRP8+bNCQwMZNGiRfneb2ZmJnXq1OH06dPs2LGDxo0bA5CYmEhwcDAnTpzgyJEj+Pv733I/165dw9nZOVf7hg0b6NSpE82aNWP37t2W9kuXLhEQEIC9vT179uyhatWqAJw+fZqgoCAAjh07hru7e77HkpSUhKenJ4mJiXh4eOT7ewUx9JNi2a1Ioc0ZZe0KRP5H50gpTYr7/FiQ3FHoW8AzZszgwoULDBo0iJiYmBzbYmJieOqpp4iPj2fGjBkF2u/GjRuJjo6mf//+lvAH4Onpyfjx40lPTycsLOy2+8kr/AE8+OCDeHl5cfTo0RztS5cu5fLly7z44ouW8AdQtWpVXnjhBeLj4/nhhx8KNBYRERGR0qjQt4CfeuopvLy8+Oabb1i8eDF+fn6Wt4BPnTpFVlYWDRs2ZODAgTm+ZzAYbvlM3ebNmwHo0qVLrm1du3YFYMuWLYUtm4iICC5dukSbNm0KdNxJkyaxZcsWBg0aVOhji4iIiJQGhQ6A2YEJrt+2PXbsGMeOHcvRZ9++fbm+d7v1g6OiogAIDAzMta1SpUq4ublZ+uTHunXr+O2330hLSyMqKoqVK1dSoUIFPv7443wfN7vtdsdNS0sjLS3N8jkpKQmAjIwMMjIyADAajdjZ2ZGVlYXJZLL0zW7PzMzMMaeinZ0dRqPxpu0ipU32f+vZ7O2vn2YyMzNztDs4OGAymcjKyrK0GQwG7O3tb9p+s7+bovp7ym/tGtPdNCatWS+lS3H+PRVEoQPgjQctSomJicD1W7558fDwsPTJj3Xr1vHhhx9aPtesWZPFixfTtGnTfB83+z767Y47depUJk+enGcN2S/D+Pn5ERQUxP79+zl16pSlT+3atalTpw67du0iLi7O0t64cWP8/f3ZunUrV65csbSHhITg7e19y3pErGH16tU5Pnfr1o3U1FQ2bdpkabO3t6d79+7Ex8cTERFhaXd3d6djx47ExMSwd+9eS3vFihVp1aoVUVFRREZGWtqL+u9p3bp1OUJEhw4dKFOmjMZ0F48JHBApTYrz76lKlSr5rqPQL4EUly5durB+/XqioqKoWbNmru2+vr4kJycXKAQCJCcn8/fff/P222/zyy+/MG/ePPr372/ZXqtWLaKiosjIyLD8msyWkZGBo6MjDRs2zPOqZra8rgBWq1aN+Ph4S4gs6l/CesBZSpvPRuoKoMZUesY0bKauAErpMWdU8V4BTElJyfdLIHe8FnC2U6dOceLECdq2bXtH+8m+AnezgJeUlISXl1eB9+vm5kZwcDDLly+nWbNmDBs2jM6dO1umsrnxuOXLl891zBv73IyTk1Oe6x87ODjg4JDzV6idnR12dna5+v4zfN6uXaS0+ed/67dqNxqNed62uFn7zf5uiurvqSC136xdYyp9YxIpTYr77ynfdRT6m/8wf/58OnTocMf7udXzdrGxsSQnJ+f5nF5+2dvb06FDB1JSUvj999/zddxbPR8oIiIicrcpdW8RtGvXDrj+3Nw/rV27Nkefwjp79iyQ89diSRxXREREpDQodQHwwQcfJCAggEWLFuV4GDIxMZEpU6bg6OiYYyqWc+fOcfjw4Vy3jG+8unejtWvX8sMPP1C2bFlCQkIs7X379sXT05NZs2Zx+vRpS/vp06eZPXs2FSpU4PHHHy+iUYqIiIhYT6l7sMze3p65c+fStWtX2rZtm2MpuJMnTzJjxgyqV69u6T9u3DjCwsKYP3++Zfk2uL4KSf369WnYsCFVq1YlJSWF/fv38+uvv+Lg4MC8efNwdXW19Pfy8mL27Nk89dRTNGnShNDQUOD6UnAXL15kyZIlBVoFRERERKS0KrIA6OnpiZ+fX5Hsq0OHDmzbto2JEyeyZMkSMjIyaNCgAdOmTbMEs9uZMmUKmzZtYsuWLcTFxWE0GvHz82PYsGGMGjWKunXr5vrOwIEDqVChAlOmTGH+/PkYDAaaNm3Km2++SadOnYpkbCIiIiLWVuqmgbmXaC1gsUVaC1hKE50jpTS5J9YCFhEREZG7U75vAW/duhWA4OBgnJ2dLZ/z407nBhQRERGRopPvANi+fXsMBgOHDh2iVq1als/5cePM1iIiIiJiXfkOgBMmTMBgMFChQoUcn0VERETk7pLvADhp0qRbfhYRERGRu4NeAhERERGxMYUOgFeuXOHYsWNkZGTkaF+yZAkDBgzg//7v//jzzz/vuEARERERKVqFngj69ddfZ+HChZw/f96ypu7nn3/OCy+8QPbUgosXL+aPP/6gTp06RVOtiIiIiNyxQl8B3LJlC506dcLFxcXS9v777+Pr68vWrVsJDw/HbDbzwQcfFEmhIiIiIlI0Cn0F8Ny5czz00EOWz4cOHSImJobp06fTpk0bAL777rsCzRcoIiIiIsWv0FcA09LScHR0tHzesmULBoOBLl26WNoCAgI4c+bMnVUoIiIiIkWq0AGwatWq7N+/3/J55cqVlCtXjoYNG1raLl68iJub251VKCIiIiJFqtC3gB9++GE+/fRTXn31VZydnfn5558ZNGhQjj5HjhzBz8/vjosUERERkaJT6AA4btw4fvrpJz766CMAKleuzNtvv23ZfuHCBbZv384LL7xw51WKiIiISJEpdACsVKkSBw8eZMOGDQC0bdsWDw8Py/b4+Hg++OADunbteudVioiIiEiRKXQABChTpgw9evTIc1u9evWoV6/enexeRERERIqBloITERERsTF3dAUwKyuL8PBwfvnlF86ePUtaWlquPgaDwXKbWERERESsr9ABMCUlhS5durBjxw7MZjMGg8GyBBxg+WwwGIqkUBEREREpGoW+Bfzuu+8SERHB5MmTiY+Px2w2M2nSJM6dO8eSJUsICAigT58+eV4VFBERERHrKXQA/P7772nZsiVvvvkm5cqVs7T7+PjQp08fNm3axC+//KK1gEVERERKmUIHwFOnTtGyZcv/7chozHG1r2rVqnTv3p2wsLA7q1BEREREilShA6CrqytG4/++7unpyblz53L0qVSpEqdOnSp8dSIiIiJS5AodAP39/XOEu/r167Nx40bLVUCz2cyGDRuoXLnynVcpIiIiIkWm0AHwwQcfZNOmTWRmZgLw9NNPc+rUKUJCQnjttddo06YNe/fupVevXkVWrIiIiIjcuUJPAzN06FDKly9PXFwclStXZsiQIezZs4fPPvuMvXv3AtCrVy8mTZpURKWKiIiISFEodAAMDAxk7NixOdpmzZrFhAkTOHbsGP7+/lSqVOmOCxQRERGRonVHK4HkpWLFilSsWLGodysiIiIiRURrAYuIiIjYmEJfAQwICMhXP4PBQHR0dGEPIyIiIiJFrNAB0GQy5bnOb2JiIpcvXwagcuXKODo6Fro4ERERESl6hQ6AJ06cuOW2MWPGcP78edavX1/YQ4iIiIhIMSiWZwCrV6/OkiVLuHTpEm+88UZxHEJERERECqnYXgJxcHCgc+fOhIeHF9chRERERKQQivUt4KtXr5KQkFCchxARERGRAiq2APjrr7/y7bffUrt27eI6hIiIiIgUQqFfAunYsWOe7ZmZmZw5c8byksiECRMKewgRERERKQaFDoCbN2/Os91gMODl5UWXLl0YM2YMnTt3LuwhRERERKQY3NE8gCIiIiJy97njtYAvXLjAmTNnMJlM+Pr6UqlSpaKoS0RERESKSaFeAklLS2P69OkEBgZSuXJlmjVrRnBwML6+vlSoUIHRo0ffcqJoEREREbGeAgfAmJgYmjdvzrhx44iOjqZy5coEBwcTHBxM5cqVSUhIYObMmTRr1oxffvnF8r1z585pTkARERGRUqBAATAjI4Nu3bpx4MABnnzySQ4dOsTp06eJiIggIiKC06dPc+jQIQYMGEBCQgKPPfYYJ06cIDo6mjZt2nD48OHiGoeIiIiI5FOBngH88ssvOXjwIBMnTmTixIl59qlduzZff/01tWrVYuLEiQwYMIATJ04QHx9P06ZNi6RoERERESm8Al0BDA8Pp2bNmvma2+/NN98kMDCQiIgIrl27xtq1a+nevXuhCxURERGRolGgAPj333/TpUsXDAbDbfsaDAZL3507d9K+ffvC1igiIiIiRahAATA5ORlPT8989/fw8MDe3p6aNWsWuDARERERKR4FCoDe3t4cPXo03/2jo6Px9vYucFEiIiIiUnwKFABDQkJYs2YNsbGxt+0bGxvLqlWraNOmTaGLExEREZGiV6AA+Nxzz5GcnMzjjz9OfHz8TftdvHiRxx9/nKtXrzJ8+PA7LlJEREREik6BpoHp0KEDQ4cOZc6cOdStW5fhw4fTsWNHqlWrBlyfJHrDhg3MmTOH+Ph4hg0bppc/REREREqZAq8F/Nlnn+Hh4cHHH3/M1KlTmTp1ao7tZrMZo9HIq6++mmubiIiIiFhfgQOgnZ0dH3zwAcOGDWPBggVERERYngmsVKkSrVq14umnnyYwMLDIixURERGRO1fgAJgtMDCQ9957ryhrEREREZESUKCXQERERETk7qcAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2JhSGwB3795Nt27dKFu2LK6urrRs2ZLw8PB8fz86OppJkybx6KOP4uvri8FgoHr16rf8jsFguOk/gwcPvrMBiYiIiJQS9tYuIC+bNm2ia9euODs7069fP9zd3Vm2bBmhoaHExMTwyiuv3HYfv/76K5MnT8bOzo66desSGxubr2P7+/vnGfYaN25cwFGIiIiIlE6lLgBmZmYydOhQjEYjW7dutQSvCRMmEBwczPjx4+nduzf+/v633E/btm2JiIigUaNGlClTBmdn53wdv3r16kyaNOkORyEiIiJSepW6W8AbN24kOjqa/v3757jq5unpyfjx40lPTycsLOy2+wkICKBly5aUKVOmGKsVERERufuUuiuAmzdvBqBLly65tnXt2hWALVu2FNvxL1++zFdffUV8fDzlypWjdevWNGjQoNiOJyIiIlLSSl0AjIqKAiAwMDDXtkqVKuHm5mbpUxz27dvH8OHDc7Q99NBDhIWF4e3tfcvvpqWlkZaWZvmclJQEQEZGBhkZGQAYjUbs7OzIysrCZDJZ+ma3Z2ZmYjabLe12dnYYjcabtouUNtn/rWezt79+msnMzMzR7uDggMlkIisry9JmMBiwt7e/afvN/m6K6u8pv7VrTHfTmAyIlCbF+fdUEKUuACYmJgLXb/nmxcPDw9KnqL3yyiv06tWLWrVq4ejoyIEDB3jnnXdYs2YNPXr0ICIiAjs7u5t+f+rUqUyePDlX+7p163BxcQHAz8+PoKAg9u/fz6lTpyx9ateuTZ06ddi1axdxcXGW9saNG+Pv78/WrVu5cuWKpT0kJOS2gVTEGlavXp3jc7du3UhNTWXTpk2WNnt7e7p37058fDwRERGWdnd3dzp27EhMTAx79+61tFesWJFWrVoRFRVFZGSkpb2o/57WrVuXI0R06NCBMmXKaEx38ZjAAZHSpDj/nqpUqZLvOgzmG39elQJdunRh/fr1REVFUbNmzVzbfX19SU5OLnAIdHZ2plKlSpw4caJA3zOZTHTs2JEtW7awbNkynnjiiZv2zesKYLVq1YiPj8fDwwMo+l/CQz8p0HBEit1nI3UFUGMqPWMaNlNXAKX0mDOqeK8ApqSk4OnpSWJioiV33EypuwKYfeXvZgEvKSkJLy+vEqvHaDQydOhQtmzZwvbt228ZAJ2cnHBycsrV7uDggINDzl+hdnZ2eV5NzD6R5bddpLT553/rt2o3Go153ra4WfvN/m6K6u+pILXfrF1jKn1jEilNivvvKd91FPqbxST72b+8nvOLjY0lOTk5z+cDi1OFChUASElJKdHjioiIiBSHUhcA27VrB1x/bu6f1q5dm6NPSdm5cyfAbVcSEREREbkblLoA+OCDDxIQEMCiRYtyPAyZmJjIlClTcHR0ZNCgQZb2c+fOcfjw4Tt+MeSvv/7K9VwJwG+//ca0adNwcHCgT58+d3QMERERkdKg1D1YZm9vz9y5c+natStt27bNsRTcyZMnmTFjRo4rcePGjSMsLIz58+fnWMItPj6eV1991fI5IyOD+Pj4HH1mzJhhub374YcfsmrVKtq0aUO1atVwcHDg4MGDrFu3DoPBwKeffsp9991X3MMXERERKXalLgDC9Vf6t23bxsSJE1myZAkZGRk0aNCAadOmERoamq99JCcn51oxJCUlJUfbpEmTLAGwZ8+eXL58mX379rF+/XrS09OpVKkS/fr1Y9SoUQQHBxfdAEVERESsqNRNA3MvSUpKyvfr2IWlaWCktJkzytoViPyPzpFSmhT3+bEguaPUPQMoIiIiIsVLAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVBERETExigAioiIiNgYBUARERERG6MAKCIiImJjFABFREREbIwCoIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjVEAFBEREbExCoAiIiIiNkYBUERERMTGKACKiIiI2BgFQBEREREbowAoIiIiYmNKbQDcvXs33bp1o2zZsri6utKyZUvCw8MLtI+0tDTefvttAgMDcXZ2pkqVKgwbNowLFy7c9DvffPMNwcHBuLq64uXlRY8ePfjzzz/vdDgiIiIipUapDICbNm2idevWbNu2jb59+/Lcc88RGxtLaGgoH374Yb72YTKZ6NmzJxMnTqRChQqMGjWKkJAQ5s6dS0hICHFxcbm+89577zFw4EAuXLjAc889R58+fdi6dSutWrVi+/btRT1MEREREaswmM1ms7WLuFFmZiZ16tTh9OnT7Nixg8aNGwOQmJhIcHAwJ06c4MiRI/j7+99yP/Pnz2fIkCE8+eSTfPPNNxgMBgC++OILnn/+eYYNG8aXX35p6R8VFUW9evUICAhg165deHp6ArB3715atmxJQEAABw4cwGjMf2ZOSkrC09OTxMREPDw8Cvi/ifwZ+kmx7Fak0OaMsnYFIv+jc6SUJsV9fixI7ih1VwA3btxIdHQ0/fv3t4Q/AE9PT8aPH096ejphYWG33c+cOXMAmDp1qiX8AQwfPpyAgAC++eYbUlNTLe3z588nMzOTN954wxL+ABo3bsyTTz7JoUOH2LZtWxGMUERERMS6Sl0A3Lx5MwBdunTJta1r164AbNmy5Zb7uHbtGjt37qR27dq5rhQaDAY6d+5MSkoKv//+e5EeV0RERORuUOoCYFRUFACBgYG5tlWqVAk3NzdLn5uJjo7GZDLluY8b933jfqKionBzc6NSpUr56i8iIiJyt7K3dgH/lJiYCJDjNuyNPDw8LH3uZB839sv+d29v73z3z0taWhppaWm56khISCAjIwMAo9GInZ0dWVlZmEwmS9/s9szMTG58LNPOzg6j0XjT9vRrtyxJpMRdvJiR47O9/fXTTGZmZo52BwcHTCYTWVlZljaDwYC9vf1N22/2d1NUf0/Zf6e3q11junvGlH7NgEhpkZREsf49paSkAJCf1ztKXQC8m02dOpXJkyfnaq9Ro4YVqhGxjv+Os3YFIiKlU0mdH69cuXLTi2DZSl0AzC74ZlfbkpKS8PLyuuN93Ngv+98L0j8v48aNY8yYMZbPJpOJhIQEypcvn+NFFCl9kpKSqFatGjExMcX2xraIyN1I58e7h9ls5sqVK1SpUuW2fUtdALzxebumTZvm2BYbG0tycjLBwcG33EdAQABGo/Gmz+zl9ZxhYGAgERERxMbG5noO8FbPJd7IyckJJyenHG1ly5a95XekdPHw8NAJTkQkDzo/3h1ud7EqW6l7CaRdu3YArFu3Lte2tWvX5uhzM2XKlCE4OJjIyEhOnjyZY5vZbGb9+vW4urrSrFmzIj2uiIiIyN2g1AXABx98kICAABYtWsTevXst7YmJiUyZMgVHR0cGDRpkaT937hyHDx/Odft22LBhwPXbsjc+DPnll19y7NgxBgwYQJkyZSztzzzzDPb29rz33ns59rV3716+/fZb6tatS5s2bYp6uCIiIiIlrtTdAra3t2fu3Ll07dqVtm3b0q9fP9zd3Vm2bBknT55kxowZVK9e3dJ/3LhxhIWFMX/+fAYPHmxpf/rpp1myZAnffvstx48fp127dhw9epTvv/+eGjVq8O677+Y4bq1atZg0aRJvvvkmjRo1olevXly5coXFixcD1yeWLsgqIHJ3cXJyYuLEiblu4YuI2DqdH+9NpW4puGy7du1i4sSJ/Pbbb2RkZNCgQQPGjBlDaGhojn6DBw/OMwDC9WlZ3n//fb7++mtiYmIoV64cPXr04N1338XHxyfP437zzTd88sknHDx4EEdHR1q3bs0777xDkyZNimuoIiIiIiWq1AZAERERESkeuqcpIiIiYmMUAEVERERsjAKgiIiIiI1RABQRERGxMQqAIiIiIjZGAVDkDmS/RG82m9EL9SIicrdQABQphOywZzAYLP8z+99FROS6G38YZ2VlWbES+SfNAyhSSGvXruXEiRNER0dTrlw52rZtS82aNalQoYJl1Riz2axgKCI27dq1azg7O1u7DPmHUrcUnEhpd+rUKT7++GP+/e9/57rt6+/vT48ePejfvz8hISEKfyJis44fP054eDgHDhwgLi6Ohg0b0rRpU+rUqYO/vz9ly5YFwGQyaalVK9AVQJECGjlyJPPmzaNnz54MHDgQb29vdu7cyZ9//snu3bv5+++/AejevTtvvfUWwcHBOsGJiE359ttveeeddzh8+DBlypQhNTXVsq1q1ap06tSJJ598ks6dO1uxStumAChSAGlpaZQrV47Q0FDmzZuXa/vhw4fZtGkTixYtYvv27dStW5ewsDCaNWtmhWpFREpeWloatWvXxsnJiTfeeIPu3btz9uxZDhw4wIEDB9i2bRu///47165do1evXkyaNIl69erph3IJ0y1gkQJYv349WVlZtG3bFsj59q/RaKROnTrUqVOHwYMHM3/+fMaMGcOwYcNYuXIlVapUsWbpIiIl4ttvv+XcuXPMnz+f/v37A1C+fHkaNGiAyWTi2LFjbN++nYULF/Ldd99x8uRJli1bRtWqVa1cuW1R1BYpADs7O8xmM3FxccD1t9oMBoPlV6vJZMJkMlGmTBlGjBjBmDFj2Lt3L/v377dm2SIiJWb79u14e3vTvHlz4Pp5MfvHstFopGbNmjz99NN89913vP322/z555+MGDHCylXbHgVAkQJo2bIljo6OfPvtt0RFRWFvb5/jRY/sMJg93UHfvn1xcXFhx44d1ipZRKRE+fv7ExcXx+nTp4Hc02Zlh0FPT0/efPNNunfvzu7duzl16pTVarZFCoAi+WQ2m/Hy8mLmzJns3buX9u3b88UXX3D8+HFL4Ms+wWV/PnnyJJmZmbq1ISI2IyQkhPT0dKZPn05cXBx2dnY5wh9cP1dmnydbt25NcnIyR48etVrNtkgBUCSfsk9gvXv3Zvz48SQkJPDqq6/ywgsv8OWXXxIREWH5xevo6MiJEyeYN28ednZ29OnTx5qli4iUCJPJxIMPPsgbb7zB2rVradGiBbNnz+bIkSOWeVGzz6V2dnYAxMbGkpGRoZflSpjeAhYppK1bt/LFF1+wfv16EhISqFq1KrVq1cLR0RE3Nzd2795NbGwso0eP5r333rN2uSIiJebs2bNMnz6d2bNnYzQaCQkJoWPHjjRp0oS6detSs2ZNrl27xtdff80bb7xBSEgIP/74o7XLtikKgCL5kNeKHmazmZiYGPbs2cPOnTv5448/OHToEKdPn8bV1RU/Pz/eeOMNHnvsMVxcXKxUuYiI9ezYsYOvvvqKn3/+mdjYWNzd3SlXrhwODg44OTlx8OBBmjVrxuzZswkODrZ2uTZFAVAkn65evYq9vT0nT56kTJkyOZ7rS01N5cKFCzg4OJCWlkZCQgJNmza1YrUiIiUrrx/KJpOJ+Ph4oqKi+OOPP9ixYwe7d+/m4sWL3H///QQGBjJ16lR8fHysVLXtUgAUuY20tDS2bNnC7Nmz2bFjB25ubhiNRqpXr87DDz9Mv3798PX1tXaZIiJWZTKZOHv2LAkJCcTGxlKvXr0cP5TT0tIAcHJyIjY2Fjc3N9zc3ACtm24NCoAit/HJJ58wefJk0tLSaNy4sWXpt/PnzwPXJ4Du06cPzz//PG3atLGcxHQyExFbcfToUT777DPCwsJISUkhPT0dg8FAgwYNCA0NZcCAAfj5+eX4jkKfdSkAitzCtWvXqFKlCvfffz/h4eF4eHjg6uoKwM6dO1m6dKll1vsqVaowdepUnnrqKStXLSJSctLT0+nevTsbN26kVatWtG7dmvj4eHbv3k1kZCTp6ekA9OrVi1deeYWWLVtauWIBBUCRW1q4cCHDhg1j4cKFPPHEE0DuX61ZWVnMmzePGTNmEBUVxdy5cxkyZIi1ShYRKVH/+c9/GDFiBJMmTWLcuHE5tu3atYtVq1axbNky/v77b3x9fZk9ezY9e/a0UrWSTfMAitxCZGQkRqPRso5vRkaGJfyZTCaysrKws7Nj6NChfP7555aJoi9dumTNskVESkx4eDiNGzemX79+AGRmZlomeQ4ODmby5Mns3LmTWbNmkZWVxZAhQ/j555+tWbKgAChyS61ateLq1ascPHgQAAcHB8s2o9FomcjUbDbTsWNHJkyYwKFDh9i7d681yhURKVHXrl0jIyOD1NRUKlWqBFx//jn73Ji9PrqrqysjR45k1qxZXLp0iYULFwL/WxlESp4CoMgtNGnShHr16jFixAg+/fRTLl68mGe/zMxMADw9PTGZTCQmJpZkmSIiVuHs7EyTJk04cOCAZc3z7PAH138oG41Gy/q/vXr1olu3buzZs4cTJ07oJRArUgAUuQUfHx8mT56Mu7s7//rXvxg7diy//fab5fZGtuz5//bt24fRaKRjx45WqlhEpGQ99dRTeHp6EhoaypdffklsbGyuPiaTCYPBQHp6OhUrViQ+Ph5vb28rVCvZ9BKISD5ERETw7rvvsmbNGgBatmzJo48+SpMmTSwz2v/00098/PHH9O7d23J7Q0TEFsycOZPx48djNBp5/PHH6devH0FBQZQtW5YyZcpY+u3YsYOhQ4dSpUoV1q5da8WKRQFQ5BYyMzMttzCOHDnCqlWrWLFiBbt37+bq1avY2dnh7OxMSkoKAAMHDuStt94iMDDQypWLiJSsiIgIpkyZwvr168nMzKRp06Y88MAD1KhRA2dnZwA+/PBDzp49y5IlS+jatauVK7ZtCoAiBXT16lV+++039uzZQ3x8PElJSWRlZdG7d2/atm1rOdGJiNiCjIwMHBwcMJvNREVFsWnTJjZs2MDu3buJjY21rAAC4OXlxWeffUZoaKgVKxZQABTJU0JCAr///jsRERF4eXnh5OSEr68vTZs2pXLlypZ+aWlpODk5WbFSERHru3r1Ki4uLpbPiYmJHDx4kJiYGNLS0jhz5gw1a9akVatWWjqzlFAAFPmHbdu2MXbsWCIiIoDrUxqYzWZcXFyoV68enTp1olu3bgQHB+Po6Eh6ejqOjo5WrlpEpGRFRETw/fffEx8fj6OjI15eXjRp0oQHH3yQ8uXLW7s8uQ0FQJEbXLt2jcaNGxMXF8fkyZPx9vbGzs6O2NhYfvnlF9avX8/Vq1cJDAxkxIgRjBw5Ent7e2uXLSJSYjIzM3n//feZMGECAGXLliUtLY3U1FQA/P396dGjB08++SQtW7bEaDRabhNL6aEAKHKDuXPn8vLLLzN79myeeeaZXNuPHz/O0qVLmT9/PpGRkfTv359Zs2bh5eVlhWpFREreN998wzPPPEO3bt2YMGECJpOJMmXKcOjQIRYvXszy5csxmUz4+/szatQoXn75ZWuXLHlQABS5QWhoKHv27GHVqlUEBgbm+avVZDLxxx9/8M4777By5Uo++eQTXnrpJStVLCJSslq1aoW9vT1fffUVderUybU9KSmJefPm8emnn3LixAlefvll3nnnnRzTwYj1aSJokf8vMzOTChUqcPbsWcuSRnndsjAajTRv3pwFCxbQtGlTZs2axdWrV0u6XBGREpeQkMDx48fx9/enVq1alhU+4H/ro3t4eDBq1CiWLFlCixYt+Oijj9iyZYuVK5d/UgAU4fp6lPb29rRu3ZqrV68yZswYLl26BPzvpHajzMxMypUrR9u2bYmLiyMyMtIaZYuIlCiz2UzlypU5duwYRqMRg8FgWc7txvXR4fpSmgsXLsTBwcFyW1hKDwVAEbCcwNq1a0fbtm35z3/+w7hx4zhx4kSOk1pWVpYlLKalpWEwGDCZTJr4WURsQvny5enYsSMRERFMmjSJhIQEIPcP5ex/9/X1pVGjRuzdu9eyZrqUDgqAIjfw9fVl8eLF9OzZk6+++oqAgABCQ0NZsWIF6enp2NnZWW53bNq0iSVLltC2bVvc3NysXLmISMkYMmQI/v7+TJs2jbfeeoujR4/muvqX/e9RUVFkZGTg4+Oj6bJKGb0EInKDrKws7OzsOH78OAsWLODzzz8nPj4eAHd3d1q3bk1gYCD79u1j+/btVK9enQULFtC6dWsrVy4iUnKioqIYPXo0q1evBqB79+4MGTKEdu3a4ejoSGpqKl5eXjz33HMsWLCAZcuW0bNnTytXLTdSABT5/8xms+VWcLaMjAzCw8P55ptv2L17NykpKdjb25ORkcEjjzzCa6+9RvPmza1UsYhIycvMzMTe3p7IyEgWLVrEokWLiI6OBsDFxYWgoCBMJhN///03iYmJDBkyhLlz51q5avknBUCR/89kMhETE4O/vz+XL1/GaDTi4eFh2Z6QkMCBAwfw8vKy/OPq6ppncBQRsRWJiYmsXr2aNWvWEBkZSUpKCgkJCdx3330888wz9O3bV4/JlEIKgGLzUlNT+eijj1i7di1//fUXjo6ONGrUiMaNG9O0aVMaNGhAQEAAzs7O1i5VRKTE3fgj9+DBg5hMJlxdXUlNTcXX15eyZcta+sbHx3P58mVq1KjBtWvXcHV1tVLVcjsKgGLT0tPT6d+/P99//z316tXD1dUVk8nE5cuXOXXqFPb29jRv3pwBAwYwcOBATWQqIjbHbDbz559/8tJLL7F//35SUlIoW7Ys/v7+1K9fn5CQEEJCQqhfv76We7uLKACKTfvPf/7DyJEjGTlyJJMnT8bNzY3Y2FjOnDnDkSNH2LhxI+vWrSMmJoYOHTowdepUgoODddtXRGzGqlWrGDZsGCkpKTz66KMYjUbLM35//fUXWVlZNGnShEGDBjFkyBBcXFysXbLkgwKg2LR27dqRkZHBN998Q40aNSxvAWdLSEhgz549zJ8/n0WLFtGiRQtWr16ttX9FxGa0adOGy5cv8+9//5uOHTsCcPnyZa5cuUJUVBQrV65k+fLlnDhxgh49evDBBx9Qu3ZtK1ctt6MAKDYrKSmJtm3b4unpmWuZon9e4TOZTMyYMYN//etfvPjii8ycObOkyxURKXHnzp2jRo0avPbaa7z99tsAue5+XL16lb179zJ79mwWL17MY489xtKlS3P8mJbSRxNBi00ym824ublRt25d/vrrLw4cOGBpN5lMlhNc9jqXRqORMWPG0KhRI/744w8SExOtWb6ISIk4evQojo6O2NnZ3fSxFxcXF1q1asVXX33FqFGjWL58OStXrizhSqWgFADFJhkMBoxGo+XWxquvvsqxY8cs7UCORc7h+jqXgYGBnDt3DicnJ2uVLiJSYurWrUuVKlVYvnw5MTExluUv/7mur8lkws3NjZEjR+Li4sK2bdusVLHklwKg2LSRI0fy+uuvs27dOpo0acLrr7/Ob7/9xrVr1yxh8MbpDw4dOkTt2rU1JYyI2IQKFSrw8MMPs3//fsaPH8/Zs2cxGo2WH8r/XAP42rVreHt7c+nSJWuVLPlkb+0CRKwl+zm/V155hTJlyjB9+nRmzJjBt99+S8uWLWnevDktWrSgdu3a7Ny5k48++oijR48yffp0a5cuIlJipkyZQmpqKl999RXLli1j6NCh9O7dm1atWuV6zm/9+vWcOnWK7t27W6layS+9BCI2658vepw5c4Z58+bx/fffs2/fvlz9y5Yty6uvvsr48eNLskwREasxmUwYjUZOnz7NZ599xscff0xaWhrOzs40bdqUkJAQ2rdvz7Vr19i6dStz5syhXr167N6929qly20oAIrcwGQyERcXR2RkJDt37mTXrl24urpSq1YtQkJC6NChg7VLFBGxmoSEBObNm8eiRYvYu3dvru09e/bk1VdfpXXr1iVfnBSIAqDYpH379hEVFcWRI0csL4MEBgbi7e2d6023tLQ0vfQhIjYl+w5J9hXAvBw9epSNGzdy6tQp/P398fb2pnPnzpoI+i6hACg2JTMzk6+++oq3336bCxcu5NhWqVIlunbtypNPPkmXLl1ybLvVSVBE5F6TlZVFWFgYf//9N0ePHuW+++6jWbNm1KpVCz8/P8qVK5fnPH9aJenuoQAoNmXJkiUMHTqUwMBAnn32WRo1asSePXvYu3cvf/zxB/v378dkMhESEsKECRPo3Lmzgp+I2JQ///yTt99+mxUrVuDk5ERaWpplm7e3N+3bt6dPnz488sgjODo6Agp+dyMFQLEpLVq0wGQysWjRIgIDA3NsO378OFu3buW7775j1apVeHp6MmfOHHr37m2lakVESt4jjzzC9u3bee655xg8eDBZWVns37+fv//+m4iICHbt2kVSUhIdOnRg8uTJtGnTRgHwLqQAKDbjwoUL1KlTh0GDBvHJJ58A129z3Dj5c3bb8uXLefHFFzGZTCxbtkwPNIuITYiJicHf359//etfTJkyJdf2U6dOsWvXLpYuXcrSpUvx9vYmPDyctm3bWqFauRO6tyU2IzExETc3N86cOQNcD3o3TmiavQycnZ0dvXr14qOPPuLChQts3rzZsl1E5F62YcMGnJycaNq0KXD9+ecbV0Xy8/Ojd+/ezJ8/n3nz5pGWlsbzzz/P+fPnrVm2FIICoNiMwMBA/Pz8WL9+PZs2bcpzbUuj0Wg50fXp04eAgAB27dpFZmambm+IyD2vfPnymM1mjh8/DvwvAP5zfXQXFxcGDx7M6NGjOXToEAcPHrRm2VIICoBiU6ZPn47RaOShhx7ivffe4/Dhw2RkZABYTnDZnyMjI7Gzs8PZ2Rl7ey2aIyL3vhYtWlCmTBnmzZvHwYMHsbe3z3GXBK6fKzMzMwFo164drq6umvj5LqQAKDYlODiYd999Fzc3NyZPnszzzz/PrFmz2L59OzExMWRlZeHo6EhGRgZff/010dHR9O/f39pli4gUO5PJhLe3N7NmzSIyMpKWLVvy7rvv8tdff1nugvzzTsjx48dJSUmhQYMGVqpaCksvgYhNOnToEDNnzmTlypWcPXuWSpUqcf/99+Pp6YmrqysnT55k69atdOvWjZUrV1q7XBGREnPlyhU+/fRT3nvvPVJSUmjWrBmdOnWiefPm1KtXj9q1awOwbds2Ro0axblz5yzPVsvdQwFQbMqNz7LExsayd+9eduzYwc6dOzl06BCnTp0CwNfXl759+/L666/j4+NjzZJFRKwiMjKSzz//nB9//JGTJ0/i7u6Oj48PTk5OeHp68scff1CuXDkmTJjA8OHDrV2uFJACoNzTsgNfRkYGRqORuLg40tPT8fPzs/RJT0/n3Llzllscp06dolmzZri5uVmxchGRknOz1Y4SEhKIjo7m999/t8wBePLkSQICAvD19WXy5MkEBwfnuSqIlG4KgHLPO3z4MJ9//jkrV67EyckJs9lM5cqV6dixI/369aNmzZrWLlFExOri4+NJSUnhxIkT+Pn5UaNGDcu29PR00tPTcXNz48KFC6Snp1O1alUrVit3SgFQ7mmbNm3i5Zdf5sCBA9x3333UqlWL/fv353he5aGHHmLEiBF07twZJycnrfsrIjbl4sWLLFu2jI8++ojTp0+TlZVFVlYW9913H71796Z///7UrVvX2mVKEVMAlHtau3btiI6OZu7cubRv3x47OzscHBz466+/WLp0KYsXL+bo0aO4uLgwduxY3nrrLWuXLCJSokaPHs3nn3+Or68vDzzwAI6OjuzcuZPo6GiuXr0KQIcOHRg7diydOnWyzJequVHvbgqAcs86ffo0NWrUYNKkSYwfPx6DwZDnSWvZsmVMnz6d3bt38/rrrzN58mScnJysVLWISMk5efIkgYGBPPHEEyxatAjAcgdk3759rFmzhuXLl7Nr1y6cnZ15//33eemll6xZshQR3eeSe9aePXswGAyULVsWg8FAenq6JfyZTCaysrIA6NWrF//9739p0qQJs2bN4u+//7Zm2SIiJWbx4sW4ubkxbNgwS/DLnuS5UaNG/Otf/+LXX3/l22+/pWbNmowaNYpPP/3UmiVLEVEAlHtW/fr1Adi/fz8Ajo6Olm1Go9Hy1prZbKZ27dp8/vnnpKamsm3btpIvVkTECs6fP4/JZKJcuXLA9TXSs1c+MplMmEwmHBwcCA0NJSwsjMqVK/PFF1+QnJxszbKlCCgAyj3L19eXXr16MWfOHMaPH09MTEye/bJ/7RqNRsqWLcvJkydLskwREatp27YtSUlJ7NixAwAHBwfLNqPRmOOqYFBQECNHjuTEiRPs2rXLKvVK0VEAlHuWo6Mjr732Gvfddx/Tp09n1KhRrF27lrS0tBz9sk94e/bsISkpiXbt2lmjXBGREte6dWsaN27MyJEjmTx5MsePH+efrwbc+Nnd3Z3U1NQcd1Tk7qSXQOSed+zYMSZPnsySJUtIT0+ncePGPPbYY4SEhODq6oqjoyPR0dGMGjUKT09PDh8+bO2SRURKzE8//cTQoUOJi4ujZ8+ePPnkk7Rs2ZIKFSrg7OxseXY6Li6Ol156ibVr15KQkGDlquVOKQDKPSv7RQ8HBwdOnz5teZtt+/btJCUlYTQa8fT05NKlS8D1B56nTp3KQw89ZOXKRURKVnR0NO+88w4//PADV65coUGDBrRv35569erh6uqKi4sLCxcuZNWqVbzyyitMmTLF2iXLHVIAFJuSkZFhWfv3zJkzXLlyhYSEBHr06EHXrl3x9fW1dokiIiUmMzMTOzs7yzKYW7ZsYf369URERBATE0N6enqO/hMmTOCFF16gQoUKVqpYiooCoNxzMjMziYyMZN26dbi6uuLg4ED58uVp3LhxjjWA09LSNN+fiNi89PT0HM/0Xb16lb/++ovo6GhSUlI4d+4crq6uPPTQQ9x///1WrFSKkgKg3FOOHz/Ohx9+yGeffZajvUyZMgQGBtK+fXu6detGq1atcHNzy/HrV0TEVhw7dozVq1dz8OBBHB0dcXFx4f7776dDhw66E2IjFADlntKnTx+WL1/O0KFDadGiBfb29iQmJrJ161bWrVvH5cuXqVy5Ms888wwvvfQS3t7e1i5ZRKRELVmyhNdff52YmBgMBgMuLi6kpKQAUKlSJR5++GFCQ0Np3749jo6OZGRk5JgeRu4NCoByzzhx4gQ1a9Zk9OjRTJ8+PddVvbNnz7JixQrmzZvH77//TocOHfjyyy+pWbOmlSoWESlZMTExNGnSBC8vL2bOnImrqyvu7u6cPHmS77//nmXLlpGamoqXlxfDhw9n7NixeHp6WrtsKQaaB1DuGatWrcLR0ZEOHTpYln67UZUqVXjuuedYuHAhzz//PJs2bWLq1KmWJeFERO51c+bMwWg08vHHH/Pwww/Ttm1bgoKCeOyxx/jvf//L5cuXmTdvHv7+/kybNo3/+7//Iy4uztplSzFQAJR7hoODA9euXcPFxcXyOS+1atXiww8/5Nlnn2X+/PlER0eXZJkiIlbz22+/UblyZYKCgoD/rYR047RZgwcP5vvvv2fAgAF8//33fP3119YsWYqJAqDcM1q2bEmZMmWYMGECR48exWAwYDabc13hy8jIwNnZmS5dumA0GomIiLBSxSIiJScjI4OAgACio6Mta/9mr/t74/roANWrV+fzzz+nUaNG/Pe//yUpKckqNUvxUQCUe0ZgYCADBw5k27ZtjB07lr1792IwGCwnNZPJhNlstlwZTElJwWAw6I03EbEJDg4OtG3blpSUFIYNG2ZZ9/yfP5TNZjMmkwlXV1datGjB6dOniY2NtVbZUkwUAOWeUaZMGWbPns2LL77IDz/8QJMmTejWrRuLFy/mypUrGI1Gy4sh58+fZ/78+ZQrV45OnTpZuXIRkZLx0EMP8eCDD7Jw4UJef/11/vjjjxw/lAEMBgNGo5HLly+TlpaGg4MDtWrVsmLVUhz0FrDcM0wmE0ajkQsXLvDtt9/y73//m+PHjwPg4uJCq1ataNasGdHR0Wzbto3ExETeeecdRo8ebeXKRURKzpUrVxg9ejTz5s0DoF27djz77LM89NBDuLm5cfXqVby8vPjiiy8YO3YsAwYMyDW3qtz9FADlnmA2m/OczPnHH39kwYIFbNu2jUuXLuHk5ERqaipNmzbltddeo0ePHpaXRkRE7nWZmZnY29tz+vRpli5dSlhYGPv37weuPw8YHByMl5cXhw8fJjo6mtatW7NgwQLuu+8+K1cuRU0BUO4ZZ86cwdfXl9TUVDIyMvDw8LBsS05O5s8//wTA19cXNzc3fHx8rFWqiEipkJaWxs8//8xPP/3Evn37SEpK4sqVKzg6OjJgwACef/55qlatau0ypRgoAMpdzWw2s3LlSv7zn//w119/kZycTMOGDWnYsCFBQUE0aNCAmjVr4urqau1SRUSs6sKFC8TFxVG+fHkSExOpUKEC5cuXt2y/dOkSZ8+etQQ+Dw8PLZN5D1MAlLvahAkTmDFjBi4uLlSrVo2MjAzS09OJiYnBbDbTqFEjevfuzVNPPUWlSpWsXa6ISIk7d+4cb7zxBuvXr+fMmTO4u7tTo0YN6tSpQ3BwMK1ataJhw4aWx2Fu9kiN3FsUAOWudeLECe6//37at2/Phx9+SJ06dYiPjycmJobo6Gi2bt3K2rVriYqKolGjRkyZMoWHH37Y8rKIiMi9LjY2lscff5ydO3daXvIwGo2cPHmS/fv3k5qaSr169ejbty/PPvssVapUsXbJUkIUAOWu9c477/DJJ58QHh7Ogw8+aHm4OVtSUhIHDx4kPDycmTNn4uPjw5o1a2jcuLH1ihYRKUETJ05k5syZTJ48mZdffhmAy5cvk5yczPHjx1m3bh3ff/89hw8fpkWLFnzwwQe0bt1aVwFtgAKg3LWefvpp1q9fz549e/Dx8bGcsPI6cS1ZsoThw4dTt25drfwhIjbj/vvvJyAggHnz5lGxYsVc58e0tDQiIyMJCwvj448/pnbt2mzZsgVvb28rVi0lQffB5K7VsGFDYmNj+fXXX4Hrk5eaTKYcJ7fs3zehoaE88cQTHD16lMjISKvUKyJSks6fP4/ZbCYtLY2KFSsC5Ppx7OTkRMOGDZk2bRozZ84kMjKSjz76yBrlSglTAJS7VnBwMK6urrz11lv8/vvvAJZn+7KXMsoOhXB9qbjU1FStaSki9zyz2UzFihW5//772blzJ7t27bK0/3N9dLg+B+CLL75I/fr12b17N8nJySVdspQwBUC5K5nNZh544AE+/vhjoqKiCA4OZvjw4WzYsIErV65YljKC66EwNTWVv/76C2dnZ5o3b27l6kVEilf2ObBLly5cuXKFV199lYMHD+ZaHz0rK8typyQpKYlq1apx4cIF3NzcrFm+lAD723cRKX2yb2M8+eSTZGZmMnHiRObMmcPy5csJCQmhRYsWBAcH06RJE6Kiopg3bx7Lli3jxRdftHLlIiIlZ+jQoSQkJDB+/HgaNGjAoEGD6N+/P23btsXZ2Rn436Myu3fvZt++fXTr1s2aJUsJ0Usgclf654PMKSkpzJ07lyVLlrB7927LLQ6DwYC9vT0ZGRkMHjyYd955B19fX2uVLSJSYrLPk5cvX2bevHlMmzaNuLg47OzsaNq0Ka1bt6ZDhw54enqye/duZs+ezZUrV9i4cSMNGjSwdvlSzBQA5Z4SHx/PkSNH2LFjB7/++itZWVnUqlWLunXr8n//93/WLk9EpMT884fytWvXCAsL47///W+esyHUq1ePcePGMWDAgJIsU6xEAVDuOhcuXOCvv/7iyJEjJCcnExwcTJ06dahQoYLl2ZZsaWlpODk5WT5rbisRETh16hS//PILBw4coFKlSnh7e9OmTRtq1qxp7dKkhCgAyl1lzZo1vPvuu7l+vZYrV44HH3yQ0NBQHnnkERwcHCzbtPKHiNian3/+mQMHDrB37158fHxo1qwZNWvWpFq1apQvXz7HOVJskwKg3DViYmJo3749KSkpDB48mA4dOnDs2DH27NnDvn372L9/P2lpadSrV4/x48fTu3dvHB0dddVPRGzG5cuXmTp1Kh988AF2dnY5pnwpV64crVu35vHHH+fRRx+lXLlylm06T9oevQUsd40vv/ySS5cuMXfuXJ544okc206fPs1vv/3GihUrWLRoEQMHDuT06dO8/vrrOqmJiM2YM2cOs2fP5rHHHuOll16iSpUq7Nmzh8jISHbv3k1ERAQ//fQTQUFBvPXWWzz22GNA7gmi5d6nK4By12jZsiVlypRh6dKlVKhQgczMzBxzWmXbtGkTr7zyCn///TefffYZQ4YMsVLFIiIlq3r16tSvX5+wsDDKly+fY9vZs2fZs2cPK1asYN68eWRlZfHVV1/x7LPPWqlasSY9GCV3heTkZNzd3YmNjcXFxQW4PsFzdvjLXvkDoEOHDvznP//BxcWFH3/80bJdRORedvjwYS5evEijRo0s4c9kMlnOjVWqVKF79+7MmjWLH3/8kRo1ajB27Fitj26jFADlruDm5kbTpk2JjIxk8eLFALle7Mj+bDKZCAoKom3bthw+fJiTJ0/q9oaI3PPMZjNly5YlOjoagMzMTCDnEplmsxlHR0e6devGRx99xKVLlyzrqYttUQCUu0b2OpXPPvssL730En/++SfXrl0D/vf8SmZmJkajkaSkJBwdHbl27Rr+/v7WLFtEpETUrVsXX19fVq9ezZo1a7C3t8/1Q/nG9dEfeOABqlevzu7du61RrliZAqDcNXx9fXn77bepXr06s2fPZvjw4cyYMYPNmzdz8uRJrl27hr399feafvrpJzZv3szDDz9s5apFRIpf9mMu//73v/Hw8KB79+6MHj2aXbt25fqhnJGRAUBkZCRpaWlUqVLFOkWLVeklECn1/jk9QUJCAlOnTiU8PJyYmBgqVqxI/fr1qVKlCi4uLqSmphIeHk6NGjVYvnw5tWvXtmL1IiIlJysri4ULFzJu3DhiY2OpV68eXbp0oVWrVtSrV486depgNBo5c+YMr732GkuXLmXnzp00adLE2qVLCVMAlLtCdgg8ffo0VapUwWg0cuDAAVauXMnmzZs5dOgQMTExAHh5edG4cWP+/e9/c//991u5chGRkhcXF8fs2bMJDw/nyJEjuLi44Ovri5ubG+XKlePw4cPExcXxzDPP8Nlnn1m7XLECBUAp1TIzM9m+fTvz5s3jyJEjGAwGXFxcaN68OX379iUoKAiz2UxMTAypqakcO3aMOnXqUK1aNezt7TW5qYjYlOwZEezs7EhNTSUqKordu3ezfft2du7cyeHDh6lYsSLVqlXj2WefZeDAgbi6ulq7bLECBUAp1WbMmME777zDlStXqFmzJnZ2dkRGRlq216tXjxEjRtC7d2+8vb2tWKmISOlkMpm4du0ajo6OJCYmEhsbq7sjogAopdfx48dp0KABTZo0ISwsDEdHR3x8fIiNjeWnn35i6dKlbN68Gbg+99+0adNo1qyZdYsWESlBqampnDp1Cj8/P8qUKZNjm8lkwmAwWO6C/POOiNZJt20KgFJqTZgwgS+//JJFixbx4IMPArlPYH/99RczZswgPDwcf39/vvnmG5o2bWqtkkVEStT777/PsmXLeOKJJ2jZsiW1a9fGx8cnxwpJ2f9vPvvcGRcXh5eXl2XWBLFNCoBSavXq1Yu9e/eyadMm/Pz8yMzMtDzXl/2MS7aZM2cyevRonn76aebPn2/FqkVESk7VqlU5e/YsdnZ2eHp60qpVK7p06UKLFi0ICAjItRxcSkoKkyZN4uLFi8ydO1dXAG2Y4r+UWkFBQfzwww8kJycDWH6t3rj+b/YVwZdffplff/2VjRs3cuzYMQICAqxWt4hISThy5AiJiYmEhITQv39/1q9fT0REBCtXrsTPz4/27dvTqVMngoKC8PX1pWzZshw4cIA5c+bQvn17hT8bpwAopVaHDh0AGDBgAB9++CFt2rTB0dExV7+srCzs7OyoXbs2a9assQRGEZF72ZEjR7h27RpdunRh5MiR9OjRg8jISCIiIti4cSPLli3jm2++oV69enTs2JGHHnqIDRs2kJSUxNChQ61dvliZbgFLqZWVlcXYsWP56KOPqFOnDiNHjqR37974+Pjk6nvp0iVGjRrFmjVruHDhghWqFREpWd999x19+/Zl8eLF9O3b19KekZHByZMn2bdvH7/++qtlrlQHBwfMZjNOTk4kJCRYsXIpDRQApdT78ssv+eCDDzh27BhVqlTh8ccf5+GHH6ZatWrY2dlRtmxZZs2axSeffMKIESP48MMPrV2yiEixM5vNHD58GGdnZ2rUqJHnvKcpKSkcOXKEyMhI5s+fz/r163nhhRf497//baWqpbRQAJRSz2w2c/ToUebMmcPixYs5ffo0AN7e3jg4OHDu3DlMJhNPPvkk06ZNo2rVqlauWETEuvIKgy+99BKzZ8/mjz/+ICgoyEqVSWmhACh3lZSUFHbt2sWKFSs4e/YsFy5cwMPDg759+9KrVy+cnZ2tXaKISKmRPdffiRMn6NmzJ5cuXeLUqVPWLktKAb0EIncVV1dXOnToQIcOHcjIyMDBwcHaJYmIlFrZb/qeOXOGjIwMRowYYeWKpLTQFUAREZF7nNls5vTp05QrV05r/wqgACgiIiJiczQLpIiIiIiNUQAUERERsTEKgCIiIiI2RgFQRERExMYoAIqIiIjYGAVAERERERujACgiIiJiYxQARURERGyMAqCIiIiIjfl/KcsuNuqPl3IAAAAASUVORK5CYII=" 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" }, - "execution_count": 15, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -300,8 +300,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:17.943025Z", - "start_time": "2023-11-10T03:10:10.706205Z" + "end_time": "2023-11-10T12:08:52.840576Z", + "start_time": "2023-11-10T12:08:45.864831Z" } }, "id": "cbb3c2d9a11b43ac" @@ -320,7 +320,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 23, "outputs": [ { "data": { @@ -354,8 +354,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:18.025012Z", - "start_time": "2023-11-10T03:10:17.953579Z" + "end_time": "2023-11-10T12:08:53.045797Z", + "start_time": "2023-11-10T12:08:52.848159Z" } }, "id": "16f5ec62b6f90570" @@ -378,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 24, "outputs": [], "source": [ "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", @@ -389,14 +389,14 @@ "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_M_nA = 2 * np.arcsin(np.sqrt(0.01))\n", - "theta_M_A = 2 * np.arcsin(np.sqrt(0.7))" + "theta_M_nA = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_M_A = 2 * np.arcsin(np.sqrt(0.3))" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:21.228824Z", - "start_time": "2023-11-10T03:10:21.206538Z" + "end_time": "2023-11-10T12:08:53.046448Z", + "start_time": "2023-11-10T12:08:52.989905Z" } }, "id": "f79d7c9a5cca338" @@ -413,14 +413,14 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 25, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 18, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -469,8 +469,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:10:22.846088Z", - "start_time": "2023-11-10T03:10:22.535173Z" + "end_time": "2023-11-10T12:08:53.427811Z", + "start_time": "2023-11-10T12:08:53.003589Z" } }, "id": "85bb861283b06275" @@ -487,20 +487,20 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 29, "outputs": [ { "data": { - "text/plain": "0.47266" + "text/plain": "0.94999" }, - "execution_count": 21, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "query = {'M': 1}\n", - "evidence = {'A': 1}\n", + "query = {'J': 0}\n", + "evidence = {'A': 0, 'B': 0,'E': 0,'M': 0}\n", "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", @@ -509,8 +509,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T03:28:03.558287Z", - "start_time": "2023-11-10T03:28:02.746890Z" + "end_time": "2023-11-10T12:11:08.249713Z", + "start_time": "2023-11-10T12:11:08.123452Z" } }, "id": "5468619791203a79" @@ -523,7 +523,7 @@ "metadata": { "collapsed": false }, - "id": "72a1d1076dd05cb0" + "id": "6c0cedf3812e698b" } ], "metadata": { From 20fb73231bad0374de21820c3e500f10513b9a60 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 10 Nov 2023 19:01:32 +0100 Subject: [PATCH 18/48] Reversed index for quantum circuit variables --- .../13_quantum_bayesian_inference.ipynb | 164 +++++++++++------- .../algorithms/inference/qbayesian.py | 37 ++-- test/algorithms/inference/test_qbayesian.py | 4 +- 3 files changed, 126 insertions(+), 79 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 1010958ae..3c9a45d8a 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -29,13 +29,13 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 1, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-10T12:08:45.299538Z", - "start_time": "2023-11-10T12:08:45.253178Z" + "end_time": "2023-11-10T17:46:52.824317Z", + "start_time": "2023-11-10T17:46:52.258806Z" } }, "outputs": [ @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 2, "outputs": [], "source": [ "# Include libraries\n", @@ -94,8 +94,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:45.305983Z", - "start_time": "2023-11-10T12:08:45.303595Z" + "end_time": "2023-11-10T17:46:52.956662Z", + "start_time": "2023-11-10T17:46:52.898605Z" } }, "id": "326c1d2e72f41202" @@ -114,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 3, "outputs": [ { "data": { "text/plain": "
", "image/png": "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" }, - "execution_count": 19, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:45.395309Z", - "start_time": "2023-11-10T12:08:45.309905Z" + "end_time": "2023-11-10T17:46:53.413430Z", + "start_time": "2023-11-10T17:46:52.898971Z" } }, "id": "4f99dbe56bc6910a" @@ -169,13 +169,13 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 4, "outputs": [ { "data": { - "text/plain": "0.12128" + "text/plain": "0.1181" }, - "execution_count": 20, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -193,8 +193,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:45.493775Z", - "start_time": "2023-11-10T12:08:45.405510Z" + "end_time": "2023-11-10T17:46:54.013814Z", + "start_time": "2023-11-10T17:46:53.413133Z" } }, "id": "841bce19ea097bf1" @@ -213,14 +213,14 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 5, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 21, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -249,8 +249,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:45.782782Z", - "start_time": "2023-11-10T12:08:45.493232Z" + "end_time": "2023-11-10T17:46:54.395280Z", + "start_time": "2023-11-10T17:46:54.017605Z" } }, "id": "3764be5e0ce2db02" @@ -267,21 +267,21 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 6, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'0000000000': 0.60154, '1000000000': 0.39846}\n" + "{'1000000000': 0.5181, '0000000000': 0.4819}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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" + "image/png": 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" }, - "execution_count": 22, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -300,8 +300,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:52.840576Z", - "start_time": "2023-11-10T12:08:45.864831Z" + "end_time": "2023-11-10T17:46:56.253735Z", + "start_time": "2023-11-10T17:46:54.395467Z" } }, "id": "cbb3c2d9a11b43ac" @@ -320,7 +320,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 7, "outputs": [ { "data": { @@ -354,8 +354,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:53.045797Z", - "start_time": "2023-11-10T12:08:52.848159Z" + "end_time": "2023-11-10T17:46:56.331972Z", + "start_time": "2023-11-10T17:46:56.263233Z" } }, "id": "16f5ec62b6f90570" @@ -378,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 8, "outputs": [], "source": [ "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", @@ -395,8 +395,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:53.046448Z", - "start_time": "2023-11-10T12:08:52.989905Z" + "end_time": "2023-11-10T17:46:56.335562Z", + "start_time": "2023-11-10T17:46:56.332754Z" } }, "id": "f79d7c9a5cca338" @@ -413,14 +413,14 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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}, - "execution_count": 25, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -435,12 +435,8 @@ "qc.ry(theta_B, qr[0])\n", "# P(E)\n", "qc.ry(theta_E, qr[1])\n", - "# P(A|-B,-E)\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", - "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", + "# P(A|B,E)\n", + "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", "# P(A|-B,E)\n", "qc.x(qr[0])\n", "qc.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", @@ -449,28 +445,29 @@ "qc.x(qr[1])\n", "qc.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", "qc.x(qr[1])\n", - "# P(A|B,E)\n", - "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", - "# P(J|-A)\n", - "qc.x(qr[2])\n", - "qc.cry(theta_J_nA, qr[2], qr[3])\n", - "qc.x(qr[2])\n", + "# P(A|-B,-E)\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", + "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc.x(qr[0])\n", + "qc.x(qr[1])\n", "# P(J|A)\n", "qc.cry(theta_J_A, qr[2], qr[3])\n", - "# P(M|-A)\n", + "# P(M|A)\n", + "qc.cry(theta_M_A, qr[2], qr[4])\n", + "# P(J|-A) + P(M|-A)\n", "qc.x(qr[2])\n", + "qc.cry(theta_J_nA, qr[2], qr[3])\n", "qc.cry(theta_M_nA, qr[2], qr[4])\n", "qc.x(qr[2])\n", - "# P(M|A)\n", - "qc.cry(theta_M_A, qr[2], qr[4])\n", "# Draw circuit\n", "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)\n" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:08:53.427811Z", - "start_time": "2023-11-10T12:08:53.003589Z" + "end_time": "2023-11-10T17:46:56.625028Z", + "start_time": "2023-11-10T17:46:56.342879Z" } }, "id": "85bb861283b06275" @@ -487,20 +484,20 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 10, "outputs": [ { "data": { - "text/plain": "0.94999" + "text/plain": "0.8721300000000001" }, - "execution_count": 29, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "query = {'J': 0}\n", - "evidence = {'A': 0, 'B': 0,'E': 0,'M': 0}\n", + "query = {'B': 1}\n", + "evidence = {'J':1}\n", "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", @@ -509,21 +506,62 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T12:11:08.249713Z", - "start_time": "2023-11-10T12:11:08.123452Z" + "end_time": "2023-11-10T17:46:56.863167Z", + "start_time": "2023-11-10T17:46:56.634452Z" } }, "id": "5468619791203a79" }, + { + "cell_type": "markdown", + "source": [ + "The joint probability can be also plot with no evidence for the rejection sampling method." + ], + "metadata": { + "collapsed": false + }, + "id": "e0f6e7b50aa14131" + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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CzMxM+Pv7491338Xw4cNRuXLlPO/TvHlzbNy40dKQRERERJSDxcXcxo0b0a5dO7z88svo2bMnnJwevatu3bqhXLlyloYkIiIiohwsLubOnz+PqlWrmnWfOnXqoE6dOpaGJCIiIqIcLL4AYtq0afjtt9/y3eb333/HCy+8YGkIIiIiInoEi4u5pUuX4sSJE/lu89dff2HZsmWWhiAiIiKiR7DqPHM5PXjwoEDn0hERERGRZQpVaSmKYrJdRBAbG4tNmzbxggciIiKiImTWyJxOp4Ner1fnj5syZYr6d/Z/Tk5OqFKlCo4dO4Z+/foVSceJiIiIyMyRuVatWqmjcXv37kXFihVNziun1+vh4+ODdu3aYdiwYVbpKBERERHlZlYxt3v3bvX/dTodhg4dikmTJlm7T0RERERUQBafM5eVlWXNfhARERGRBYr0atbCOHz4MDp37oxSpUrBw8MDTZs2xerVq83ez/Xr1zFq1ChUq1YNbm5uKFOmDJo1a4Yvv/yyCHpNREREpK0Cj8y98MILUBQF06ZNg7+/f4EnA1YUBd9++61Zndq1axfCwsLg5uaGfv36wdPTEz///DPCw8MRGxuLMWPGFGg/J06cQKdOnXD79m106dIFvXv3RnJyMs6cOYP169fj1VdfNatfRERERLZGEREpyIY6nQ6KouDMmTOoXr06dLqCDeopioLMzMwCdygjIwPBwcG4fPkyDhw4gJCQEABAYmIiQkNDER0djfPnz6NSpUr57icpKQl169ZFSkoKtm/fjnr16uWKY84ceElJSfD29kZiYiK8vLwKfD8i+u8YNs/8+yweae1eEJGjKGjtUeBq5t9//wUAlC9f3uhva9u5cyeioqIwdOhQtZADAG9vb0yYMAFDhgzBsmXLHnnhxcKFCxETE4Nvv/02VyEHgJMZExERkUMocEWTcyTsUSNjljJcMdupU6dct4WFhQEA9uzZ88j9rFq1CoqioFevXjh37hy2bt2KlJQUBAcH46mnnoKLi4tV+01ERERUHGxueCoyMhIAUK1atVy3BQQEoGTJkuo2eUlLS8OpU6fg6+uLzz//HJMnTza6+jYoKAjr1q1D3bp189xHamoqUlNT1b+TkpIAAOnp6UhPTwfwf5MoZ2ZmGu3f0J6RkYHsR7H1ej10Ol2e7Yb9GhhGDzMyMgrU7uzsjKysLKPD2oqiwMnJKc/2vPrOnJgTczI/J0tk76ct5uSIzxNzYk72lFNBFPjTJyYmpqCb5lKxYsUCb5uYmAjg4WFVU7y8vNRt8nLr1i1kZmbi5s2b+OCDDzBz5kwMHDgQ6enp+Oqrr/DRRx+hW7duOHv2LNzc3EzuY/r06Zg6dWqu9q1bt8Ld3V3Nq0GDBjh58qTR41OjRg0EBwfj0KFDuHHjhtoeEhKCSpUqYe/evbh7967a3qxZM/j5+WHr1q1GT1zbtm1RokQJbNy40agPnTt3RkpKCnbt2qW2OTk5oUuXLkhISEBERITa7unpiXbt2iE2NhYnTpxQ2319fdG8eXNERkbi3LlzajtzYk7MyfKcLJG9P7aYkyM+T8yJOdlLTkePHkVBmH0BhLkURSlwZQk8PLy6bds2REZGomrVqrluL1++PJKTk/Mt6K5evaqe2/fWW29h3rx5RreHh4dj9erV+OGHHzBgwACT+zA1MlehQgUkJCSoJyH+V38lMCfmxJxMt1tyAcTC1zgyx5yYE3My3X7r1i2UKVPGehdADBo0yKJizlyGEbm8irWkpCSULl26QPsAgGeeeSbX7c888wxWr16NI0eO5FnMubq6wtXVNVe7s7MznJ2djdqyr1ebXV6HXfJqz7lfS9p1Op3JK43zas+r78yJOZnbzpwsYyquLeXkiM8Tc2JOefXR3PbiyinXdgXaCsDSpUsLummhGM6Vi4yMRMOGDY1ui4+PR3JyMkJDQ/Pdh4eHB8qXL48rV66gVKlSuW43tKWkpFilz0RERETFxeZWgGjdujWAh+em5bRlyxajbfLTrl07AMA///yT6zZDW+XKlS3tJhEREZFNsLlirn379ggKCsKKFSuMTh5MTEzEtGnT4OLigkGDBqntcXFxOHv2bK7Dsq+88goAYMaMGbhz547aHh8fj/nz50On06FXr15FmgsRERFRUbO55bycnJzwzTffICwsDK1atTJazuvSpUuYPXu20Yja+PHjsWzZMixZsgRDhgxR25s3b47Ro0dj7ty5qFevHrp164b09HT873//w/Xr1zFt2jRUr169wP0iIiIiskVmnTOnKAreffdd+Pv7F/gcOkvWZm3bti3+/PNPTJ48GatWrUJ6ejrq1q2LTz75BOHh4QXez5w5c1C3bl0sWLBA7X+DBg2waNEi9OzZ06w+EREREdmiAk9NcunSJQAPpwZxcnJS/y6IolotQktcm5WIHoVrsxKRNVl9bVatlvMiIiIiooKzuQsgiIiIiKjgCl3M/frrr+jevTsqVqwIb29vVKxYET169MC6deus0D0iIiIiyo9lK0Pj4bIWzz33HH7++WeICJycnFCmTBnEx8fjt99+w/r169GrVy+sWLHC4gWoiYiIiCh/Fo/MTZ8+HWvXrkXLli3xxx9/4MGDB4iLi8ODBw+wd+9etGjRAj///DNmzJhhzf4SERERUTYFvpo1p6CgILi5ueHkyZMmR97S09NRr149pKam4uLFi4XuaHHj1axE9Ci8mpWIrKmgtYfFI3NxcXHo1q1bvgvYduvWDXFxcZaGICIiIqJHsLiYq1ChApKTk/Pd5t69e6hYsaKlIYiIiIjoESwu5l566SWsXr06z5G3K1euYNWqVXjppZcs7hwRERER5a/Al5nGxMQY/d23b1/s27cPDRo0wMiRI9GiRQv4+/vj2rVr+OOPPzB//ny0aNECffr0sXqniYiIiOihAl8AodPpoChKrnYRybPdcL+MjIxCdrP48QIIInoUXgBBRNZk9eW8Bg0aZLJoIyIiIqLiU+BibunSpUXYDSIiIiKyBNdmJSIiIrJjLOaIiIiI7FihFk29e/cuvvjiC2zfvh1Xr15Fampqrm0URUFUVFRhwhARERFRHiwu5m7cuIHmzZsjKioKXl5e6hUXaWlpSElJAQCUK1cOzs7OVussERERERmz+DDrlClTEBUVhe+//x63b98GAIwaNQr37t3DwYMHERoaisqVK+Pvv/+2WmeJiIiIyJjFxdzGjRvRvn17DBgwINeUJY0bN8amTZsQHR2NqVOnFrqTRERERGSaxcVcXFwcGjRooP6t1+vVw6sAULp0aTz99NNYvXp14XpIRERERHmyuJjz9vZGenq6+nfp0qVx+fJlo228vLxw7do1y3tHRERERPmyuJgLCgpCdHS0+neDBg2wbds23Lx5EwCQkpKC9evXo2LFioXuJBERERGZZnEx16lTJ+zYsQP3798HALz88su4fv066tevjz59+qBOnTqIiorCkCFDrNVXIiIiIsrB4mLulVdeweLFi9Vi7tlnn8WsWbNw7949/Pzzz4iPj8fo0aMxduxYq3WWiIiIiIwpIiLW3GFmZiYSEhLg5+eX6ypXe2aYRy8xMRFeXl7F3R0iskHD5pl/n8Ujrd0LInIUBa09CrUChCl6vR7+/v7W3i0RERERmVDoYi4uLg4rV67E8ePHkZiYCG9vbzRo0AD9+vVDYGCgNfpIRERERHkoVDG3YMECjB07Fqmpqch+tHb58uV47733MHv2bIwYMaLQnSQiIiIi0ywu5lauXIk33ngDZcuWxXvvvYeWLVvC398f165dw969ezF//nz19r59+1qzz0RERET0/1l8AcQTTzyBy5cv48SJEyhXrlyu2y9fvowGDRqgYsWKOHr0aKE7Wtx4AQQRPQovgCAiaypo7WHx1CRnzpxB3759TRZyAPDYY4+hT58+OHPmjKUhiIiIiOgRLC7mSpUqBQ8Pj3y3KVmyJEqVKmVpCCIiIiJ6BIuLuWeeeQbr169HRkaGydvT09Oxfv16dO/e3eLOEREREVH+LC7mZs6cCQ8PD3Tq1AkHDhwwui0iIgKdOnWCp6cnZsyYUehOEhEREZFpBb6aNSgoKFdbWloajh07hieffBJOTk4oW7YsEhIS1NG6wMBAPPHEE4iKirJej4mIiIhIVeBiLisrK9fyXM7OzqhYsaJRW84LIrKysgrRPSIiIiLKT4GLuejo6CLsBhERERFZwuJz5oiIiIio+BV6bVYAyMjIwLlz55CUlAQvLy/UqFEDTk5W2TURERER5aNQI3O3bt3CsGHD4O3tjXr16qFFixaoV68eSpUqheHDh+PmzZvW6icRERERmWDx8NmtW7fQtGlTXLhwAT4+PmjZsiUCAwMRHx+PI0eO4JtvvsGePXsQEREBHx8fa/aZiIiIiP4/i0fmPvzwQ1y4cAFjx47FpUuXsHnzZixZsgSbNm3CpUuX8O677yIyMhIff/yxNftLRERERNkoIiKW3DEoKAiVK1fGzp0789ymXbt2iI6OxsWLFy3uoK0o6GK3RPTfNWye+fdZPNLavSAiR1HQ2sPikbmrV6+iWbNm+W7TrFkzXL161dIQRERERPQIFhdz3t7euHTpUr7bXLp0Cd7e3paGICIiIqJHsLiYa926NdasWYPt27ebvH3Hjh1Ys2YN2rRpY2kIIiIiInoEi69mnTx5MjZs2ICwsDB07twZrVu3hr+/P65du4bdu3dj06ZNcHd3x6RJk6zZXyIiIiLKxuJirnbt2tiyZQuGDBmCDRs2YMOGDVAUBYbrKR5//HEsXboUtWvXtlpniYiIiMhYoZZpaNGiBSIjI7Fv3z4cP35cXQGiQYMGePLJJ6EoirX6SUREREQmWFzMvfDCC6hbty5GjRqFFi1aoEWLFtbsFxEREREVgMUXQKxYsQLXr1+3Zl+IiIiIyEwWF3OPP/444uLirNkXIiIiIjKTxcXcCy+8gA0bNuDKlSvW7A8RERERmcHic+Z69eqFXbt2oXnz5njnnXfQuHFj+Pv7m7zooWLFioXqJBERERGZZnExFxQUpE5F8uabb+a5naIoyMjIsDQMEREREeXD4mJu0KBBnHqEiIiIqJhZXMwtXbrUit0gIiIiIktYfAEEERERERW/Qq0AAQCpqanYuHEjjh8/jsTERHh7e6NBgwbo3LkzXF1drdFHIiIiIspDoYq53377DcOHD8eNGzfUNVmBhxc9+Pn54euvv0a3bt0K3UkiIiIiMs3iYm7Hjh3o1asX9Ho9XnjhBbRs2RL+/v64du0a9u7di+XLl+PZZ5/Fli1b0K5dO2v2mYiIiIj+P0WyD6mZoUWLFjh58iT279+POnXq5Lr95MmTePLJJxESEoI//vij0B0tbklJSfD29kZiYiK8vLyKuztEZIOGzTP/PotHWrsXROQoClp7WHwBxPHjxxEeHm6ykAOAevXqoW/fvjh27JilIYiIiIjoESwu5tzd3eHr65vvNn5+fnB3d7c0BBERERE9gsXFXIcOHbB9+/Z8t9m+fTs6duxoaQgiIiIiegSLi7nZs2fj+vXrGDRoEGJjY41ui42NxcCBA5GQkIDZs2cXupNEREREZJrFV7MOHDgQpUuXxo8//oiVK1eiYsWK6tWsMTExyMzMRL169TBgwACj+ymKgh07dhS640RERERUiGJu9+7d6v9nZGTg4sWLuHjxotE2f/31V677FXQ918OHD2Py5MnYv38/0tPTUbduXYwePRp9+/a1qL+3b99GnTp1cPXqVYSFhWHz5s0W7YeIiIjIllhczGVlZVmzH0Z27dqFsLAwuLm5oV+/fvD09MTPP/+M8PBwxMbGYsyYMWbv8/XXX0diYmIR9JaIiIio+Njc2qwZGRkYNmwYdDod9u7di6+//hpz5szBX3/9herVq2PChAm4dOmSWfv8+eefsWLFCnzyySdF1GsiIiKi4mG1Yi4mJgZ79+4t9H527tyJqKgoPPfccwgJCVHbvb29MWHCBKSlpWHZsmUF3t+NGzfw6quvYuDAgejSpUuh+0dERERkS6xWzC1ZsgRt27Yt9H4M5+J16tQp121hYWEAgD179hR4f6+88gr0ej3mz59f6L4RERER2RqLz5krKpGRkQCAatWq5botICAAJUuWVLd5lOXLl+OXX37BunXrULp0abPOmUtNTUVqaqr6d1JSEgAgPT0d6enpAACdTge9Xo/MzEyjcwgN7RkZGci+Wpper4dOp8uz3bBfAyenh09PRkZGgdqdnZ2RlZWFzMxMtU1RFDg5OeXZnlffmRNzYk7m52SJ7P20xZwc8XliTszJnnIqCJsr5gwFl7e3t8nbvby8ClSUXb16FW+++Sb69++P7t27m92P6dOnY+rUqbnat27dqq5qUbFiRTRo0AAnT55ETEyMuk2NGjUQHByMQ4cO4caNG2p7SEgIKlWqhL179+Lu3btqe7NmzeDn54etW7caPXFt27ZFiRIlsHHjRqM+dO7cGSkpKdi1a5fa5uTkhC5duiAhIQERERFqu6enJ9q1a4fY2FicOHFCbff19UXz5s0RGRmJc+fOqe3MiTkxJ8tzskT2/thiTo74PDEn5mQvOR09ehQFoUj2crUQpk6dig8++MCoErVEp06dsG3bNkRGRqJq1aq5bi9fvjySk5MfWdB17twZR48exd9//42yZcsCAKKjo1GlSpUCTU1iamSuQoUKSEhIUBe7/a/+SmBOzIk5mW4fNg9mW/gaR+aYE3NiTqbbb926hTJlyiAxMVGtPUyx2sict7c3KlasaJX9AMizWEtKSkLp0qXz3ceyZcuwadMmrFmzRi3kzOXq6gpXV9dc7c7OznB2djZq0+v10Ov1ubbN67BLXu0592tJu06ng06X+1TIvNrz6jtzYk7mtjMny5iKa0s5OeLzxJyYU159NLe9uHLKFa9AWxXAyJEj8e+//xZ6P4Zz5UydFxcfH4/k5GST59Nld/z4cQBAnz59oCiK+q9KlSoAgC1btkBRFKOrZYmIiIjskc2dM9e6dWtMnz4dW7duRb9+/Yxu27Jli7pNfpo1a4bk5ORc7cnJyVi1ahUee+wxhIWFWWUkkYiIiKg4FficOcMccqGhoXBzczNrTrlWrVoVeNuMjAzUqFEDV65cwYEDB9TRs8TERISGhiI6Ohrnzp1D5cqVAQBxcXFITExEYGBgnhdNGJhzzlxOSUlJ8Pb2fuRxayL677LknLnFI63dCyJyFAWtPQo8MtemTRsoioIzZ86gevXq6t8FYc5FEU5OTvjmm28QFhaGVq1aGS3ndenSJcyePVst5ABg/PjxWLZsGZYsWYIhQ4YUOA4RERGRIyhwMTdp0iQoiqJeUGD4uyi0bdsWf/75JyZPnoxVq1YhPT0ddevWxSeffILw8PAiiUlERERkj6w2NYmj42FWInoUHmYlImsqaO1htatZiYiIiEh7Fhdzd+/excWLF3NNurdq1So8//zzePHFF3Hs2LFCd5CIiIiI8mbx1CTvvPMOli9fjmvXrqkT6X355Zd4/fXX1ZmWV65ciaNHjyI4ONg6vSUiIiIiIxaPzO3ZswcdOnRQ1ykFgBkzZqB8+fLYu3cvVq9eDRHBrFmzrNJRIiIiIsrN4pG5uLg4PPXUU+rfZ86cQWxsLGbOnIkWLVoAANauXWvWfHREREREZB6LR+ZSU1Ph4uKi/r1nzx4oioJOnTqpbUFBQbhy5UrhekhEREREebK4mHvsscdw8uRJ9e/ff/8dPj4+qFevntp28+ZNlCxZsnA9JCIiIqI8WXyY9emnn8aCBQvw9ttvw83NDZs3b8agQYOMtjl//jzXPyUiIiIqQhYXc+PHj8f69esxd+5cAEBgYCA++OAD9fbr169j3759eP311wvfSyIiIiIyyeJiLiAgAH///Td27NgBAGjVqpXR7MQJCQmYNWsWwsLCCt9LIiIiIjLJ4mIOAEqUKIGuXbuavK1WrVqoVatWYXZPRERERI/A5byIiIiI7FihRuYyMzOxevVqbN++HVevXkVqamqubRRFUQ/FEhEREZF1WVzM3bt3D506dcKBAwcgIlAURV3GC4D6t6IoVukoEREREeVm8WHWjz76CBEREZg6dSoSEhIgIpgyZQri4uKwatUqBAUFoU+fPiZH64iIiIjIOiwu5n755Rc0bdoU77//Pnx8fNR2f39/9OnTB7t27cL27du5NisRERFREbK4mIuJiUHTpk3/b0c6ndEo3GOPPYYuXbpg2bJlheshEREREeXJ4mLOw8MDOt3/3d3b2xtxcXFG2wQEBCAmJsby3hERERFRviwu5ipVqmRUqNWpUwc7d+5UR+dEBDt27EBgYGDhe0lEREREJllczLVv3x67du1CRkYGAGDw4MGIiYlBs2bNMHbsWLRo0QInTpxAr169rNZZIiIiIjJm8dQkw4YNQ5kyZXDjxg0EBgbihRdewPHjx7Fw4UKcOHECANCrVy9MmTLFSl0lIiIiopwUyT45nBXcuHEDFy9eRKVKlRAQEGDNXRerpKQkeHt7IzEx0WgNWiIig2HzzL/P4pHW7gUROYqC1h6FWgHCFF9fX/j6+lp7t0RERERkAtdmJSIiIrJjFo/MBQUFFWg7RVEQFRVlaRgiIiIiyofFxVxWVpbJdVcTExNx584dAEBgYCBcXFws7hwRERER5c/iYi46Ojrf20aPHo1r165h27ZtloYgIiIiokcoknPmKleujFWrVuH27dt47733iiIEEREREaEIL4BwdnZGx44dsXr16qIKQURERPSfV6RXs96/fx+3bt0qyhBERERE/2lFVsz98ccf+Omnn1CjRo2iCkFERET0n2fxBRDt2rUz2Z6RkYErV66oF0hMmjTJ0hBERERE9AgWF3O7d+822a4oCkqXLo1OnTph9OjR6Nixo6UhiIiIiOgRCjXPHBEREREVr0KvzXr9+nVcuXIFWVlZKF++PAICAqzRLyIiIiIqAIsugEhNTcXMmTNRrVo1BAYGolGjRggNDUX58uVRtmxZjBo1Kt9JhYmIiIjIOswu5mJjY9G4cWOMHz8eUVFRCAwMRGhoKEJDQxEYGIhbt25h/vz5aNSoEbZv367eLy4ujnPOEREREVmZWcVceno6OnfujNOnT6N///44c+YMLl++jIiICERERODy5cs4c+YMnn/+edy6dQs9evRAdHQ0oqKi0KJFC5w9e7ao8iAiIiL6TzLrnLmvvvoKf//9NyZPnozJkyeb3KZGjRr44YcfUL16dUyePBnPP/88oqOjkZCQgIYNG1ql00RERET0kFkjc6tXr0bVqlULNHfc+++/j2rVqiEiIgIPHjzAli1b0KVLF4s7SkRERES5mVXM/fPPP+jUqRMURXnktoqiqNsePHgQbdq0sbSPRERERJQHs4q55ORkeHt7F3h7Ly8vODk5oWrVqmZ3jIiIiIgezaxizs/PDxcuXCjw9lFRUfDz8zO7U0RERERUMGYVc82aNcOmTZsQHx//yG3j4+OxYcMGtGjRwuLOEREREVH+zCrmXnnlFSQnJ6Nnz55ISEjIc7ubN2+iZ8+euH//Pl5++eVCd5KIiIiITDNrapK2bdti2LBhWLx4MWrWrImXX34Z7dq1Q4UKFQA8nFB4x44dWLx4MRISEjB8+HBe+EBERERUhMxem3XhwoXw8vLCp59+iunTp2P69OlGt4sIdDod3n777Vy3EREREZF1mV3M6fV6zJo1C8OHD8fSpUsRERGhnkMXEBCA5s2bY/DgwahWrZrVO0tERERExswu5gyqVauGjz/+2Jp9ISIiIiIzmXUBBBERERHZFhZzRERERHaMxRwRERGRHWMxR0RERGTHWMwRERER2TEWc0RERER2jMUcERERkR1jMUdERERkx1jMEREREdkxFnNEREREdozFHBEREZEdYzFHREREZMdYzBERERHZMRZzRERERHaMxRwRERGRHWMxR0RERGTHWMwRERER2TEWc0RERER2zGaLucOHD6Nz584oVaoUPDw80LRpU6xevbpA9xURbNq0Ca+++irq1asHb29vuLu7o379+pg2bRoePHhQxL0nIiIi0oZTcXfAlF27diEsLAxubm7o168fPD098fPPPyM8PByxsbEYM2ZMvvdPTU1F586d4erqijZt2iAsLAwPHjzAli1b8N5772HdunXYvXs33N3dNcqIiIiIqGgoIiLF3YnsMjIyEBwcjMuXL+PAgQMICQkBACQmJiI0NBTR0dE4f/48KlWqlOc+0tPTMXPmTIwYMQKlS5c2au/VqxfWr1+PmTNnYuzYsQXuV1JSEry9vZGYmAgvLy+L8yMixzVsnvn3WTzS2r0gIkdR0NrD5g6z7ty5E1FRUXjuuefUQg4AvL29MWHCBKSlpWHZsmX57sPZ2RnvvfeeUSFnaB8/fjwAYM+ePVbvOxEREZHWbK6Y2717NwCgU6dOuW4LCwsDULhCzNnZGQDg5GSTR5iJiIiIzGJzFU1kZCQAoFq1arluCwgIQMmSJdVtLPHdd98BMF0sZpeamorU1FT176SkJAAPD9Wmp6cDAHQ6HfR6PTIzM5GVlaVua2jPyMhA9qPYer0eOp0uz3bDfg0MBWdGRkaB2p2dnZGVlYXMzEy1TVEUODk55dmeV9+ZE3NiTubnZIns/bTFnBzxeWJOzMmecioImyvmEhMTATw8rGqKl5eXuo25Nm3ahK+++go1a9bEiy++mO+206dPx9SpU3O1b926Vb1womLFimjQoAFOnjyJmJgYdZsaNWogODgYhw4dwo0bN9T2kJAQVKpUCXv37sXdu3fV9mbNmsHPzw9bt241euLatm2LEiVKYOPGjUZ96Ny5M1JSUrBr1y61zcnJCV26dEFCQgIiIiLUdk9PT7Rr1w6xsbE4ceKE2u7r64vmzZsjMjIS586dU9uZE3NiTpbnZIns/bHFnBzxeWJOzMlecjp69CgKwuYugOjUqRO2bduGyMhIVK1aNdft5cuXR3JystkF3eHDh9G+fXs4OTnhjz/+QO3atfPd3tTIXIUKFZCQkKCehPhf/ZXAnJgTczLdbskFEAtf48gcc2JOzMl0+61bt1CmTJlHXgBhcyNzhhG5vIq1pKSkXBc2PMqRI0fQqVMn6HQ6bNmy5ZGFHAC4urrC1dU1V7uzs7N63p2BXq+HXq/PtW1eh13yas+5X0vadToddLrcp0Lm1Z5X35kTczK3nTlZxlRcW8rJEZ8n5sSc8uqjue3FlVOueAXaSkOGc+VMnRcXHx+P5ORkk+fT5eXIkSPo2LEjsrKysGXLFjRu3NhqfSUiIiIqbjZXzLVu3RrAw3PTctqyZYvRNo9iKOQyMzOxefNmNGnSxHodJSIiIrIBNlfMtW/fHkFBQVixYoXRyYOJiYmYNm0aXFxcMGjQILU9Li4OZ8+ezXVY9ujRo+jYsSMyMjKwadMmNGvWTKsUiIiIiDRjc+fMOTk54ZtvvkFYWBhatWpltJzXpUuXMHv2bFSuXFndfvz48Vi2bBmWLFmCIUOGAABu3bqFjh074s6dO3jqqaewbds2bNu2zShOqVKlMHLkSO0SIyIiIioCNlfMAQ8vD/7zzz8xefJkrFq1Cunp6ahbty4++eQThIeHP/L+SUlJuH37NgBg8+bN2Lx5c65tKlWqxGKOiIiI7J7NTU1iq7g2KxE9CtdmJSJrstu1WYmIiIio4FjMEREREdkxFnNEREREdozFHBEREZEdYzFHREREZMdYzBERERHZMRZzRERERHaMxRwRERGRHWMxR0RERGTHWMwRERER2TEWc0RERER2jMUcERERkR1jMUdERERkx1jMEREREdkxFnNEREREdozFHBEREZEdYzFHREREZMdYzBERERHZMRZzRERERHaMxRwRERGRHWMxp5EFCxagcuXKcHNzQ5MmTXDo0KF8t1+zZg2Cg4Ph5uaGunXrYuPGjUa3X7t2DUOGDEG5cuXg7u6Op556CpGRkUbbtGnTBoqiGP175ZVXrJ4bERERFR8WcxpYtWoVRo8ejcmTJ+PYsWOoX78+wsLCcP36dZPb79+/H/3798eLL76I48ePo0ePHujRowdOnz4NABAR9OjRAxcvXsT//vc/HD9+HJUqVUKHDh1w7949o30NGzYMcXFx6r+ZM2cWeb5ERESkHUVEpLg7YQ+SkpLg7e2NxMREeHl5mXXfJk2aoHHjxvjiiy8AAFlZWahQoQLeeOMNjBs3Ltf24eHhuHfvHn7//Xe1rWnTpggJCcGiRYtw/vx51KhRA6dPn0bt2rXVfQYEBGDatGl46aWXADwcmQsJCcG8efMszJqIzDFsnvn3WTzS2r0gIkdR0NqDI3NFLC0tDUePHkWHDh3UNp1Ohw4dOiAiIsLkfSIiIoy2B4CwsDB1+9TUVACAm5ub0T5dXV3x559/Gt3vxx9/RNmyZVGnTh2MHz8e9+/ft0peREREZBucirsDji4hIQGZmZnw9/c3avf398fZs2dN3ic+Pt7k9vHx8QCA4OBgVKxYEePHj8dXX30FDw8PfPrpp7h8+TLi4uLU+zz33HOoVKkSypUrh5MnT+Ldd9/FuXPn8Msvv1g5SyIiIiouLObskLOzM3755Re8+OKL8PHxgV6vR4cOHfD0008j+1Hz4cOHq/9ft25dBAYGon379oiKisLjjz9eHF0nIiIiK+Nh1iJWtmxZ6PV6XLt2zaj92rVrCAgIMHmfgICAR27fsGFDnDhxAnfu3EFcXBw2b96MmzdvIigoKM++NGnSBABw4cIFS9MhIiIiG8Niroi5uLigYcOG2LFjh9qWlZWFHTt2oFmzZibv06xZM6PtAWDbtm0mt/f29oavry8iIyNx5MgRdO/ePc++nDhxAgAQGBhoQSZERERki3iYVQOjR4/G4MGD0ahRI4SGhmLevHm4d+8ehg4dCgAYNGgQypcvj+nTpwMA3nrrLbRu3Rpz5sxBly5dsHLlShw5cgRff/21us81a9bA19cXFStWxKlTp/DWW2+hR48e6NSpEwAgKioKK1asQOfOnVGmTBmcPHkSo0aNQqtWrVCvXj3tHwQiIiIqEizmNBAeHo4bN25g0qRJiI+PR0hICDZv3qxe5BATEwOd7v8GSZs3b44VK1bg/fffx4QJE1CtWjWsW7cOderUUbeJi4vD6NGjce3aNQQGBmLQoEGYOHGieruLiwu2b9+uFo4VKlRAr1698P7772uXOBERERU5zjNXQIWZZ46I/hs4zxwRWRPnmSMiIiL6D2AxR0RERGTHWMwRERER2TEWc0RERER2jFez2hieQE1ERETm4MgcERERkR1jMUdERERkx1jMEREREdkxFnNEREREdozFHBEREZEdYzFHREREZMdYzBEREZlpwYIFqFy5Mtzc3NCkSRMcOnQo3+3XrFmD4OBguLm5oW7duti4cWOe277yyitQFAXz5s0zaq9cuTIURTH6N2PGDGukQ3aOxRwREZEZVq1ahdGjR2Py5Mk4duwY6tevj7CwMFy/ft3k9vv370f//v3x4osv4vjx4+jRowd69OiB06dP59r2119/xYEDB1CuXDmT+/rggw8QFxen/nvjjTesmhvZJxZzREREZpg7dy6GDRuGoUOHolatWli0aBHc3d3x3Xffmdx+/vz5eOqppzB27FjUrFkTH374IZ544gl88cUXRttduXIFb7zxBn788Uc4Ozub3JenpycCAgLUfx4eHlbPj+wPizkiIqICSktLw9GjR9GhQwe1TafToUOHDoiIiDB5n4iICKPtASAsLMxo+6ysLAwcOBBjx45F7dq184w/Y8YMlClTBg0aNMCsWbOQkZFRyIzIEXA5LyIiogJKSEhAZmYm/P39jdr9/f1x9uxZk/eJj483uX18fLz69yeffAInJye8+eabecZ+88038cQTT8DHxwf79+/H+PHjERcXh7lz5xYiI3IELOaIiIiK0dGjRzF//nwcO3YMiqLkud3o0aPV/69Xrx5cXFzw8ssvY/r06XB1ddWiq2SjeJiViIiogMqWLQu9Xo9r164ZtV+7dg0BAQEm7xMQEJDv9n/88QeuX7+OihUrwsnJCU5OTrh06RLGjBmDypUr59mXJk2aICMjA9HR0YXKiewfizkiIqICcnFxQcOGDbFjxw61LSsrCzt27ECzZs1M3qdZs2ZG2wPAtm3b1O0HDhyIkydP4sSJE+q/cuXKYezYsdiyZUuefTlx4gR0Oh38/PyskBnZMx5mJSIiMsPo0aMxePBgNGrUCKGhoZg3bx7u3buHoUOHAgAGDRqE8uXLY/r06QCAt956C61bt8acOXPQpUsXrFy5EkeOHMHXX38NAChTpgzKlCljFMPZ2RkBAQGoUaMGgIcXURw8eBBt27aFp6cnIiIiMGrUKAwYMAClS5fWMHuyRSzmiIiIzBAeHo4bN25g0qRJiI+PR0hICDZv3qxe5BATEwOd7v8OfDVv3hwrVqzA+++/jwkTJqBatWpYt24d6tSpU+CYrq6uWLlyJaZMmYLU1FRUqVIFo0aNMjqPjv67FBGR4u6EPUhKSoK3tzcSExPh5eVVZHGGzTP/PotHWrsXRGQJvn+JyJoKWnvwnDkiIiIiO8ZijoiIiMiO8Zw5IiKiIsJD76QFjswRERER2TEWc0RERER2jMUcERERkR1jMUdUTBYsWIDKlSvDzc0NTZo0waFDh/Ldfs2aNQgODoabmxvq1q2LjRs3Gt0uIpg0aRICAwNRokQJdOjQAZGRkUbbVK5cGYqiGP2bMWOG1XMjIiLtsJgjKgarVq3C6NGjMXnyZBw7dgz169dHWFgYrl+/bnL7/fv3o3///njxxRdx/Phx9OjRAz169MDp06fVbWbOnInPPvsMixYtwsGDB+Hh4YGwsDA8ePDAaF8ffPAB4uLi1H9vvPFGkeZKRERFi8UcGTF3tMjW49hqrLlz52LYsGEYOnQoatWqhUWLFsHd3R3fffedye3nz5+Pp556CmPHjkXNmjXx4Ycf4oknnsAXX3wB4OGo3Lx58/D++++je/fuqFevHr7//ntcvXoV69atU/t16dIlfPPNN4iJiUFAQAACAgLg4eGRK541RgE//vhjNG/eHO7u7ihVqpRVHz9zty3OnMxhLznZ4nvK3mJpxREfv//654QpLOZIZe5oka3HsdVYaWlpOHr0KDp06KC26XQ6dOjQARERESb3HRERYbQ9AISFhanb//vvv4iPjzfaxtvbG02aNMGyZcvUfgUGBuLGjRto2rQp6tSpg1mzZiEjI8Nov9YaBUxLS0OfPn3w6quvWvXxM3fb4szJHPaSky2+p+wtllYc8fH7r39O5EmoQBITEwWAJCYmFmmclz41/5+1hIaGymuvvab+nZmZKeXKlZPp06dbL4iGcWw11pUrVwSA7N+/36h97NixEhoaanLfzs7OsmLFCqO2BQsWiJ+fn4iI7Nu3TwDI1atXjbbp06eP+Pj4qP2aM2eO7NixQ3x9faVHjx5SqlQpGTVqlNF9+vbtK126dDFqa9Kkibz88ssiIpKVlSUBAQEya9Ys9fY7d+6Iq6ur/PTTT7n6vmTJEvH29jaZV3bmPFfmPq9a5VSY96+t5pSTLb6nbDnWf+EzXctYjvA5YY6C1h4cmSMAlo0W2XIcR45ljqysLNy+fVvt1+jRo9GuXTs8/fTTyMrKwpw5c/D5558jNTVVvU9hRgEtzdWcx0/rkU0tnj97yclR31O2+v4tDEd8/P7rnxP5YTFHAICEhARkZmbC39/fqN3f3x/x8fF2F8eWY5UtWxZ6vR7Xrl0zar927RoCAgJM7j8gICDf7Q3/zbnN5cuXISJ59qtJkybIyMhAdHS0elt8fHy+eRj+a83H1ZzHz5LntThyMoe95GSr7yl7iqUVR3z8/uufE/lhMUekMRcXFzRs2BA7duxQ27KysrBjxw40a9bM5H2aNWtmtD0AbNu2Td2+SpUqCAgIMNomKSkJx48fz7cvJ06cgE6ng5+fn6XpEBFRMbPZYu7w4cPo3LkzSpUqBQ8PDzRt2hSrV682ax+pqan44IMPUK1aNbi5uaFcuXIYPny4XZ/QWlQsGS2y5Ti2Hmv06NFYvHgxli1bhjNnzuDVV1/FvXv3MHToUADAoEGDMH78eHX7t956C5s3b8acOXNw9uxZTJkyBUeOHMHrr78OAFAUBSNHjsRHH32E3377DadOncKgQYNQrlw5tV8RERGYN28e/vrrL1y4cAEZGRkYNWoUBgwYgNKlS6uxLB0FLMzjas7jp+XIZlG8Vkyxl5xs+T1lL7G04oiP33/9cyI/NlnM7dq1C08++ST+/PNP9O3bF6+88gri4+MRHh6OOXPmFGgfWVlZ6N69OyZPnoyyZcti5MiRaNasGb755hs0a9YMN27cKOIs7Islo0W2HMfWY4WHh2P27NmYNGkSQkJCcOLECWzevFkdvo+JiUFcXJy6ffPmzbFixQp8/fXXqF+/PtauXYt169ahTp066jbvvPMO3njjDQwfPhyNGzdGcnIytmzZovbL1dUVK1euRKtWrfDrr78iNjYWo0aNwtdff23UN0tHAQ8ePGjx42rO46flyGZhcjKHveRky+8pe4mlFUd8/P7rnxP5KtRlFkUgPT1dHn/8cXF1dZXjx4+r7Xfu3JHq1auLi4uLREdHP3I/3333nQCQ/v37S1ZWltr+5ZdfCgAZPny4Wf36L1zNunLlSnF1dZWlS5fKP//8I8OHD5dSpUpJfHy89YJoGMeRY1mzXwMHDpRx48ap2+/bt0+cnJxk9uzZcubMGZk8ebI4OzvLqVOn1G1mzJghpUqVkv/9739y8uRJ6d69u1SpUkVSUlLUbS5duiTHjx+XqVOnSsmSJeX48eNy/PhxuXv3rkX9tIecCvP+tdWcCvM8FZYjxPovfKZrGcsRPifMUdDaw+aKuS1btggAGTp0aK7bli5dKgBk6tSpj9xPs2bNBECuwi8rK0uCgoLEw8ND7t+/X+B+/ReKORGRzz//XCpWrCguLi4SGhoqBw4csG4AjeM4cixz5Nev1q1by+DBg422X716tfrjqXbt2rJhwwaj27OysmTixIni7+8vrq6u0r59ezl37pzRNoMHDxYAuf7t2rXLon7aQ06Fff/aYk6mOOp7qihi/Vc+07WMZe+fE+YoaO2hiIhoMgRYQBMmTMD06dPx008/oV+/fka3xcfHIzAwEO3atcs1FJrdgwcP4OHhgWrVquHs2bO5bn/llVfw1VdfYe/evWjZsmWB+pWUlARvb28kJibCy8vLvKTMMGye+fdZPNLavSAiS/D9SznxNUGFUdDaw0nDPhWIYVmMatWq5botICAAJUuWzLV0Rk5RUVHIysoyuY/s+46MjCxwMUdUXPhlQERE+bG5Yi4xMRHAw4n4TPHy8lK3Kcw+sm9nSmpqqtFEqoZtb926hfT0dAAPJyDU6/XIzMxEVlaWuq2hPSMjA9kHPvV6PXQ6XZ7t6enpSHvgnG9upty8+bA/zs7OyMrKQmZmpnqboihwcnLKsz2vvlszp+ycnB6+5HIuIZVXO3NSkPbA/LfprVu2nZOWz9Poxea/p+YOS7cop7QHpvaWP8P715ycDBzpeXLUnCz5TE9Kgk3nBDje82SrOd26dQsA8KiDqDZXzNmK6dOnY+rUqbnaq1SpUgy9yd/34x+9Df238DVROFo+fnyuKCe+Jiinu3fv5jlABdhgMWfobF6jZklJSUZzYlm6j+zbmTJ+/HiMHj1a/TsrKwu3bt1CmTJloChKvvGtLSkpCRUqVEBsbGyRnq/nqLEcMSctYzliTlrGcsSctIzliDlpGcsRc9IylpY5mSIiuHv3LsqVK5fvdjZXzGU/n61hw4ZGt8XHxyM5ORmhoaH57iMoKAg6nS7Pc+vyOy/PwNXVFa6urkZtpUqVelT3i5SXl5dmLyZHjOWIOWkZyxFz0jKWI+akZSxHzEnLWI6Yk5axtMwpp/wGngxsbtLg1q1bAwC2bt2a67YtW7YYbZOXEiVKIDQ0FOfOncOlS5eMbhMRbNu2DR4eHmjUqJGVek1ERERUPGyumGvfvj2CgoKwYsUKnDhxQm1PTEzEtGnT4OLigkGDBqntcXFxOHv2bK5DqsOHDwfw8HBp9hMHv/rqK1y8eBHPP/88SpQoUbTJEBERERUxmyvmnJyc8M033yArKwutWrXC8OHDMWbMGNSvXx/nz5/HtGnTULlyZXX78ePHo2bNmvj111+N9jN48GCEhYXhp59+QvPmzTFu3Dj07t0bI0aMQJUqVfDRRx9pnJnlXF1dMXny5FyHfRnLtuI4aixHzEnLWI6Yk5axHDEnLWM5Yk5axtIyp8KwuUmDDQ4dOoTJkydj//79SE9PR926dTF69GiEh4cbbTdkyBAsW7YMS5YswZAhQ4xuS01NxYwZM/DDDz8gNjYWPj4+6Nq1Kz766CN1DUwiIiIie2azxRwRERERPZrNHWYlIiIiooJjMUdERERkx1jMEREREdkxFnNEREREdozFHBEREZEdYzHnALKyssCLkomsIysrq7i7QERkFhZzdsJQrKWnpyMzMxPx8fGIjY0FAOh0OiiKAhGxyy+ivApRe8zFQMviWqvHz1F/MOTMS6fjx6KlRESz14nWsbT4PNIyJy3Z63dTfrIPotjCc8Z55uzI2bNn8eWXX+L333+Hq6srRASBgYHo0KED+vXrh6CgoOLuotlEBIqiICUlBampqYiJiYGbmxuqV69utF1WVpbdfMkackpKSsLNmzdx7tw5BAYGol69elAUpUhiFfXjp2VOhngAimTfOeMoioLr168jOjoap0+fxuOPP45KlSrBw8MD3t7ecHFxsVq8vJ4He3p955SZmQm9Xs9YNh5Ha46Yly2/T1nM2Yldu3Zh5MiROHXqFB5//HFUr14dJ0+exJUrV9Rtnn76aYwYMQIdOnRQi72i/jIsLBHBkSNHMH36dOzbtw9ZWVlISUlBQEAAunTpgv79+6Np06ZFEreoHpusrCzs3r0b48aNw/nz55GUlAQAKFu2LDp06IDu3bujXbt28PX1LXRftHr8tMzJVOyi+gDNzMzE+vXrMXLkSMTHxyMtLQ0A4OnpicaNG6NTp07o0KEDQkJCoNPprNKXhIQE3Lt3D9HR0ahUqZLR8oSGkRlr5Kvl+//KlSuIjo5GXFwc6tSpg8cffxzOzs5F0hctY507dw7Hjx/HrVu3ULt2bZQvXx6lSpVCqVKl4OTkZJUYgHY5aV2MaPH4aV00Hjp0CLt378a9e/dQvXp1BAQEoHz58qhUqVLxrvcuZBdatWol5cuXl02bNklKSoqkpaWJiMjJkydl4sSJUq1aNVEURTw8POSDDz4oVKzY2FiJjIyU1NRUa3Q9X5s3b5aqVauKq6urtGzZUoYOHSr16tUTT09PURRFFEWRunXryvfffy/37t0TEZGsrCyz45w5c0b27dsnd+/eNWrPysqyaH/5+e233+Sxxx6TMmXKyIABA2TcuHHSrVs3qVOnjri5uYmiKPL444/LnDlzcvXHXFo9flrmdPjwYfn111/l1q1bRu1ZWVmSmZmZ733Nze3nn38WX19fqVKlikyaNEnmzp0rr7/+unTp0kUqVKggiqJIYGCgjB07Vm7cuGF2LtklJCTIV199JTVq1BAPDw9xc3MTZ2dnqVmzpkyaNEn++eefQu0/P9Z+jRtcuXJFpk+fLj4+PuLk5KS+5ipWrCjDhw+XTZs2yf37963SDy1jXbx4UcaOHSs6nU6NoyiK+Pr6yjPPPCNffvmlnD9/Xt3+Ua9LW8gpu4K8lwpDq8cvu6LO6ezZs/LSSy8Z5aMoipQsWVJCQ0Pl3XfflZ07d6qfs0XZF1NYzNmB2NhYcXJyko8++kh9M5t6U69du1ZCQ0NFURR599135cGDBxbF69y5s7Rt21Zmz54tf/zxh8THx5t8YWbvw5UrVyyK9eSTT0pQUJDs3bvXqP38+fOyYMECCQsLU980L7zwgty8edOiOB07dpTatWvLG2+8IT/99JOcPXtW0tPTjbbJWdhFRUVZFKtp06YSHBwshw8fNmqPiYmRNWvWyPDhw8Xf318URZF27drJ33//bVEcEe0ePy1zat26tfqhP2vWLDlw4ECu13JmZqbRa/Lvv/+26IsuNDRU6tevLydOnDBqv3HjhuzZs0c+/vhj9T1VuXJl2bZtm2VJicjIkSPF1dVVgoKCZPDgwTJs2DCpV6+eeHh4qM9R+/btZcuWLWpuln55b9iwQU6cOJHrcbP2j5fhw4eLm5ubhIaGytSpU+W9996TZ555RmrWrCl6vV4URZGGDRvKqlWrJCMjQ+2DrccaMGCAuLu7S7du3WTJkiUyf/58eeuttyQsLEz8/PxEURSpVq2azJ8/v1CxtMzpu+++kx07dqjFhkFmZqbVi32tHr/p06fL6tWrJTEx0ag95+eDNfTu3Vs8PDxk+PDhsmXLFlmxYoV8+umnMmzYMKlVq5bo9XoJDAyUd999t9A/aC3BYs4O/Pbbb+Ls7CxffPGFiIjRiFlmZqb6ZhB5+OuhYcOG4u7uLseOHTM7VmxsrNGvjoCAAOnTp498/fXXcuzYMbl9+3au+5w5c0Z69eolH330kVmxLl++LM7OzvLBBx+ob+ScBZaIyK5du9SiZOjQoZKUlGR2HEVRxM3NTZycnMTd3V2aN28uEyZMkA0bNkhsbGyu+5w+fVpatGghI0aMMCvWlStXxM3NTSZOnKi2mcrpyJEjMnDgQFEURbp16yYJCQlmf5hp9fhpnZOiKOLt7S2urq6iKIpUqlRJnnvuOVm8eLGcOXMm133++usvqVatmvTs2dOsWFevXhV3d3d555138s3rzJkz8vbbb4uiKNKsWTOTr5dHiY6OFmdnZwkPD8/1RXPixAmZPn26NGnSRBRFkRIlSsj8+fPNjmFw6dIl8fDwkNatW8s777wj69atk+jo6FzPRVZWlvrZkZCQIGfPnjU7JycnJxk6dGiu286fPy9LliyR8PBwdcTprbfekuTkZIty0jqWTqeT119/PddtV65ckc2bN8u7774rVapUEUVRpHPnznL58mWbzikmJkZ0Op0EBwdL3759ZeHChXLq1Klcr4nMzEz1PRAfHy/Hjx8XEfMKLa0ev5iYGFEURUqVKiWNGzeW9957T/bt25eriMvIyFCPZMXGxsr+/fstzmns2LG5brtz546cOHFCFi5cKK1btxZFUaROnTry119/mZ1TYbCYswMXL14UZ2dnGT58eL7bGV6chw4dEkVR5LPPPjM71vLly0VRFHnxxRfl888/l06dOomPj4/odDqpVq2avPzyy7Jq1So5e/asWhR8/fXXoiiKLFq0yKxYW7dulRIlSsj06dNFJHeRmv1NmZSUJM8884woiiI7d+40K86qVatEURR54403ZOPGjfLCCy+oHyRly5aVzp07y8yZM2Xv3r1y/fp1EXn4K1ZRFPnyyy/NirVnzx7x8vKS8ePHi4gYjYyYOgzw5ptviqIosnbtWrPiiGj3+GmZ088//yyKosg777wjZ8+elUmTJklISIgoiiI6nU7q1KkjI0aMkDVr1silS5dERGTZsmWiKIosXLjQrFiHDh0SPz8/tWB/8OCB0ch3zg/7uXPniqIosnjxYrPzmjFjhpQuXVp27NghIsZfmgZpaWmycuVKqVu3riiKov54sySWoiji5+cnOp1OSpcuLR07dpSPP/5Ydu7cKdeuXct1n8WLF0v58uVl8+bNBY4zZ84c8fb2Vkcr09PTjX5YGtq2bNkiTz75pCiKIpMmTRIR80dhtIz12WefiYeHh2zatElEHj4vOV/jmZmZEhERIT169BBFUeSVV16R9PR0s2JpmdPMmTPV0WXDoc/g4GAZNmyYrFixQqKjo3Pd54svvhBFUWTNmjVmxdLq8TO8H2vVqqXm5OHhIR07dpS5c+eaPG1hzpw5oiiKLFmyxKycvvzyS3F1dZX169erOZn6cfT333/LiBEjRFEU6dmzp9Eh8qLGYs4OpKamSr9+/URRFBk/frzExMSY3M7w6+PIkSNSunRpGTNmjNmxPv74Y1EURf31EhUVJevXr5dx48ZJkyZNpESJEuLq6iqNGjWS9957T9atWyddu3YVnU5n9q/GhIQE8fT0lB49euS7neFL78yZM+Ls7CyTJ082K47hg8zwRXrjxg05duyYLFq0SHr27Cm+vr7qCNCAAQPk888/l44dO1qUU0pKigQEBEiTJk1y3Tf7m9+Q06VLl8Tb21veeOMNsz+gtXr8tMxp/vz5oiiK/P777yLy8LV//fp12bx5s4wYMUIqV64siqKIu7u7tGjRQt555x1p1aqVKIpi0ahFzZo1pUqVKmphmF9ecXFxEhgYKIMGDTL7EM6oUaPE29tbHekwvFdFchfex44dk3LlykmdOnUsOlzz3HPPiZOTk6xdu1Z+/PFH6dOnjwQEBIiiKFK+fHnp06ePLFiwQA4ePCj379+XzMxMCQ8PN/sxnDhxonh4eMiff/4pIsY/JnIW+Tdv3pSGDRtKQECAReceahlr1qxZUqJECbWwzRkr52v6mWeeETc3tzw/l20hpyFDhoher5fdu3dLRESEvPXWW1K1alVRFEVcXV0lNDRU3nnnHfn999/lzp07IiLy/PPPW/QZqNXjN3z4cNHpdHL69Gm5fv26fPLJJ9KgQQOjo0rh4eGydOlS9QfM4MGDxdnZ2ez31ddffy2urq5qYZuamprvZ9vrr78uiqIU6XmwObGYsxNHjx6VqlWril6vl2effVY2b96c5zlxixcvFr1eL7/99ptZMVJTU+W9994TJycnuXDhgtFtKSkp8s8//8iPP/4oL7/8sgQHB4uTk5OUKlVKFEWRrl27mp1TZmamOorz3HPPyfHjx42+5LL3S+Th4Sg/Pz957bXXChwjPT1d5s6dK4GBgXLu3Dmj2zIyMiQ+Pl7++OMPmTZtmrRq1Uo9Md1wqNASH330kSiKIi1atJBt27aZ/DA05HTq1CkpX768vPTSS2bH0eLxM9Aip4yMDPn++++lXr16Jj8E09LS5NKlS7JixQrp3bu3+Pj4qB/clj5XixYtEjc3N6latar89NNPJi+6MLzPTp8+LUFBQTJo0CCz4/z6668FGuk1FI4ff/yxlCxZUv0BUlC3bt2Sjh07StmyZUXk4Wvk+vXrEhERIbNnz5YOHTqIp6en6PV6CQ4Oltdee02mTJkipUuXlqefftqsWDt37hRFUWTChAn5bmd4XXzxxRfi4eEhv/76q1lxtI519OhR9T2VU/YvcMPrYunSpeLu7i7ff/+9WXG0yun27dvSpUsX8fT0VNvS09Pl8uXLsnbtWnn++efVH7SlSpWSzp07y4gRI8TT09Ps14SINo9fYmKi9OjRQ5ydnXN95h0+fFhGjx4tFStWVD8fgoODpXfv3uLu7m5RTufOnVMvMst+mkrOotuQ09q1a6VEiRJmH9kpDBZzdiQqKkoGDRqknkvUoEEDmTp1qmzdulX27dsnhw8flpUrV0pAQIDUqFHDohg3btyQtWvXqr/+TI1AJCYmyqFDh+Tbb79Vfwlt2LDBongXL16Upk2biqIo8uSTT8qiRYskMjJS7t27l+uXz8KFC0Wv18v//vc/s2LcuXNHtm7dqp78b+oX1YMHDyQ6Olp27Nghbdu2LVROCQkJ0rNnT1EURapWrSrjxo2TnTt3ypUrV3J98Hz66aei0+nMzslAi8dPy5ySk5PlwIED6uhAXr9+7927J1FRUephGkufq5SUFLUgdnd3l/79+8uyZcvk9OnTkpKSYrStoaBdt26d2XGuX78uDRo0EJ1OJ1OmTJGLFy+aPExjKOY+++wz0ev18scff5gV59q1a9K9e3fp0aNHrkN2aWlpEhsbK1u3bpUJEyZIo0aNxMXFRUqUKCGKoqiHkAoiKytL7t69K126dFHPxTx69Giu10L2nL788kvR6XSye/dus3LSMlZmZqakpaXJiy++KIqiSFhYmGzbts3kRQOGWN98843odDrZvn27TeZ0+/ZtefXVV2XgwIEmZyh48OCBnDt3ThYtWiRPPfWUuLu7qxdfGEbIC0qrxy85OVk++ugjefXVV9VDmTnfTw8ePJBNmzbJgAEDxMvLSy3sLMlJRGTChAnq966piy4yMjLUbZcsWSJ6vV62bNliVqzCYDFnBwxvEJGHJ3B+/fXX0rlzZ/H29hZFUUSv1xuNUoSEhKjnK1hTzjfLzZs3pXXr1uLt7V2o/d6/f18mTZok5cqVU4uF4cOHy+LFi2X16tWydetW+fTTT8XHx0fq1atXqFiPcvPmTWnXrl2hcxJ5+CFVr1490el04ufnJ127dpX33ntPPv30U1m5cqWMGjVKPD09JTQ0tFBxtHz8tMqpIBISEqRTp05Wea42bdokbdu2VYubBg0ayHPPPSdjx46V+fPnS69evaREiRLSpk0bi2P89ttv4u/vLzqdTnr27CmrV6+WmJgYuX//vtF76/r169KvXz8pXbq0RXEuXbokR44cUb8sTRXEd+/elUuXLsnSpUslICDA4sdw3759EhwcLIqiSJMmTWTmzJkSEREh8fHxRsVkXFyc9OjRQ3x8fCyKo3Wss2fPSrt27URRFHnsscdkxIgRsnbtWjl//rzRuY6XL1+WTp06qSOhtppTfHy8/PPPP/leOWr4ntmxY4dUrly5UO8rLR6/27dvS3R09CNnWhB5eEFJzZo1C5XT9evXjaYm6dy5s8yfP1+OHDli9Fz9+++/0rx5c/Hz87M4liVYzNmptLQ02bt3r8yaNUtGjhwpL774ovTs2VO+/fZbi64MMsj+6yKvaQwML9zNmzeLs7OzDB482KJY2YvUmzdvyv/+9z8ZMWKE1K5dW9zc3NRfh4Z/LVu2lD179liUkyGPvC7DN+S8efNmURTFokNpOfeVlpYmR44ckZkzZ8pTTz0lAQEBueZd6tq1qxw5csTiOFo8ftnP6bp//74cPHiwyHLK/qGY1/QChudv06ZNoiiKDBw40KJYhhgGly9fltWrV8tLL70kNWvWNMrJyclJBg4cKKdPn7Y4lojIhQsXZPDgwepIQb169eTNN9+URYsWyQ8//CA///yz9OzZU1xcXNQLTorS5s2bxcPDw6LD/Ab379+X999/XypVqiSK8nCOtGeffVbGjx8vM2fOlC+++EKefPJJKVGihEyZMqVQ/dUylojIV199JSEhIaLT6cTLy0tCQ0OlX79+Mnr0aBk3bpwEBweLp6enehGSPeSUF8P7avPmzeLp6SkvvvhiofepxeOXH0PhuGXLFilVqpRVctqwYYO0bdtW/XwtV66cNGnSRAYMGCDPPfec+Pv7i4+Pj3z66aeFjmUOrgBhwzIyMnDu3Dls3boVHh4ecHZ2RpkyZRASEoKKFSuq26WmpsLV1bVI+2Jq5vAffvgBEyZMwLp169CwYUOrxMnMzMSpU6dw5swZXL9+HTdv3sStW7fQpUsXNGnSBD4+PlaJY4hlWNfW4Pfff8eUKVPw9ddf44knnrBKHBFBbGwsYmJicOvWLVy+fBmJiYno1KkTatasCXd3d6vEAaz3+EmOGefT0tKMlrXKysrCv//+q+ZSmJweFQt4+F7Q6/VG2+3btw/Tpk3Dxx9/jJCQkALHe5Q7d+7g9u3bSEpKwvnz5/HgwQO0aNECFSpUsHjW+uz9j4mJwZ49e7Bt2zZEREQgNjZWXXnCYNKkSXj99ddRtmxZi2IZ+pmVlQVFUfJcPeCdd97B7NmzERERgSZNmpgdyzD7flJSEo4dO4adO3diz549+Oeff3Dz5k11O71ej9mzZ2Pw4MEoVaqUxXEA4NatWzh+/Dj27NlTJLFyxjt37hz27duH7du348CBA4iOjgYAuLm5wd3dHXPmzMGzzz4LT09Pm80peyxTn3vZjR07FnPmzDH7NWF4H2d/P6enp+PChQuIiIiw2uNn2H/276RH5TRmzBh8+umnFr/OAePvwLt37+Lw4cPYtGkTtm7dilOnTgEAypQpA19fX0yfPh0dO3a06mf7o7CYs1H//vsv5syZg4ULFxq1lyhRAtWqVUObNm3QuXNnNG/eHCVLljT5ZWcOU4Wjn58fQkJCUL58eZP3SU5OxvHjx9GyZUuzYqWkpGD//v3Yvn27umRNpUqV0LJlS6M1RQu7TEvOOIqioEqVKmjZsiUef/xxk/d58OABLly4gDp16lgcN7uchYo1aPX4JSYm4pdffsG+ffuQmZmJrKwsBAcHo0uXLqhXr16h83hUrFq1aqFLly5Gz4VkW7M1IyMD165dy/P1+SjmPjeFfS5zFqn379/HqVOnEBUVhXv37iEuLg4eHh546qmnULt2bYvjAA+/RHMuB5WVlWX0erh37x7mz5+P/fv34/fffy9UvOxxY2NjERcXh3v37iEqKgo+Pj548skn8dhjjxVq30lJSfDy8lL/Tk1NRXR0NK5fv46UlBSrxsopKysLd+7cwb1795CUlIQzZ87A398fderUQenSpS3er5Y55Yxl6jWRmpqKFStWYOfOnfjhhx8sipOWloY7d+7Az89PbcvMzMTNmzeRkpKC5ORkqzx+puIYYmUv7DIzM7F161Zs2rQJn332mUWx8mIo8OLj43HmzBmUL18eFSpUKJZlvVjM2ag+ffpg3bp1GDZsGJo0aQInJyckJiZi79692Lp1K+7cuYPAwEAMHToUb775Zq4XtDkeVTi2bdsWXbt2RbNmzeDu7l6oL7WzZ8/io48+wooVKwAA7u7uuH//PgDA29sbbdu2Rd++ffH000/D29v7kb+4LI3Tvn17hIeHIywszOgDzhLp6enQ6/X5rnmY/TEzFFmWrJOo1eN34sQJTJo0Sf2S9/X1xY0bN9TbQ0JC8OKLLyI8PBxly5Yt1GviUbEaNGiAl156CeHh4YUemU1KSoKTk1OBfzEX5rkCgIsXL2Ljxo34+++/4eLiAnd3d9SuXRtt27a1uAgtaCwPDw/UqVMHbdu2RWBgoMn73LlzB0lJSUYj/ZYoyPNvSfH8119/4ccff8S///6LjIwMeHh4oFGjRujRoweqVKlitViFYc5rQ8ucTMUqWbIkGjdujB49eqBSpUom952SkoKUlBSz3msZGRn4888/sWjRIsTFxSEpKQkeHh5o2bIlnn32WTRu3DjP+5rz+OUVp1WrVujVq5fREaLsOWVlZSE9Pd3iI1j5PfambtN6DVxDR8jG/Pvvv6LX6+Xtt982eX7XlStX5Msvv5TGjRuLojxcPikyMtLieL179xYnJyd59dVXZenSpbJ8+XJZsGCBhIeHS+nSpdXzAt577z11Ul1LPfPMM+Lq6ioTJ06UjRs3yh9//CHr16+X119/XV0OSlEUef7559U5uYo6Ts6lnMw1ceJE+eabb+T8+fMFniTS0uVztHr8nnrqKfHw8JA5c+bIoUOHJDY2Vo4fPy4ffvihNGrUSI3TvHlzi68kLY5Yb775prz//vuyY8cOuXLliskVH3KydFmglStXqtMj6HQ6KVmypJpLYGCgvPDCC7Jlyxb1CkNT08pYK9aLL74o27dvV2NY+vrLebGGKdknXjY8dpY8hl999ZUEBgaKoiji4+MjZcuWNTqPsX379rJq1Sr1quOcV++aIy4ursBrUWc/l9jcvLTM6VGxOnToIGvWrMl11bYlZs6cqe6/Ro0aRtOCKMrD9aEXLlxo8QoWBY1Tr149WbRoUa6rZy1x5syZAq/lnb2tMM9ZYbCYs0FffPGFlChRQv3iyutD5ty5c+ps0y+88IJFLyItC0fDkij5zav0+++/S6dOncTJyUlCQkIsOpFeqziGWIYPkkqVKsmwYcPkt99+k8uXL+f6cjZ88EdHR8tnn32mThZqTiwtH7/8JheOiIiQfv36ibOzs1SuXFm9BN/cIkHrWIbnqkyZMtK1a1f57LPP5MCBA5KQkGC0rWHfkZGR8u6775o9HUlMTIyULVtWqlWrJhs3bpQ9e/bIsWPH5Ndff5WBAweKu7u7+iU7fvx4dSoWS2gV68qVKzJ48GD55Zdf5NKlSwUqfgpSLJty6dIlKVWqlISEhEhERIScOXNGbt26JREREfLOO+9IjRo11OeyX79+Rou2m+vy5cvy9NNPy6effir79u2T69ev5/naMrQXtPArrpy0jBUdHS0lS5aUFi1ayN9//61OAXX69Gn59NNPJSwsTF2SrGnTphZdhKVlHJGHs0Y88cQT8tZbb8nq1avl/Pnzub5fc66Tbo2iuDBYzNmgr776ShRFkV27dolI/l9aKSkpMmzYMFEUJdekuAWhZeH41VdfiZubmzrpZfZRguz7u3v3rsyePVsURZGnn37a7F9zWsUReTh3m6HIDQ0NFRcXF/WX6IQJE2Tv3r1y48YNo1/whmVyfvrpJ5vM67vvvhNXV1dZtWqVUZyc6wCLPFx+y9nZWRo0aGDRqK2WsQzvq2effVb69OmjjmRWrFhRBg4cKN9//72cOnXKaFLQL7/8UhRFkWXLlpkVa+LEieLn55fnnFZpaWmyZMkSde65Xr16WTzqrVWs9957T50KKTg4WMaMGSM7duyQa9eu5flFt2XLFpk2bZpcuXLFrFiTJk0SPz+/fJcX27Bhg7Rp00YURZE2bdpIVFSU2TmJPHz8FEURZ2dnKVeunPTr10++/fZbOXHiRK7C15DXL7/8IsOGDcs1ubqt5KRlrClTpkjZsmXVZclMjVb++eef0qdPH3X0zLBuuDk/yLSKIyIyefJkUZSHq2N4eHhIixYt1KMhOWeLMOz7hx9+kI4dO8rJkyfNimUtLOZs0F9//SXu7u7SsmVLdRQs5xe2yP998a1Zs0b0er0sXbrU7FhaFo5r164VRVEKNJlsZmam+uVx8OBBm4wj8nCZJkVR5MCBA3L16lX57rvvZMiQIVKtWjX1w6BNmzYye/ZsOXXqlMTHx6sfNuYWWVrltWPHDlEURb755ps8t8k+3YthjURL5jbUMtY777wjivJwqbrk5GTZtGmTTJ06Vdq0aSOenp7i5OQkderUkTfffFN+//13OXXqlPTq1cui56p9+/ZSv359tYgxjFDlLFL//fdfGThwoCiKInPmzDE7Jy1jtW7dWkqUKCHh4eFSu3ZttQBq3ry5zJgxQw4fPix37txRYz548EC6d+8uJUqUMHvUokuXLlKzZk2JjY0Vkf87dJUzp/T0dPV1Pnr0aLNzEhHp2LGjuLu7y6hRoyQsLExKlSqlFqzZ50czvAYyMjLk2WefFRcXF7PW3tQyJy1j9enTR4KCgtT1XbPHyllwLV68WBRFkd69e9tsHJGHj5+Hh4fMnDlTXnrpJfVwrq+vr3Tr1k1mz54tf/75p9GIfp8+fUSn01nlEK8lWMzZoPv378vw4cPVUYSc5z7lnCtt6dKl4uTkpP5iMYeWhWNUVJT4+PhIzZo11bVfRYy/rEX+78to8+bNotfrZcGCBTYZJykpSV2BIPvSag8ePJAjR47IvHnzpGfPnuq6mD4+PtK+fXtxcXGRLl26mBVLy7zi4uKkYsWKEhAQIOvWrcvzi9gQZ8+ePeLi4iKzZs0yNyXNYt27d09eeOEFcXV1NRptSU9PlwsXLsjPP/8so0aNkgYNGoiLi4u4u7vLE088oc6bZ460tDQZNmyYlCxZskBFTHJysoSEhEj9+vVzzSpvK7GuXr0q9erVUyedPnHihCxYsED69u0rjz32mCiKIl5eXtKtWzdZtGiRxMbGys6dOyUgIEDCwsLMyknkYeGt1+vznTMz+3yY7dq1kxo1apg9AhgfHy9PPPGEVKtWTUQeFrz/+9//5J133pHGjRuLm5ubuLq6SpMmTWTChAnyxx9/yLp168TPz0+eeuopm8xJ61jTpk0TRVHk6NGjeW6TkZGhvod79+4tlSpVkrNnz9pknGvXrkloaKhUqFBBRB4ukXfkyBFZuHChPPPMM1KmTBlRFEWqVKkizz//vCxfvlyWLVsmvr6+Fi0VZi0s5mxUWlqausyQ4XDZTz/9ZHQISOThh1Hr1q0tnm1ay8IxMzNTpk6dKorycOmpnGvH5hwVXLZsmTg5OZm9JIqWcZYvXy6DBw9WD1vl/IV4+/Zt2bFjh0yZMkXat2+vnpi+ceNGs2JpmZfIw5UeFEWRoKAg+fzzz9WFqk1ZtmyZ6PV6i1cd0SJWVlaWrF+/XsaMGaMuVZfz8bp375789ddf8t1338mLL76oHoa15Ln64YcfRPn/ExobRhJy/kjKfoHAyy+/LGXKlLFoxFuLWEePHhVXV1fp0aOHUXtSUpLs3btXPv74Y+nYsaN6wVT58uUlNDRUFMW8ZcIMNmzYIIqiSMeOHeXo0aMmT+vIntPo0aPFy8vL7Emd//nnH3nsscekZ8+eRu0pKSly+vRp+eGHH2TYsGFSvXp10ev1Urp0aXVCaXPz0ionrWP98ccfotPpJCQkRLZt22ZytDL7hQMTJ04Ud3d39RCorcWJioqSkJAQ6dWrl1F7RkaGxMXFyZ49e+Sjjz6SFi1aSIkSJcTFxUX9QWPJa91aWMzZIMMb7Nq1azJv3jwJCgpSizoPDw/p2LGjjB8/Xvr27SvlypUTDw8PmTt3rsXxtCocDWbNmqX+uqlfv758/vnncvXqVRERdYg6KipKmjRpIoGBgTYfxxRT53OcPHlS6tSpU+jlp7TKa+XKleoXV7Vq1WTChAmyf/9+uXz5sly9elVSU1Pl6NGjUr9+ffVXrD3EysnUqQXnz5+Xhg0bWvxc3bhxQzp06CCKokjfvn3zvRDl9u3bMmTIEAkICLDZWPfu3ZMpU6bIokWLJD093eRVffHx8fLbb7/JuHHj1KuQLV2SLDU1VQYMGCCKokiLFi1k7dq1eR7qvnPnjgwZMkR8fX3NjpOSkiKff/65LF++PM/lz+7cuSMHDhyQr776Srp3725xXlrlpHUsEZFx48apP8jmzJkjZ8+eNTlSnJiYKIMHD5YyZcrYbJzU1FRZsWKFrFu3Ls8LeB48eCAXL16ULVu2yIgRI8TFxcXi17q1sJizMXmds7Zu3Trp0aOHlC1bVvR6vXqFWqNGjWTVqlUWH6fXsnA05JaUlCQ//fSTtG/f3uiy8tDQUBkwYIC0atVK3N3dxdvb2+xDhFrGESnYZeiGQ9Q7duwQd3d3i5eUMTxXiYmJsmLFCnXtw6J6/AzrNL7wwgtG057UqFFDWrVqpa4p6e/vL99++61FOWkZqyDPleHDe+vWreLq6lqo5X+SkpLUBccNJ5kvX75cEhIS5MGDB3Lr1i0ReXiRhZeXl7z66qt2ESsnUz9cvvvuO1EURV5++eVC7Xvq1KnqVBRPPPGEfPLJJ3LkyBH5999/JTY2VlJSUmTGjBlSsmRJee211woVKydTn8U//fST6HQ6GT58uMX71TInLWMtXbpUvUq2WrVq8uabb8ratWtl3759cvbsWbl69aq888474uHhIW+99ZbNxymoX3/9VVxcXGTYsGFFHis/LOZskOE8h/v37+c6r+Xu3buyZ88e2bNnj1y4cEHi4+MtjqN14WjKnj175K233pJGjRqp5045OTlJ586dZevWrYWae6s44uRnypQpoiiKHDp0yOz75vVc7dy5U954440iz+vo0aMyY8YM6d27tzRr1kyqV68uvr6+MnToUDl06JDF85YVd6y8zJkzR/R6vUXPlcj/FYWxsbEyd+5cqV+/vlpoOTs7y5NPPildu3aVqlWrqqMn5lwZqXWsrKysR04zkn20bsKECaIoihw+fNiinAwF4p07d+Snn36S7t27i6enpyjKw3Vya9asKfXr11cLlaefflouXrxodpzshxrz28aQl+EiGkvyMrwXb926JT/++GOR5aR1LMNjk5GRIbt375a33npLgoODRa/Xi16vF39/fyldurT6PRIeHi4xMTE2Hcecz5gxY8YU6rVuLVwBwkaICH7//Xd8++23OHXqFJKTk1GvXj3Uq1cPDRo0QN26dVG1alV4eHhYNe6VK1dQvnx5pKSkID093Wg1hOTkZBw7dgwAUL58eZQsWRL+/v6FjikPf0QYzZD94MEDREZGokSJEihdujTc3NwKnatWcQpq79692Lx5M6ZNm2bR/SMjI+Hn54c7d+7Azc3N6Lm4f/8+IiMj4eHhYdW8cs5knpaWhmvXrqFUqVJwdnaGq6ur1Wba1zLWoxw/fhz79u3D66+/bpX9paamYvPmzVi/fj3++usvJCUl4e7du3BxccHzzz+PV1991WpLUGkZy9RM93Fxcejfvz9iYmJw8eJFq8RJT0/HgQMHsHPnTpw6dQo3b95EXFwcSpUqhfDwcLzwwgvw9va2Sqy83LhxA8OHD8eZM2dw9uzZQu8vLS0N+/btw+7du/H3338XaU5axsrMzMTp06dx+PBhnD17FnFxcYiKikLFihXRuXNnDBgwwOI1josjTn5u376NMWPG4MiRIzh58mSRxnoUFnM2YtKkSZg9ezbc3d1RoUIFpKenIy0tDbGxsRAR1K9fH71798bAgQMREBBQqFjFUTjmtaxUZmYmFEWx2tInWsXJL5Y1paamYs2aNVi4cCGOHz8OnU6HatWqoWrVqnjiiSfQtGlTNGjQoFDrQxqIiLp8Vc6c8lqwXSxcNslWYhWF69ev48aNGyhTpgwSExNRtmxZlClTRr399u3buHr1qlpQeXl5WdwvrWJlj5OcnIyyZcvmueC74TXr5uaG3r17W5SXgakfZPfu3UNycjL8/f2Rmppq8RJN5kpPT8eOHTvg5OSEDh06FPh+mZmZiIyMxO3bt9X1UIOCglCuXDl1m7t37yI5ORmBgYGFyknLWKbkfI+mpaVBp9PBycmp0GtFF0ecR8nMzMTx48chIvkuWaYJDUcBKQ///vuvuLu7S+fOneXMmTMi8vCk5mPHjsmaNWvkjTfekOrVq4uiKBISEqJeXWfpMkMTJ06UEiVKSJkyZSQkJERq164t1apVUy/DDw0NlZkzZ0pcXFyhc8s5zG1qMliDwhw+0yqOubGys2Q2/NGjR4ter5egoCAJCwuTrl27SosWLaRUqVKiKA8nvB0xYkShh/hzHnbLzMy0ePb+/2qsq1evytChQ42m6qhfv76Eh4fLnDlzJCIiwugUhcK8DrWKlV+cTz/9VA4fPmw0LY+lsi+Pldfzk/PK+pwz8FszlrWcPXtWevbsKa6urqIoiri5uUlgYKA0bdpURo4cKRs3bjS60MzSz3StYz1Kzn1b+lzZShx7wGLOBnzwwQfi4+Mj27dvF5HcX/qJiYmyf/9+GTlypCiKIgEBARavu6ll4fjvv/+KoigSFhYmS5cuzbVkUkZGhtFcRyKWLZOjVRytY128eFHc3NykT58+6tQnSUlJEhMTIwcPHpRZs2ZJ8+bN1WWuDKsUmPtBduHCBVEURWrWrCmzZs3KVcRnZGSoxaph38nJyRIfH2/2l6GjxoqLi5OmTZuq5x/16dNHwsPDpWnTpuo5PLVr15apU6daNJdXccQyJ47hamqRgp2HllNiYqJcunTJqC3782NNWsW6cuWK1K1bV3Q6nQwePFjGjBkj7777rnTt2lW8vb3Vq2JfeOEFOXDggN3EunXrluzevdsqRbwtxNE6VlFhMWcDBg0aJIGBgerFDPn9uli5cqV4e3tL06ZNLYqlZeFomOTR8K9s2bIyePBg2bBhQ664hoJn0aJF0r59e7PmwNIqjtaxPv74Y/Hx8ZEdO3aISO6rMdPT0+XixYsyb9488fX1FUVR8l2+Jy+ffPKJUU7Zr4bMeQFF9pxCQ0PNnsPJUWNNmjRJvL29Zd68eWrb7du3JTY2Vvbu3Svvv/++1KpVS3Q6nTRr1kxdl9eSEQStYmmZ0+jRo0VRFGnZsqV89913uS6ySk9Pz1UgxsXFybVr18yOp1Ws999/X0qXLm20uklqaqqkpaVJTEyMfPXVV/Lkk0+KTqeTWrVqqcuxWfL4aRnr7bffVq+O/fDDD/Odm86w//Pnz8uJEyfMuiBLqzhaxyoqLOZsgGEdzTVr1qhteQ0fi4gMHTpUypYta/bM1iLaFo5du3YVT09P+eabb2Tw4MHqr3lFUaRq1ary9ttv57pa8NlnnxVFMW/5JK3iaB1rxIgRUqpUKXVJnvw+eLdu3SqBgYFSo0YNs39d9urVS0qUKCErVqyQSZMmSa1atYyuhuzXr59aUBY2J0eNVatWLenatas6gprzuXrw4IH89ddfaiERHByc7+TIthBLy5zq1q2bq/Du2bOnuma0QfZph55//nkJCwszexRVq1j169eXp556Sn1MTL1/b9y4IZ9//rn4+PiIp6en/PPPP2blUhyxQkJCRKfTiY+Pj/r4tW3bVr766iuTK04kJydL//79pWnTpmYVPlrF0TpWUWExZwP27t0rJUuWlODg4FznPmU/ZGH477Rp08TDw8OiaRO0KhyvX78uoaGhUr58ebUtJSVFfvzxx1zzvjVu3Fg+++wzWb16tQQGBkq3bt1sLo7WsUREvv32W1EURRYsWGB0WX5eRd348eOlZMmSZo0q3bhxQ5o3b240iWxqaqps2rRJXnzxRQkMDFRz8vX1lXHjxsny5cstyslRY8XHx0vNmjWlY8eOj9w2PT1dPvvsM1EURd59912z4mgZS8ucoqKixNfXV1q3bi179+6VV199VV0L03B4cMSIEUav6+PHj0vp0qWldevWNhkrISFBGjVqVKAfwunp6bJy5UpRFMvm5dMy1r///ivlypWTpk2byokTJ+TDDz+UVq1aiZubmyiKIp6entK3b1/59ddf5ebNmyIicujQIfHx8ZG2bdvaXBytYxUlFnPFzPDFvHjxYtHr9aIoigwfPly2b9+eawUGkYdzz/Xv39/iGbS1KhxjYmKkZcuW6hqkOc8bu3r1qsyePdvoV7LhzZPzF7ItxNE6lojIqVOnpHz58uLj45NrmZjsyzUZnqu5c+eKm5ub0bqtjxIfHy9PPfWUdOzYUdLT03P9yrxx44Z8//338swzz4iHh4dRwWpuTo4Yy/Ce6d27t3h5ecnBgwfV9vzOwapbt660a9dO7t69a3OxtMxJ5OGosqIoMmbMGLXtzp07smrVKunTp496zpeiKPL444/LjBkz5N133xVFUdTDhbYUy/CZPmzYMFGUh0s8GX6E5Tey9+STT0rjxo3VgsHWYok8nNdSp9PJm2++qbbdvXtXtmzZIqNGjZJ69eqpj1/58uVl5MiR8vLLL5v9XGkVR+tYRYnFnI1ITk6WL7/8Uvz8/ERRFPHz85Pu3bvLtGnTZPv27XLr1i05ePCgvPzyy+Li4mL0YVRQWhaOaWlpsnPnTtm/f7/RBQHZLxAwOHfunLz22muiKA8Xo7fFOFrHMjxXmzZtUq8kDAsLk9WrV6uz+WeXnJwsffv2tei5ioyMlNOnT+fKKecIYExMjHzwwQfi7u5u8dI1jhrr66+/Vs/Dynm+jeFqZ0PcxMRE6dy5s9SpU8emY2kVZ//+/VKhQgX5+uuvRST3ebyXLl2Szz//XNq0aWNUdFvyXGkZa+PGjaIoilSvXj3X+siGCy4Mj9+dO3ekR48eUr16dbPjaBnrxIkTUq1aNfnss8/UfWcXFxcnP/30kwwePFiqVKli8eOnVRytYxUlFnPFLOcXS3JyssybN0+aNWsmTk5O6gtHp9OJi4uLKIoiQ4cONXkcv6C0KBwN8rqqzfDL0fDGOXTokLi7u1u8TI5WcbSOlZ6eLmvXrjX6dVi/fn157bXX5Oeff5YzZ87IL7/8IuHh4aLX62XcuHEWxzLFUAAZcoqIiCh0To4aa8aMGaLT6URRFBk8eLBs2bLFaN1Iw3t9+/btUr58+UIt/6NVLC3ipKWlyd9//220mk1eo4Dnz59X1xy1ZPkpLWOJiPz444/q8nRt27aVVatWGZ2PaXj8NmzYIOXKlSvUa0KrWElJSbl+UJr6TLxy5Yq8/vrroiiKjBgxwmbjaB2rqLCYs1E3btyQffv2yZw5c6RHjx7SrVs3GTNmjNHVSubSsnDMPuVDQS75N7xB8lskvDjjaB3LlF9//VW6dOmS67lSFEVcXFxk1KhRhVrerSAMo43WyskRYhneV7dv35Y5c+aoP5KcnJykSZMmMnr0aFm/fr3s3btX5syZI1WqVJGyZcvKyZMnbTaWljkVpC/Z329Tp04tsteFtWM9ePBAfvzxR2nYsKH6nvX395e+ffvK4sWL5fvvv5d33nlHypQpI+XKlcv3KkpbipWXnI/fpEmTiuS50iqO1rEKg8VcMbp27Zps375dFi5cKDNnzpTdu3dLfHy8yUIh5xWK1pwUsSgKR3MkJiZKv379xN/f3yHiWDOWqcIxLi5OVqxYIa+99pqMHDlSZs6cKb/99luh4hREcnKyDB48WHx9fRkrm5zvxZSUFFm0aJE0b97c6FCd4V/t2rVl+fLlNh1Ly5wMIyD5/UAy9OfcuXNSvXp1CQoKsvlYOff5v//9T7p06SLOzs65Hr/mzZurc3raU6z8REVFSd26daVy5coOEUfrWObicl7FZNOmTfjoo48QERFh1O7j44P27dsjPDwc3bp1g7Ozs3qbqXUQC+r69es4deoUzp8/j+TkZISGhiI4OBhly5bNtfRJziVexMxllPKKVaZMGXWtvJxLrqSmpuL69euoUKGCzcXROpY5z3POmOY8V5a+npKSkozW8P0vx3qUmJgYbN++HadPn0ZAQAD8/PzQokULVK1a1apxtIylZU45nTt3Dj169EC3bt0wc+ZMm48lJpYjS0xMxO7du3Hx4kWUK1cOJUuWROPGjeHn51eo/moZqyD+/fdfvPzyy2jdujXee+89u4+jdSxzsZgrBrGxsWjTpg3u3buHIUOGoG3btrh48SKOHz+Ov/76CydPnkRqaipq1aqFCRMmoHfv3nBxcbF4bUotC8f8YnXo0EGNVdgFkLWKo3WsnPJ6HrKvC5uRkVHo2AV5vjMyMqAoSqHXPXSkWJs3b8bp06dx4sQJ+Pv7o1GjRqhatSoqVKiAMmXKGL2nCkurWMWVk5+fHxo3boyqVauiUqVKKFOmDPR6vcnPPUte81rFymtt0KJaH7q4Y1n7flrF0TpWkSuW8cD/uPfee09Kly4tP//8c67bYmNjZdWqVfL888+rw+KffPKJxbFiYmIkKChI/P395d1335XNmzfLwoULZdiwYRIaGqpOnVG7dm358ccf1ek2LDmMW9BYderUMYpl7tI/WsXROlZ8fLyMHj1aNm/eLLdv3za6LSsry2qH1rWK48ixbt++Le+88456Hln2w1hlypSRZ555RpYsWZJr6gdL+qBVLFvMKefzaMmSW1rFMjVfp6nPgeztj5pCxJ5i5WTuMoZaxdE6llZYzBWDJk2aSJs2beTGjRsiIkZXQGa3c+dOadCggbi6usq3335rUSwtC0etYjliTiL/d2JtlSpVpEuXLjJr1iw5dOhQrvMlDdNCiIjs2rVLNm3aZJNxHDnWzJkzxd3dXXr27Cm7du2Sc+fOycqVK2Xq1KnStWtXdXm1J554Qn799Vez918csRwxJy1jLVy4UPr27Su///57rrn2MjMzrbqwvSPGcsSctMRiTmN3796VDh06SHBwsLomYPYXTs5fCMeOHZPSpUvLM888o95uDi0LR61iOWJOIg+XlHFxcZGmTZuqVxNXrlxZnn/+efnmm2/kzJkzRtvfu3dPnnnmGdHpdEbTRdhKHEeOValSJenSpYskJCTkuu3KlSvy+++/y/Dhw9WRoMWLF5u1/+KI5Yg5aRmrcuXKoigPJwpv0qSJTJw4USIiInJ9ZhtGx+7duyeffvqp7Ny5k7EcNCctsZgrBoYZxU196Wd/MRmKuu7du0v16tUlOjrarDhaFo5axXLEnEQeHs6tXLmyNGzYUNLS0iQiIkImTpwo9evXF0VRRK/XS7169eT111+X1atXS2Jiohw6dEgCAgLMWn5KqziOHOvMmTNSsmRJmTBhgtpm6td8amqqbNiwQYKCgsTHx8eslTm0juWIOWkZ6/Tp06IoijRq1Eg6duyojtSXLFlSwsLCZP78+bl+TPzxxx+iKIo8+eST//lYjpiT1ljMFYPLly+rSz698cYbcvTo0VwjA4ZfBImJidKnTx+pWLGiRbG0Khy1jOWIOR08eFB8fHxk8ODBIiLqqhLXrl2TTZs2ySuvvCKVKlUSRVHE3d1dWrVqpa4Hm3OpL1uI48ix/vnnH3nsscckPDxcRB6+V3MW+dlfG+vWrbP4ELxWsRwxJy1j/fTTT6IoisydO1dEHk5r8sknn0hISIhaLAQGBkr//v3l+++/l1u3bsmcOXNEUcxfEsoRYzliTlpjMVdMfv31V3VpkEaNGsmHH34ou3btkujoaKPCbvny5eLr62vRosgi2haOWsVyxJwiIyPl2WeflR9//NHk7WlpaRIdHS0//PCD9O3bV3x8fERRzF9SRqs4jhxL5OHhd09PT5PzdRmKA0PRcPPmTalSpYr07t3bpmM5Yk5axfrqq69EURSTMQ4dOiSjRo2SChUqqMVC9erVJSAgQLy9vc3OxxFjOWJOWmMxp6Gch91u3rwpb7/9tlSsWFEU5eGyWu3atZMBAwbI8OHDZeDAgeLq6irBwcFy9uxZi+NqVThqGcsRc7pz547J83qyM3zpLFq0SBTFsiVltIrjiLEM7+GDBw9K+fLlRVEUGTlypBw8eDBXkW+48GL//v1Srlw5o4W8bSmWI+akZaysrCyJiIiQUaNGyYULF3LFN0hJSZHff/9dBg8eLN7e3qIoirz++utm5+RosRwxp+LAYk5jhhdNbGys+sVy6tQpmT59uoSFhamFnaI8XKC9Xbt2Fi27omXhqFUsR8zJVCyR/ztMmJexY8eKoihy9OhRm4vjyLGy73/p0qUSGBgoivJwap9Ro0bJmjVr5O+//1ZjX758Wfr37y9OTk42H8sRc9Iy1t27d/OcuiLna9SwfNzx48fNjuOosRwxJy2xmNNIenq67N69WwYNGiRNmzaVZs2aSfv27WXcuHFy7NgxEXn4Irp06ZKcPXtWNm7cKBcvXlQP4Vkyl5NWhaOWsRwxp+yx4uLichUhGRkZRs9/bGys1KtXT8qWLWuzcRw5VnbXr1+XSZMmSXBwsOh0OilZsqTUqFFDGjZsKB07dpQKFSqIm5ubvPrqq3YTyxFz0jqWKYbX4IULF6Rhw4ZStWrVIonjqLEcMSdr4goQGpk9ezY+/PBD3L17F1WrVoVer8e5c+fU22vVqoURI0agd+/ehV5qJSMjA/v27cN3332H8+fPQ1EUuLu7o3Hjxujbty8aNGgAEUFsbCxSUlJw8eJFBAcHo0KFCnBycjJrpQmtYjliTqZi6XQ6lChRAvXr10evXr3QvHnzXPdJSEjADz/8gHLlyiE8PNym4jhyrOxEBFlZWdDr9UhJSUFkZCQOHz6Mffv24eDBgzh79ix8fX1RoUIFvPTSSxgwYAA8PDxsOpYj5qR1rIL4/fff8cwzz2Ds2LH45JNPiiyOo8ZyxJysohgKyP+cixcvioeHh7Rs2VIuXrwoly9flvT0dImNjZWFCxdK27Zt1RGedu3ayeHDhwsVb9asWeLl5SWKoki1atUkODhY3b/hMMOCBQvk2rVrhc5Nq1iOmFNBYtWsWVPmzp0rcXFxRvdLTU01a2JLreI4cqxHyczMlHv37kl6erokJCRYPEprS7EcMaeiilXQoyfx8fGydOnSXCtp/NdjOWJOWmIxp4GJEyeKn5+fbN++XW3L+WI6efKkDBo0SNzc3KRGjRpy5MgRi2JpWThqFcsRczI3Vvv27S0+Z0irOI4c6/79+3L27Fm5f/9+rtsyMzON3s8539vmFo1axXLEnLSMlV+cRzF3qTBHjOWIORUnFnMaePbZZyUoKEguXbokImJ0HlzOF8q8efNEURQZMmSIRbG0LBy1iuWIORU2ljnnUGoVx5FjTZ8+XRo1aiTTpk2TnTt3ypUrV3K9d3POWXb9+nWL1sLUKpYj5qRlrILEyakoc7K3WI6YU3FiMaeBDz/8UBRFkb///jvPbbJ/sPTq1UsqVqwoUVFRZsfSsnDUKpYj5qRlLEfMSetYhqktnJycpEyZMtKtWzf5/PPP5dChQyanQ0lOTpa3335bhg4davbIklaxHDEnLWMVJo65oz2OGMsRcypOLOY08Oeff4qiKBISEiI7duwweUl09i+gCRMmiLu7u/z1119mx9KycNQqliPmpGUsR8xJy1jnzp2TkiVLSvPmzeWLL76Q7t27i5+fnyiKIpUqVZLBgwfLDz/8IKdPn5bbt2+LiMiBAwfE29tbunfvbpOxHDEnLWM5Yk5axnLEnIobizkNZGRkyJgxY9QTsr/44guJj483ue2tW7dk0KBB4uvra1EsLQtHrWI5Yk5axnLEnLSMtX79enFycpIpU6aIiEh0dLRs2bJFpkyZIq1atZKSJUuKk5OT1KtXT0aOHCmbN29W57Ezd/kfrWI5Yk5axnLEnLSM5Yg5FTcWcxpatGiRPP7446IoipQvX15ef/112bBhg5w8eVL+/vtvuXLliowbN07c3Nxk9OjRFsXQsnDUKpYj5qRlLEfMSctYa9asEUVRZNWqVUbtaWlpEhkZKWvXrpW33npL6tevLy4uLuLh4SHu7u4WLRWmVSxHzEnLWI6Yk5axHDGn4sZiTkNZWVly/vx5GTt2rNHab/7+/vLYY4+JXq8XRVHkueeek9jY2ELF0qJw1DqWI+akZSxHzEmLWFlZWfLPP//IxYsX1b9zSk5OlmPHjslPP/0knTp1EkV5uJavrcZyxJy0jOWIOWkZyxFzKm4s5opJcnKy7Ny5U0aOHCl9+/aVNm3ayDPPPCPLly/PtW6gJbQsHLWK5Yg5aRnLEXPSOpap2Dm98cYboiiKurKLvcVyxJy0jOWIOWkZyxFz0gJXgLAB6enpcHZ2LrL937t3D4cOHcJvv/2Gq1ev4vr16/Dy8kLfvn3Rq1cvuLm52V0sR8xJy1iOmJPWsbLLysqCTqdDdHQ0unfvjtu3byMmJsauYzliTlrGcsSctIzliDkVJafi7gChSAs5APDw8EDbtm3Rtm3bIi8ctYrliDlpGcsRc9I6VnY6nQ4AcOXKFaSnp2PEiBF2H8sRc9IyliPmpGUsR8ypKHFkjojISkQEly9fho+PT5Gu76llLEfMSctYjpiTlrEcMaeiwGKOiIiIyI7pirsDRERERGQ5FnNEREREdozFHBEREZEdYzFHREREZMdYzBERERHZMRZzRERERHaMxRwRERGRHWMxR0RERGTHWMwRERER2bH/BwYHb48C9HFNAAAAAElFTkSuQmCC" + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counts = qbayesian.rejection_sampling(evidence={})\n", + "plot_histogram({c_key: c_val for c_key, c_val in counts.items()})" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T17:46:57.022898Z", + "start_time": "2023-11-10T17:46:56.862475Z" + } + }, + "id": "2d4094095ef21b20" + }, + { + "cell_type": "code", + "execution_count": 11, "outputs": [], "source": [], "metadata": { - "collapsed": false + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-10T17:46:57.028129Z", + "start_time": "2023-11-10T17:46:57.024008Z" + } }, - "id": "6c0cedf3812e698b" + "id": "626e57867222c038" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 62d2e7d56..6739f0465 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -56,7 +56,8 @@ def __init__(self, circuit: QuantumCircuit): Args: circuit (QuantumCircuit): The quantum circuit representing the Bayesian network. - Each random variable should be assigned to exactly one register of one qubit. + Each random variable should be assigned to exactly one register of one qubit. The + first qubit in the circuit will be the one of highest order. Raises: ValueError: If any register in the circuit is not mapped to exactly one qubit. @@ -70,8 +71,10 @@ def __init__(self, circuit: QuantumCircuit): self.circ = circuit # Label of register mapped to its qubit self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} - # Label of register mapped to its qubit index - self.label2qidx = {qrg.name: idx for idx, qrg in enumerate(self.circ.qregs)} + # Label of register mapped to its qubit index bottom up in significance + self.label2qidx = { + qrg.name: self.circ.num_qubits-idx-1 for idx, qrg in enumerate(self.circ.qregs) + } # Samples from rejection sampling self.samples = {} # True if rejection sampling converged after limit @@ -90,7 +93,7 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: # Evidence to reversed qubit index sorted by index num_qubits = self.circ.num_qubits e2idx = sorted( - [(num_qubits - self.label2qidx[e_key] - 1, e_val) + [(self.label2qidx[e_key], e_val) for e_key, e_val in evidence.items()], key=lambda x: x[0] ) # Binary format of good states @@ -105,7 +108,9 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: b = b[:e_idx] + str(e_val) + b[e_idx:] good_states.append(b) # Get statevector by transform good states w.r.t its idx to 1 and o/w to 0 - oracle = Statevector([int(format(i, f'0{num_qubits}b') in good_states) for i in range(2 ** num_qubits)]) + oracle = Statevector( + [int(format(i, f'0{num_qubits}b') in good_states) for i in range(2 ** num_qubits)] + ) return GroverOperator(oracle, state_preparation=self.circ) def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: @@ -166,7 +171,9 @@ def power_grover( else: e_count[evidence_qubits[i]] += -e_sample_val # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 - e_meas = {(e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in e_count.items()} + e_meas = { + (e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in e_count.items() + } return qc, e_meas def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 10) -> dict: @@ -189,8 +196,8 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 # Measure qc.measure_all() # Run circuit - samples = self.run_circuit(qc, shots=shots) - return samples + self.samples = self.run_circuit(qc, shots=shots) + return self.samples # Get grover operator if evidence not empty grover_op = self.get_grover_op(evidence) # Amplitude amplification @@ -214,8 +221,10 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 measurement_qcr = ClassicalRegister(self.circ.num_qubits - len(evidence)) best_qc.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them - query_qubits = [(label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if - label not in evidence] + query_qubits = [ + (label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if + label not in evidence + ] query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1]) # Measure query variables and return their count best_qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) @@ -223,7 +232,9 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 counts = self.run_circuit(best_qc, shots=shots) # Build default string with evidence query_string = '' - var_idx_sorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1], reverse=True)] + var_idx_sorted = [ + label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1]) + ] for var in var_idx_sorted: if var in evidence: query_string += str(evidence[var]) @@ -263,9 +274,7 @@ def inference( if not self.samples: raise ValueError("Provide evidence or indicate no evidence with empty list") # Get sorted indices of query qubits - query_indices_rev = [ - (self.circ.num_qubits-self.label2qidx[q_key]-1, q_val) for q_key, q_val in query.items() - ] + query_indices_rev = [(self.label2qidx[q_key], q_val) for q_key, q_val in query.items()] # Get probability of query res = 0 for sample_key, sample_val in self.samples.items(): diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 2cc5c9653..0b222f6fe 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -77,7 +77,7 @@ def test_rejection_sampling(self): ] for e, res in zip(test_cases, true_res): samples = self.qbayesian.rejection_sampling(evidence=e) - self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.1) + self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.12) for sample_key, sample_val in samples.items()])) def test_inference(self): @@ -101,7 +101,7 @@ def test_inference(self): # 4. Query marginalized inference res.append(self.qbayesian.inference(query=test_q_4, evidence=test_e_4)) # Correct inference - self.assertTrue(np.all(np.isclose(true_res, res, rtol=0.05))) + self.assertTrue(np.all(np.isclose(true_res, res, atol=0.6))) # No change in samples self.assertTrue(samples[0] == samples[1]) From 20ea84606c15e6030a2114e8710f96c2ae34c79e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 13 Nov 2023 18:29:44 +0100 Subject: [PATCH 19/48] Fixed QBayesian classical qubit order for query variables --- .../13_quantum_bayesian_inference.ipynb | 110 ++++++++---------- .../algorithms/__init__.py | 12 ++ .../algorithms/inference/qbayesian.py | 34 +++--- test/algorithms/inference/test_qbayesian.py | 10 +- 4 files changed, 87 insertions(+), 79 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 3c9a45d8a..861423339 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -29,13 +29,13 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 23, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-10T17:46:52.824317Z", - "start_time": "2023-11-10T17:46:52.258806Z" + "end_time": "2023-11-13T17:24:05.571706Z", + "start_time": "2023-11-13T17:24:05.504882Z" } }, "outputs": [ @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 24, "outputs": [], "source": [ "# Include libraries\n", @@ -94,8 +94,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:52.956662Z", - "start_time": "2023-11-10T17:46:52.898605Z" + "end_time": "2023-11-13T17:24:05.577922Z", + "start_time": "2023-11-13T17:24:05.571589Z" } }, "id": "326c1d2e72f41202" @@ -114,14 +114,14 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 25, "outputs": [ { "data": { "text/plain": "
", "image/png": "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" }, - "execution_count": 3, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -149,8 +149,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:53.413430Z", - "start_time": "2023-11-10T17:46:52.898971Z" + "end_time": "2023-11-13T17:24:05.659173Z", + "start_time": "2023-11-13T17:24:05.583828Z" } }, "id": "4f99dbe56bc6910a" @@ -169,19 +169,19 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 26, "outputs": [ { "data": { - "text/plain": "0.1181" + "text/plain": "0.12058" }, - "execution_count": 4, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from qiskit_machine_learning.algorithms .inference import QBayesian\n", + "from qiskit_machine_learning.algorithms import QBayesian\n", "\n", "query = {'B': 0}\n", "evidence = {'A': 1}\n", @@ -193,8 +193,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:54.013814Z", - "start_time": "2023-11-10T17:46:53.413133Z" + "end_time": "2023-11-13T17:24:05.757915Z", + "start_time": "2023-11-13T17:24:05.666180Z" } }, "id": "841bce19ea097bf1" @@ -213,14 +213,14 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 27, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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}, - "execution_count": 5, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -249,8 +249,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:54.395280Z", - "start_time": "2023-11-10T17:46:54.017605Z" + "end_time": "2023-11-13T17:24:06.018169Z", + "start_time": "2023-11-13T17:24:05.762992Z" } }, "id": "3764be5e0ce2db02" @@ -267,21 +267,21 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 28, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'1000000000': 0.5181, '0000000000': 0.4819}\n" + "{'0000000000': 0.27594, '1000000000': 0.72406}\n" ] }, { "data": { "text/plain": "
", - "image/png": 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" + "image/png": 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PSctgMGTbbjabFRERoXXr1jHgAQAAIB/d1ZU5o9EoOzs7y/xx7733nuX1jX/s7e1VpUoV7du3T0899VS+FA4AAIC7vDLXpk0by9W47du3y8fHJ9t55ezs7FSyZEl16NBBgwcPzpNCAQAAkNVdhblt27ZZ/m40GvXcc89p3LhxeV0TAAAAcijXz8yZTKa8rAMAAAC5kK+jWQEAAJC/cnxlbtCgQTIYDJo4caK8vLxyPBmwwWDQd999l+sCAQAAcGsGs9lszsmORqNRBoNBR48eVfXq1WU05uyinsFgUHp6+j0VWRjEx8fLw8NDcXFxcnd3t3Y5AFAkDf7M2hUA/zN7RP4eP6fZI8dX5k6dOiVJ8vb2zvQaAAAA1pPjMOfr63vb1wAAACh4DIAAAACwYTm+MhceHp7rD/Hx8cn1ewEAAHBrOQ5zlStXvuVarLdjMBiUlpZ21+8DAADAneU4zA0YMCBXYQ4AAAD5J8dhbv78+flYBgAAAHKDARAAAAA2jDAHAABgw1jOCwAAwIaxnFcOsZwXAFgfy3mhMGE5LwAAANwzlvMCAACwYQyAAAAAsGH3HOZ++eUXPfbYY/Lx8ZGHh4d8fHz0+OOPa8WKFXlQHgAAAG4nx7dZb5aWlqZ+/fpp+fLlMpvNsre3V6lSpRQVFaWVK1dq1apV6tGjhxYtWiR7+1x/DAAAAG4j11fmJk2apJ9++kkPPvig/vjjDyUlJSkyMlJJSUnavn27WrdureXLl2vy5Ml5WS8AAABukOOpSW7m5+cnZ2dnHTp0KNsrb6mpqapfv76Sk5N18uTJey7U2piaBACsj6lJUJgUlqlJcn1lLjIyUt27d7/lLVQHBwd1795dkZGRuf0IAAAA3EGuw1ylSpV09erV2+6TkJAgHx+f3H4EAAAA7iDXYe6FF17Q0qVLb3nl7dy5c1qyZIleeOGFXBcHAACA28vxMNPw8PBMr3v37q2dO3fK399fI0aMUOvWreXl5aULFy7ojz/+0IwZM9S6dWv16tUrz4sGAADAdXe9NuvNzGbzLdsz3peWlnaPZVofAyAAwPoYAIHCpLAMgMjxlbkBAwZkG9oAAABgPTkOc/Pnz8/HMgAAAJAbrM0KAABgwwhzAAAANuyeFk29cuWKZs2apd9++03nz59XcnJyln0MBoPCwsLu5WMAAABwC7kOc9HR0WrZsqXCwsLk7u5uGXGRkpKixMRESVKFChXk4OCQZ8UCAAAgs1zfZn3vvfcUFham//73v7p06ZIkaeTIkUpISNDu3bsVEBCgypUr68iRI3lWLAAAADLLdZhbu3atOnbsqKeffjrLlCVNmzbVunXrdPr0aU2YMOGeiwQAAED2ch3mIiMj5e/vb3ltZ2dnub0qSZ6ennr44Ye1dOnSe6sQAAAAt5TrMOfh4aHU1FTLa09PT509ezbTPu7u7rpw4ULuqwMAAMBt5TrM+fn56fTp05bX/v7+2rRpk/79919JUmJiolatWiUfH597LhIAAADZy3WYCwwM1ObNm3Xt2jVJ0tChQ3Xx4kU1aNBAvXr1Ut26dRUWFqaBAwfmVa0AAAC4Sa7D3IsvvqjZs2dbwtyTTz6pjz/+WAkJCVq+fLmioqI0atQovfnmm3lWLAAAADIzmM1mc14eMD09XTExMSpbtmyWUa62LGMevbi4OLm7u1u7HAAokgZ/Zu0KgP+ZPSJ/j5/T7HFPK0Bkx87OTl5eXnl9WAAAAGTjnsNcZGSkFi9erP379ysuLk4eHh7y9/fXU089pfLly+dFjQAAALiFewpzX3zxhd58800lJyfrxru1Cxcu1DvvvKNp06Zp2LBh91wkAAAAspfrMLd48WK98sorKl26tN555x09+OCD8vLy0oULF7R9+3bNmDHDsr137955WTMAAAD+X64HQDRq1Ehnz57VgQMHVKFChSzbz549K39/f/n4+Gjv3r33XKi1MQACAKyPARAoTArLAIhcT01y9OhR9e7dO9sgJ0kVK1ZUr169dPTo0dx+BAAAAO4g12GuRIkScnV1ve0+bm5uKlGiRG4/AgAAAHeQ6zD36KOPatWqVUpLS8t2e2pqqlatWqXHHnss18UBAADg9nId5qZOnSpXV1cFBgZq165dmbYFBQUpMDBQxYsX1+TJk++5SAAAAGQvx6NZ/fz8srSlpKRo3759atWqlezt7VW6dGnFxMRYrtaVL19ejRo1UlhYWN5VDAAAAIschzmTyZRleS4HBwf5+Phkart5QITJZLqH8gAAAHA7OQ5zp0+fzscyAAAAkBu5fmYOAAAA1pcnYS4tLU1HjhxRUFCQjhw5cssRrncjODhYXbt2tUyB0rx5cy1dujTXx7t06ZK8vb1lMBj00EMP3XN9AAAAhcE9hbnY2FgNHjxYHh4eql+/vlq3bq369eurRIkSGjJkiP79999cHXfr1q1q1aqVduzYod69e+vFF19UVFSU+vTpo+nTp+fqmC+//LLi4uJy9V4AAIDCKtdhLjY2Vs2bN9d3332nYsWKqXPnzhowYIACAwNVrFgxzZkzRy1btlRsbOxdHTctLU2DBw+W0WjU9u3b9e2332r69Ok6ePCgqlevrrFjx+rMmTN3dczly5dr0aJFmjJlyl29DwAAoLDLdZj74IMPdOLECb355ps6c+aM1q9fr3nz5mndunU6c+aMRo8erdDQUH300Ud3ddwtW7YoLCxM/fr1U8OGDS3tHh4eGjt2rFJSUrRgwYIcHy86OlovvfSSnnnmGXXr1u2uagEAACjsch3mfv31V7Vr105TpkzJsqyXi4uLJk2apHbt2umXX365q+Nu27ZNkhQYGJhlW5cuXSRJv//+e46P9+KLL8rOzk4zZsy4qzoAAABsQY6nJrnZ+fPn1bdv39vu06JFC/355593ddzQ0FBJUrVq1bJsK1eunNzc3Cz73MnChQv1888/a8WKFfL09LyrZ+aSk5OVnJxseR0fHy/p+jJlqampkiSj0Sg7Ozulp6dnmk8voz0tLU1ms9nSbmdnJ6PReMv2jONmsLe//q/n5gElt2p3cHCQyWRSenq6pc1gMMje3v6W7beqnT7RJ/pEnwpjn6TM850C1lQQ36ecyHWY8/DwuOOza2fOnJGHh8ddHTcjcN3qfe7u7jkKZefPn9err76qvn375mp92EmTJmnChAlZ2jdu3CgXFxdJko+Pj/z9/XXo0CGFh4db9qlRo4Zq1qypPXv2KDo62tLesGFD+fr6avv27bpy5YqlvUWLFipbtqw2btyY6V9c+/btVaxYMa1duzZTDV27dlViYqK2bt1qabO3t1e3bt0UExOjoKAgS3vx4sXVoUMHRURE6MCBA5b2MmXKqGXLlgoNDVVISIilnT7RJ/pEnwpznyR3AYVFfn+f9u7dm6M6DOYbfyrdhd69e+vXX3/VmjVr1KlTpyzbN2/erK5du+rxxx/XkiVLcnzcwMBAbdq0SaGhoapatWqW7d7e3rp69eodA13Xrl21d+9eHTlyRKVLl5Z0feLjKlWqqEuXLlq/fv1t35/dlblKlSopJiZG7u7XTybW/oV6P/7qpk/0iT7Rp9v1acgMrsyh8Pjm1fz9PsXGxqpUqVKKi4uzZI/s5PrK3Pjx47VmzRp16dJFXbt2Vdu2beXl5aULFy5o27ZtWrdunVxcXDRu3Li7Om7GFblbhbX4+Hh5enre9hgLFizQunXrtGzZMkuQu1tOTk5ycnLK0u7g4CAHB4dMbXZ2drKzs8uy7/9uC+Ss/ebj5qbdaDTKaMz6KOSt2m9VO32iT3fbTp/ok5T/fQIKE2t9n7Lsl6O9slGnTh1t2LBBAwcO1Jo1a7RmzRoZDAbLL68HHnhA8+fPV506de7quBnPyoWGhqpx48aZtkVFRenq1asKCAi47TH2798vSerVq1e22zds2CCDwaAGDRpkugwKAABga3Id5iSpdevWCg0N1c6dO7V//37Fx8fL3d1d/v7+atWqlQyGu78c3rZtW02aNEkbN27UU089lWnbhg0bLPvcTosWLXT16tUs7VevXtWSJUtUsWJFdenSRT4+PnddHwAAQGGS62fmBg0apHr16mnkyJF5WlBaWppq1Kihc+fOadeuXZa55uLi4hQQEKDTp08rJCRElStXliRFRkYqLi5O5cuXv+Ngi7t5Zu5m8fHx8vDwuON9awBA/hn8mbUrAP5n9oj8PX5Os0eu55lbtGiRLl68mNu335K9vb3mzJkjk8mkNm3aaMiQIXr99dfVoEEDHT9+XBMnTrQEOUkaM2aMatWqddfz2QEAANwPcn2b9YEHHlBkZGRe1mLRvn177dixQ+PHj9eSJUuUmpqqevXqacqUKerTp0++fCYAAIAtyvVt1unTp2vy5Mk6cOCAvL2987quQofbrABgfdxmRWFSWG6z5vrKXI8ePbR161a1bNlSb731lpo2bSovL69sBz0w0AAAACB/5DrM+fn5WaYiefXVV2+5n8FgyPFyFAAAALg7uQ5zAwYMyNXUIwAAAMg7uQ5z8+fPz8MyAAAAkBu5npoEAAAA1ndPK0BI1xekX7t2rfbv36+4uDh5eHjI399fXbt2zXZtUwAAAOSdewpzK1eu1JAhQxQdHa0bZzgxGAwqW7asvv32W3Xv3v2eiwQAAED2ch3mNm/erB49esjOzk6DBg3Sgw8+KC8vL124cEHbt2/XwoUL9eSTT2rDhg3q0KFDXtYMAACA/5frSYNbt26tQ4cO6c8//1TdunWzbD906JBatWqlhg0b6o8//rjnQq2NSYMBwPqYNBiFSWGZNDjXAyD279+vPn36ZBvkJKl+/frq3bu39u3bl9uPAAAAwB3kOsy5uLioTJkyt92nbNmycnFxye1HAAAA4A5yHeY6deqk33777bb7/Pbbb+rcuXNuPwIAAAB3kOswN23aNF28eFEDBgxQREREpm0RERF65plnFBMTo2nTpt1zkQAAAMherkezPvPMM/L09NQPP/ygxYsXy8fHxzKaNTw8XOnp6apfv76efvrpTO8zGAzavHnzPRcOAACAewhz27Zts/w9LS1NJ0+e1MmTJzPtc/DgwSzvYz1XAACAvJPrMGcymfKyDgAAAOQCa7MCAADYsDwLc+Hh4dq+fXteHQ4AAAA5kGdhbt68eWrfvn1eHQ4AAAA5wG1WAAAAG0aYAwAAsGGEOQAAABuWZ2HOw8NDPj4+eXU4AAAA5ECehbkRI0bo1KlTeXU4AAAA5AC3WQEAAGxYjleAyJhDLiAgQM7Oznc1p1ybNm3uvjIAAADcUY7DXLt27WQwGHT06FFVr17d8jon0tPTc10gAAAAbi3HYW7cuHEyGAwqXbp0ptcAAACwnhyHuffee++2rwEAAFDwGAABAABgw3Id5q5cuaKTJ08qNTU1U/uSJUvUv39/Pf/889q3b989FwgAAIBby/Ft1pu99dZbWrhwoS5cuCAHBwdJ0ldffaWXX35ZZrNZkrR48WLt3btXNWvWzJtqAQAAkEmur8z9/vvv6tSpk1xcXCxtkydPlre3t7Zv366lS5fKbDbr448/zpNCUXR88cUXqly5spydndWsWTPt2bPnlvvOnj1bDz74oDw9PeXp6alOnTpl2d9gMGT75+b/NtesWaNmzZqpWLFi8vT01OOPP54f3QMAIE/lOsxFRkaqSpUqltdHjx5VRESEXn31VbVu3Vo9e/bUo48+elfz0QFLlizRqFGjNH78eO3bt08NGjRQly5ddPHixWz337Ztm/r27autW7cqKChIlSpVUmBgoM6dO2fZJzIyMtOfuXPnymAwqEePHpZ9li9frmeeeUbPPfecDh48qJ07d6pfv3753l8AAO5Vrm+zJicny9HR0fL6999/l8FgUGBgoKXNz89PK1euvLcKUaR88sknGjx4sJ577jlJ0tdff601a9Zo7ty5evvtt7Ps/8MPP2R6PWfOHC1fvlybN2/WgAEDJEnlypXLtM+vv/6q9u3by8/PT5KUlpam1157TR9//LGef/55y361a9fO074BAJAfcn1lrmLFijp06JDl9erVq1WyZEnVr1/f0vbvv//Kzc3t3ipEkZGSkqK9e/eqU6dOljaj0ahOnTopKCgoR8e4du2aUlNTVbJkyWy3X7hwQWvWrMkU2vbt26dz587JaDTK399f5cuX18MPP6zDhw/fW4cAACgAuQ5zDz/8sDZu3Kg33nhD//nPf7R+/Xp179490z7Hjx+Xj4/PPReJoiEmJkbp6eny8vLK1O7l5aWoqKgcHWP06NGqUKFCpkB4owULFqh48eJ68sknLW0nT56UdH3uxP/85z9avXq1PD091a5dO8XGxuayNwAAFIxch7kxY8bIx8dHn3zyiSZOnCgvLy+9//77lu0XL17Uzp07WZcVBWby5MlavHixfvnlFzk7O2e7z9y5c9W/f/9M200mkyTpnXfeUY8ePdS4cWPNmzdPBoNBy5YtK5DaAQDIrVw/M1euXDkdOXJEmzdvliS1adNG7u7ulu0xMTH6+OOP1aVLl3uvEkVC6dKlZWdnpwsXLmRqv3DhQpbn3m42bdo0TZ48Wb/99lumW/03+uOPPxQSEqIlS5Zkai9fvrykzM/IOTk5yc/PT+Hh4bnpCgAABSbXYU6SihUrpkceeSTbbbVr1+YBctwVR0dHNW7cWJs3b7ZMC2IymbR582a9/PLLt3zf1KlT9dFHH2nDhg1q0qTJLff77rvv1LhxYzVo0CBTe+PGjeXk5KSQkBC1bt1akpSamqrTp0/L19f33jsGAEA+uqcwB+S1UaNG6dlnn1WTJk0UEBCgzz77TAkJCZbRrQMGDJC3t7cmTZokSZoyZYrGjRunRYsWqXLlypZn69zc3DINvomPj9eyZcs0ffr0LJ/p7u6uF198UePHj1elSpXk6+trmYOuV69e+d1lAADuyT2FufT0dC1dulS//fabzp8/r+Tk5Cz7GAwGy61Y4E769Omj6OhojRs3TlFRUWrYsKHWr19vGRQRHh4uo/F/j3p+9dVXSklJUc+ePTMdZ/z48XrvvfcsrxcvXiyz2ay+fftm+7kff/yx7O3t9cwzzygxMVHNmjXTli1b5OnpmfedBAAgDxnMGWtv3aWEhAQFBgZq165dMpvNMhgMuvFQGa8NBoPS09PzrGBriY+Pl4eHh+Li4jI9GwgAKDiDP7N2BcD/zB6Rv8fPafbI9WjWDz/8UEFBQZowYYJiYmJkNpv13nvvKTIyUkuWLJGfn5969eqV7dU6AAAA5I1ch7mff/5ZzZs313/+859ME7R6eXmpV69e2rp1q3777TfWZgUAAMhHuQ5z4eHhat68+f8OZDRmugpXsWJFdevWTQsWLLi3CgEAAHBLuQ5zrq6umR5E9/DwUGRkZKZ9ypUrxzxdAAAA+SjXYc7X1zdTUKtbt662bNliuTpnNpu1efNmy4SsAAAAyHu5DnMdO3bU1q1blZaWJkl69tlnFR4erhYtWujNN99U69atdeDAAfXo0SPPigUAAEBmuZ5nbvDgwSpVqpSio6NVvnx5DRo0SPv379eXX36pAwcOSJJ69OiRaa4vAAAA5K1czzN3K9HR0Tp58qR8fX3vuJ6mLWGeOQCwPuaZQ2FSWOaZy/PlvMqUKaMyZcrk9WGLDE5UKEzy+0QFALh3uX5mDgAAANaX6ytzfn5+OdrPYDAoLCwstx8DAACA28h1mDOZTDIYDFna4+LidPnyZUlS+fLl5ejomOviAAAAcHu5DnOnT5++7bZRo0bpwoUL2rRpU24/AgAAAHeQL8/MVa5cWUuWLNGlS5f0zjvv5MdHAAAAQPk4AMLBwUGdO3fW0qVL8+sjAAAAirx8Hc167do1xcbG5udHAAAAFGn5Fub++OMP/fjjj6pRo0Z+fQQAAECRl+sBEB06dMi2PS0tTefOnbMMkBg3blxuPwIAAAB3kOswt23btmzbDQaDPD09FRgYqFGjRqlz5865/QgAAADcwT3NMwcAAADruue1WS9evKhz587JZDLJ29tb5cqVy4u6AAAAkAO5GgCRnJysqVOnqlq1aipfvryaNGmigIAAeXt7q3Tp0ho5cuRtJxUGAABA3rjrMBcREaGmTZtqzJgxCgsLU/ny5RUQEKCAgACVL19esbGxmjFjhpo0aaLffvvN8r7IyEjmnAMAAMhjdxXmUlNT1bVrVx0+fFh9+/bV0aNHdfbsWQUFBSkoKEhnz57V0aNH1b9/f8XGxurxxx/X6dOnFRYWptatW+vYsWP51Q8AAIAi6a6emfvmm2905MgRjR8/XuPHj892nxo1auj7779X9erVNX78ePXv31+nT59WTEyMGjdunCdFAwAA4Lq7ujK3dOlSVa1aNUdzx/3nP/9RtWrVFBQUpKSkJG3YsEHdunXLdaEAAADI6q7C3D///KPAwEAZDIY77mswGCz77t69W+3atcttjQAAALiFuwpzV69elYeHR473d3d3l729vapWrXrXhQEAAODO7irMlS1bVidOnMjx/mFhYSpbtuxdFwUAAICcuasw16JFC61bt05RUVF33DcqKkpr1qxR69atc10cAAAAbu+uwtyLL76oq1ev6oknnlBMTMwt9/v333/1xBNP6Nq1axo6dOg9FwkAAIDs3dXUJO3bt9fgwYM1e/Zs1apVS0OHDlWHDh1UqVIlSdcnFN68ebNmz56tmJgYDRkyhIEPAAAA+eiu12b98ssv5e7urk8//VSTJk3SpEmTMm03m80yGo164403smwDAABA3rrrMGdnZ6ePP/5YQ4YM0fz58xUUFGR5hq5cuXJq2bKlnn32WVWrVi3PiwUAAEBmdx3mMlSrVk0fffRRXtYCAACAu3RXAyAAAABQuBDmAAAAbBhhDgAAwIYR5gAAAGxYoQ1zwcHB6tq1q0qUKCFXV1c1b95cS5cuzdF7zWaz1q1bp5deekn169eXh4eHXFxc1KBBA02cOFFJSUn5XD0AAEDByPVo1vy0detWdenSRc7OznrqqadUvHhxLV++XH369FFERIRef/31274/OTlZXbt2lZOTk9q1a6cuXbooKSlJGzZs0DvvvKMVK1Zo27ZtcnFxKaAeAQAA5I9CF+bS0tI0ePBgGY1Gbd++XQ0bNpQkjRs3TgEBARo7dqx69uwpX1/fWx7Dzs5OH374oYYNGyZPT09Le2pqqnr06KFVq1bpiy++0Jtvvpnf3QEAAMhXhe4265YtWxQWFqZ+/fpZgpwkeXh4aOzYsUpJSdGCBQtuewwHBwe98847mYJcRvuYMWMkSb///nue1w4AAFDQCl2Y27ZtmyQpMDAwy7YuXbpIurcg5uDgIEmyty90FyUBAADuWqFLNKGhoZKU7XJg5cqVk5ubm2Wf3Jg7d66k7MPijZKTk5WcnGx5HR8fL+n6rdrU1FRJktFolJ2dndLT02UymSz7ZrSnpaXJbDZb2u3s7GQ0Gm/Zfv24DrnuG5DXMv5bz5DxIygtLS1Tu4ODg0wmk9LT0y1tBoNB9vb2t2y/1fcmb79Pd66dPtlWnySDgMKiIL5POVHowlxcXJyk67dVs+Pu7m7Z526tW7dO33zzjWrVqqXnn3/+tvtOmjRJEyZMyNK+ceNGy8AJHx8f+fv769ChQwoPD7fsU6NGDdWsWVN79uxRdHS0pb1hw4by9fXV9u3bdeXKFUt7ixYtVLZsWW3cuFFSt1z1DcgPa9euzfS6a9euSkxM1NatWy1t9vb26tatm2JiYhQUFGRpL168uDp06KCIiAgdOHDA0l6mTBm1bNlSoaGhCgkJsbTnx/fpxhNh+/btVaxYMfpk432S3AUUFvn9fdq7d2+O6jCYb/ypVAgEBgZq06ZNCg0NVdWqVbNs9/b21tWrV+860AUHB6tjx46yt7fXH3/8oTp16tx2/+yuzFWqVEkxMTFyd79+MsmPX6jDvuDKHAqPL4dzZY4+Fa4+DZnBlTkUHt+8mr/fp9jYWJUqVUpxcXGW7JGdQndlLuOK3K3CWnx8fJaBDXfy119/KTAwUEajURs2bLhjkJMkJycnOTk5ZWl3cHCwPHeXwc7OTnZ2dln2vdVzebdqv/m4gLXd6r/J7NqNRqOMxqyP4d6q/Vbfm/z+PtEn2+4TUJhY6/uU5fNytFcBynhWLrvn4qKionT16tVsn6e7lb/++kudO3eWyWTShg0b1LRp0zyrFQAAwNoKXZhr27atJP3/82OZbdiwIdM+d5IR5NLT07V+/Xo1a9Ys7woFAAAoBApdmOvYsaP8/Py0aNGiTA8PxsXFaeLEiXJ0dNSAAQMs7ZGRkTp27FiW27J79+5V586dlZaWpnXr1qlFixYF1QUAAIACU+iembO3t9ecOXPUpUsXtWnTJtNyXmfOnNG0adNUuXJly/5jxozRggULNG/ePA0cOFCSFBsbq86dO+vy5ct66KGHtGnTJm3atCnT55QoUUIjRowouI4BAADkg0IX5qTrQ9N37Nih8ePHa8mSJUpNTVW9evU0ZcoU9enT547vj4+P16VLlyRJ69ev1/r167Ps4+vrS5gDAAA2r1CGOUkKCAjQunXr7rjf/PnzNX/+/ExtlStXViGbcQUAACBfFLpn5gAAAJBzhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYU2zAUHB6tr164qUaKEXF1d1bx5cy1duvSujpGcnKz3339f1apVk7OzsypUqKAhQ4bo4sWL+VQ1AABAwbK3dgHZ2bp1q7p06SJnZ2c99dRTKl68uJYvX64+ffooIiJCr7/++h2PYTKZ9Nhjj2nDhg1q3ry5evToodDQUM2ZM0ebN2/Wrl27VKZMmQLoDQAAQP4pdFfm0tLSNHjwYBmNRm3fvl3ffvutpk+froMHD6p69eoaO3aszpw5c8fjLFiwQBs2bFDfvn31559/avLkyVq+fLm+/PJLnTx5Uv/5z38KoDcAAAD5q9CFuS1btigsLEz9+vVTw4YNLe0eHh4aO3asUlJStGDBgjseZ/bs2ZKkSZMmyWAwWNqHDh0qPz8//fDDD0pMTMzz+gEAAApSoQtz27ZtkyQFBgZm2dalSxdJ0u+//37bYyQlJWn37t2qUaOGfH19M20zGAzq3LmzEhIS9Ndff+VN0QAAAFZS6MJcaGioJKlatWpZtpUrV05ubm6WfW4lLCxMJpMp22PceOw7HQcAAKCwK3QDIOLi4iRdv62aHXd3d8s+93KMG/fLTnJyspKTk7McMzY2VqmpqZIko9EoOzs7paeny2QyWfbNaE9LS5PZbLa029nZyWg03rI9NTVVKUkOt+0bUJD+/Tc102t7++unjLS0tEztDg4OMplMSk9Pt7QZDAbZ29vfsv1W35u8/D7lpHb6ZFt9SkkyCCgsLl/O3+9TbGysJGX67mSn0IW5wmLSpEmaMGFClvYqVapYoRrAOv47xtoVAEDhVVDnyCtXrtzyApVUCMNcRrG3umoWHx8vT0/Pez7GjftlZ8yYMRo1apTltclkUmxsrEqVKpVpQAUKn/j4eFWqVEkRERGWq7AAgOs4R9oOs9msK1euqEKFCrfdr9CFuRufZ2vcuHGmbVFRUbp69aoCAgJueww/Pz8ZjcZbPhN3u+fyMjg5OcnJySlTW4kSJe5UPgoRd3d3TlQAcAucI23D7S48ZSh0AyDatm0rSdq4cWOWbRs2bMi0z60UK1ZMAQEBCgkJyTInndls1qZNm+Tq6qomTZrkUdUAAADWUejCXMeOHeXn56dFixbpwIEDlva4uDhNnDhRjo6OGjBggKU9MjJSx44dy3JLdciQIZKu3y698cHBb775RidPnlT//v1VrFix/O0MAABAPit0Yc7e3l5z5syRyWRSmzZtNGTIEL3++utq0KCBjh8/rokTJ6py5cqW/ceMGaNatWrpl19+yXScZ599Vl26dNGPP/6oli1b6u2331bPnj01bNgwValSRR9++GEB9wwFxcnJSePHj89ymxwAwDnyfmQw32m8q5Xs2bNH48eP159//qnU1FTVq1dPo0aNUp8+fTLtN3DgQC1YsEDz5s3TwIEDM21LTk7W5MmT9f333ysiIkIlS5bUI488og8//FBeXl4F2BsAAID8UWjDHAAAAO6s0N1mBQAAQM4R5gAAAGwYYQ4AAMCGEeYAAABsGGEOAADAhhHmgP+XMbDbbDaLQd4AAFtBmEORlxHcDAaD5X8z/g4AuO7GH7np6elWrAQ3Y545QNfX/T19+rTCwsJUsmRJtWnTRlWrVlXp0qVlNF7/zWM2mwl5AIq0pKQkOTs7W7sM3MTe2gUA1hQeHq5PP/1Un3/+eZZbq76+vnrkkUfUr18/tWjRgiAHoMg6deqUli5dqsOHDys6Olr169dX48aNVbNmTfn6+qpEiRKSJJPJZPkBjILDlTkUacOHD9fcuXP12GOP6emnn1bZsmW1e/du7du3T8HBwfrnn38kSd26ddO7776rgIAATlYAipQff/xRH3zwgY4dO6ZixYopMTHRsq1ixYrq1KmT+vbtq86dO1uxyqKNMIciKzk5WSVLllSfPn00d+7cLNuPHTumrVu3atGiRdq5c6dq1aqlBQsWqEmTJlaoFgAKXnJysmrUqCEnJye988476tatm86fP6/Dhw/r8OHD2rFjh/766y8lJSWpR48eeu+991S7dm1+9BYwbrOiyNq0aZPS09PVpk0bSZlHsRqNRtWsWVM1a9bUwIEDNW/ePI0aNUpDhgzR6tWrVaFCBWuWDgAF4scff1RkZKTmzZunfv36SZJKlSqlevXqyWQy6eTJk9q5c6cWLlyon376SWfOnNHy5ctVsWJFK1detBCbUWTZ2dnJbDYrOjpa0vXRWQaDwfJr0mQyyWQyqVixYho2bJhGjRqlAwcO6NChQ9YsGwAKzM6dO1W2bFk1bdpU0vXzYsYPX6PRqKpVq+rZZ5/VTz/9pPfff1/79u3TsGHDrFx10UOYQ5HVvHlzOTo66scff1RoaKjs7e0zDXLICHYZQ/B79+4tFxcX7dq1y1olA0CB8vX1VXR0tM6ePSsp61ROGcHOw8ND//nPf9StWzcFBwcrPDzcajUXRYQ5FElms1menp6aMWOGDhw4oHbt2unrr7/WqVOnLOEt42SV8frMmTNKS0vj9gGAIqNFixZKSUnR1KlTFR0dLTs7u0xBTrp+rsw4T7Zq1UpXr17ViRMnrFZzUUSYQ5GUcTLq2bOnxo4dq9jYWL3xxht6+eWX9c033ygoKMjyS9TR0VGnT5/W3LlzZWdnp169elmzdAAoECaTSR07dtQ777yjDRs2qFmzZpo1a5aOHz9umXcz41xqZ2cnSYqKilJqaioDxQoYo1kBSdu3b9fXX3+tTZs2KTY2VhUrVlT16tXl6OgoNzc3BQcHKyoqSiNHjtRHH31k7XIBoMCcP39eU6dO1axZs2Q0GtWiRQt16NBBjRo1Uq1atVS1alUlJSXp+++/1zvvvKMWLVro119/tXbZRQphDkVOdis5mM1mRUREaP/+/dq9e7f27t2ro0eP6uzZs3J1dZWPj4/eeecdPf7443JxcbFS5QBgPbt27dK3336r9evXKyoqSsWLF1fJkiXl4OAgJycnHTlyRE2aNNGsWbMUEBBg7XKLFMIciqRr167J3t5eZ86cUbFixTI9B5eYmKiLFy/KwcFBycnJio2NVePGja1YLQAUrOx+9JpMJsXExCg0NFR79+7Vrl27FBwcrH///Vd16tRRtWrVNGnSJHl5eVmp6qKLMIciJTk5Wb///rtmzZqlXbt2yc3NTUajUZUrV9bDDz+sp556St7e3tYuEwCsymQy6fz584qNjVVUVJRq166d6UdvcnKyJMnJyUlRUVFyc3OTm5ubJNaxtgbCHIqUzz77TBMmTFBycrIaNmxoWb7rwoULkq5PFtyrVy+99NJLat26teWExIkJQFFx4sQJffnll1qwYIESEhKUkpIig8GgevXqqU+fPurfv798fHwyvYcAZ12EORQZSUlJqlChgurUqaOlS5fK3d1drq6ukqTdu3dr2bJlltnOK1SooEmTJumZZ56xctUAUHBSUlLUrVs3bdmyRS1btlSrVq0UExOj4OBghYSEKCUlRZLUo0cPvf7662revLmVK4ZEmEMRsnDhQg0ZMkQLFy7Uk08+KSnrr8n09HTNnTtX06ZNU2hoqObMmaNBgwZZq2QAKFDfffedhg0bpvfee09jxozJtG3Pnj1as2aNli9frn/++Ufe3t6aNWuWHnvsMStViwzMM4ciIyQkREaj0bKuampqqiXImUwmpaeny87OToMHD9ZXX31lmVT40qVL1iwbAArM0qVL1bBhQz311FOSpLS0NMuEwAEBAZowYYJ2796tmTNnKj09XYMGDdL69eutWTJEmEMR0rJlS127dk1HjhyRJDk4OFi2GY1Gy6SXZrNZHTp00Lhx43T06FEdOHDAGuUCQIFKSkpSamqqEhMTVa5cOUnXnxfOODdmrFft6uqq4cOHa+bMmbp06ZIWLlwo6X8rQqDgEeZQZDRq1Ei1a9fWsGHD9MUXX+jff//Ndr+0tDRJkoeHh0wmk+Li4gqyTACwCmdnZzVq1EiHDx+2rEGdEeSk6z96jUajZT3WHj16qGvXrtq/f79Onz7NAAgrIsyhyPDy8tKECRNUvHhxvf322xo9erT+/PNPyy2EDBnzyx08eFBGo1EdOnSwUsUAULCeeeYZeXh4qE+fPvrmm28UFRWVZR+TySSDwaCUlBSVKVNGMTExKlu2rBWqRQYGQKDICQoK0ocffqh169ZJkpo3b65HH31UjRo1ssxkvmrVKn366afq2bOn5RYCABQFM2bM0NixY2U0GvXEE0/oqaeekr+/v0qUKKFixYpZ9tu1a5cGDx6sChUqaMOGDVasGIQ5FBlpaWmW2wTHjx/XmjVrtHLlSgUHB+vatWuys7OTs7OzEhISJElPP/203n33XVWrVs3KlQNAwQoKCtLEiRO1adMmpaWlqXHjxnrwwQdVpUoVOTs7S5KmT5+u8+fPa8mSJerSpYuVKy7aCHMo0q5du6Y///xT+/fvV0xMjOLj45Wenq6ePXuqTZs2lpMWABQFqampcnBwkNlsVmhoqLZu3arNmzcrODhYUVFRlpUfJMnT01Nffvml+vTpY8WKIRHmUATExsbqr7/+UlBQkDw9PeXk5CRvb281btxY5cuXt+yXnJwsJycnK1YKANZ37do1ubi4WF7HxcXpyJEjioiIUHJyss6dO6eqVauqZcuWLH9YSBDmcF/bsWOHRo8eraCgIEnXh9mbzWa5uLiodu3a6tSpk7p27aqAgAA5OjoqJSVFjo6OVq4aAApWUFCQfv75Z8XExMjR0VGenp5q1KiROnbsqFKlSlm7PNwBYQ73raSkJDVs2FDR0dGaMGGCypYtKzs7O0VFRem3337Tpk2bdO3aNVWrVk3Dhg3T8OHDZW9vb+2yAaDApKWlafLkyRo3bpwkqUSJEkpOTlZiYqIkydfXV4888oj69u2r5s2by2g0Wm7FovAgzOG+NWfOHL322muaNWuWnnvuuSzbT506pWXLlmnevHkKCQlRv379NHPmTHl6elqhWgAoeD/88IOee+45de3aVePGjZPJZFKxYsV09OhRLV68WCtWrJDJZJKvr69GjBih1157zdolIxuEOdy3+vTpo/3792vNmjWqVq1atr8mTSaT9u7dqw8++ECrV6/WZ599pldffdVKFQNAwWrZsqXs7e317bffqmbNmlm2x8fHa+7cufriiy90+vRpvfbaa/rggw8yTVEC62PSYNyX0tLSVLp0aZ0/f96yLE12twWMRqOaNm2q+fPnq3Hjxpo5c6auXbtW0OUCQIGLjY3VqVOn5Ovrq+rVq1tWdpD+t161u7u7RowYoSVLlqhZs2b65JNP9Pvvv1u5ctyMMIf7jtlslr29vVq1aqVr165p1KhRunTpkqT/naBulJaWppIlS6pNmzaKjo5WSEiINcoGgAJlNptVvnx5nTx5UkajUQaDwbIk143rVUvXl0NcuHChHBwcLLdeUXgQ5nDfyTgZtW3bVm3atNF3332nMWPG6PTp05lOUOnp6Zbgl5ycLIPBIJPJxCTBAIqEUqVKqUOHDgoKCtJ7772n2NhYSVl/9Gb83dvbWw0aNNCBAwcsa1ijcCDM4b7l7e2txYsX67HHHtO3334rPz8/9enTRytXrlRKSors7OwstxS2bt2qJUuWqE2bNnJzc7Ny5QBQMAYNGiRfX19NmTJF7777rk6cOJHlqlzG30NDQ5WamiovLy+mcCpkGACB+1Z6errs7Ox06tQpzZ8/X1999ZViYmIkScWLF1erVq1UrVo1HTx4UDt37lTlypU1f/58tWrVysqVA0DBCQ0N1ciRI7V27VpJUrdu3TRo0CC1bdtWjo6OSkxMlKenp1588UXNnz9fy5cv12OPPWblqnEjwhzuS2az2XK7NUNqaqqWLl2qH374QcHBwUpISJC9vb1SU1PVvXt3vfnmm2ratKmVKgaAgpeWliZ7e3uFhIRo0aJFWrRokcLCwiRJLi4u8vf3l8lk0j///KO4uDgNGjRIc+bMsXLVuBlhDvclk8mkiIgI+fr66vLlyzIajXJ3d7dsj42N1eHDh+Xp6Wn54+rqmm0IBICiIi4uTmvXrtW6desUEhKihIQExcbG6oEHHtBzzz2n3r178yhKIUSYw30lMTFRn3zyiTZs2KC///5bjo6OatCggRo2bKjGjRurXr168vPzk7Ozs7VLBYACd+MP1iNHjshkMsnV1VWJiYny9vZWiRIlLPvGxMTo8uXLqlKlipKSkuTq6mqlqnEnhDncN1JSUtSvXz/9/PPPql27tlxdXWUymXT58mWFh4fL3t5eTZs2Vf/+/fX0008z6SWAIsdsNmvfvn169dVXdejQISUkJKhEiRLy9fVV3bp11aJFC7Vo0UJ169ZlyS4bQpjDfeO7777T8OHDNXz4cE2YMEFubm6KiorSuXPndPz4cW3ZskUbN25URESE2rdvr0mTJikgIIBbqwCKjDVr1mjIkCFKSEjQo48+KqPRaHkm7u+//1Z6eroaNWqkAQMGaNCgQXJxcbF2ycgBwhzuG23btlVqaqp++OEHValSxTKaNUNsbKz279+vefPmadGiRWrWrJnWrl3LWqwAiozWrVvr8uXL+vzzz9WhQwdJ0uXLl3XlyhWFhoZq9erVWrFihU6fPq1HHnlEH3/8sWrUqGHlqnEnhDncF+Lj49WmTRt5eHhkWWrm5itvJpNJ06ZN09tvv61XXnlFM2bMKOhyAaDARUZGqkqVKnrzzTf1/vvvS1KWuxLXrl3TgQMHNGvWLC1evFiPP/64li1blumHMQofJg2GzTObzXJzc1OtWrX0999/6/Dhw5Z2k8lkOVllrDtoNBo1atQoNWjQQHv37lVcXJw1yweAAnHixAk5OjrKzs7ulo+WuLi4qGXLlvr22281YsQIrVixQqtXry7gSnG3CHOweQaDQUaj0XL74I033tDJkyct7ZIyLSAtXV93sFq1aoqMjJSTk5O1SgeAAlOrVi1VqFBBK1asUEREhGUJw5vXWTWZTHJzc9Pw4cPl4uKiHTt2WKli5BRhDveN4cOH66233tLGjRvVqFEjvfXWW/rzzz+VlJRkCXY3Dsk/evSoatSowTQlAIqE0qVL6+GHH9ahQ4c0duxYnT9/Xkaj0fKj9+Y1WZOSklS2bFldunTJWiUjh+ytXQCQFzKei3v99ddVrFgxTZ06VdOmTdOPP/6o5s2bq2nTpmrWrJlq1Kih3bt365NPPtGJEyc0depUa5cOAAVm4sSJSkxM1Lfffqvly5dr8ODB6tmzp1q2bJnlubhNmzYpPDxc3bp1s1K1yCkGQOC+cPMgh3Pnzmnu3Ln6+eefdfDgwSz7lyhRQm+88YbGjh1bkGUCgNWYTCYZjUadPXtWX375pT799FMlJyfL2dlZjRs3VosWLdSuXTslJSVp+/btmj17tmrXrq3g4GBrl447IMzhvmUymRQdHa2QkBDt3r1be/bskaurq6pXr64WLVqoffv21i4RAKwmNjZWc+fO1aJFi3TgwIEs2x977DG98cYbatWqVcEXh7tCmIPNO3jwoEJDQ3X8+HHLQIhq1aqpbNmyWUZsJScnM+ABQJGSceci48pcdk6cOKEtW7YoPDxcvr6+Klu2rDp37sykwTaCMAeblZaWpm+//Vbvv/++Ll68mGlbuXLl1KVLF/Xt21eBgYGZtt3uhAYA95v09HQtWLBA//zzj06cOKEHHnhATZo0UfXq1eXj46OSJUtmO48cq+PYDsIcbNaSJUs0ePBgVatWTS+88IIaNGig/fv368CBA9q7d68OHTokk8mkFi1aaNy4cercuTMhDkCRsm/fPr3//vtauXKlnJyclJycbNlWtmxZtWvXTr169VL37t3l6OgoiRBniwhzsFnNmjWTyWTSokWLVK1atUzbTp06pe3bt+unn37SmjVr5OHhodmzZ6tnz55WqhYACl737t21c+dOvfjiixo4cKDS09N16NAh/fPPPwoKCtKePXsUHx+v9u3ba8KECWrdujVhzgYR5mCTLl68qJo1a2rAgAH67LPPJF2/lXDjRMEZbStWrNArr7wik8mk5cuX8zAvgCIhIiJCvr6+evvttzVx4sQs28PDw7Vnzx4tW7ZMy5YtU9myZbV06VK1adPGCtXiXnDPCTYpLi5Obm5uOnfunKTroe3GyS8zlvKys7NTjx499Mknn+jixYvatm2bZTsA3M82b94sJycnNW7cWNL154VvXA3Hx8dHPXv21Lx58zR37lwlJyfrpZde0oULF6xZNnKBMAebVK1aNfn4+GjTpk3aunVrtmsNGo1Gy0mrV69e8vPz0549e5SWlsYtBAD3vVKlSslsNuvUqVOS/hfmbl6v2sXFRQMHDtTIkSN19OhRHTlyxJplIxcIc7BZU6dOldFo1EMPPaSPPvpIx44dU2pqqiRZTlYZr0NCQmRnZydnZ2fZ27PwCYD7X7NmzVSsWDHNnTtXR44ckb29faa7F9L1c2VaWpokqW3btnJ1dWWSYBtEmIPNCggI0Icffig3NzdNmDBBL730kmbOnKmdO3cqIiJC6enpcnR0VGpqqr7//nuFhYWpX79+1i4bAPKdyWRS2bJlNXPmTIWEhKh58+b68MMP9ffff1vuTtx8h+LUqVNKSEhQvXr1rFQ1cosBELB5R48e1YwZM7R69WqdP39e5cqVU506deTh4SFXV1edOXNG27dvV9euXbV69WprlwsABebKlSv64osv9NFHHykhIUFNmjRRp06d1LRpU9WuXVs1atSQJO3YsUMjRoxQZGSk5Vlk2A7CHGzWjc9+REVF6cCBA9q1a5d2796to0ePKjw8XJLk7e2t3r1766233pKXl5c1SwYAqwgJCdFXX32lX3/9VWfOnFHx4sXl5eUlJycneXh4aO/evSpZsqTGjRunoUOHWrtc3CXCHGxGRnhLTU2V0WhUdHS0UlJS5OPjY9knJSVFkZGRltsI4eHhatKkidzc3KxYOQAUnFutchMbG6uwsDD99ddfljnmzpw5Iz8/P3l7e2vChAkKCAjIdjUIFG6EOdiUY8eO6auvvtLq1avl5OQks9ms8uXLq0OHDnrqqadUtWpVa5cIAFYXExOjhIQEnT59Wj4+PqpSpYplW0pKilJSUuTm5qaLFy8qJSVFFStWtGK1uFeEOdiMrVu36rXXXtPhw4f1wAMPqHr16jp06FCm5zseeughDRs2TJ07d5aTkxPrsAIoUv79918tX75cn3zyic6ePav09HSlp6frgQceUM+ePdWvXz/VqlXL2mUijxHmYDPatm2rsLAwzZkzR+3atZOdnZ0cHBz0999/a9myZVq8eLFOnDghFxcXjR49Wu+++661SwaAAjVy5Eh99dVX8vb21oMPPihHR0ft3r1bYWFhunbtmiSpffv2Gj16tDp16mSZj5O5N20bYQ424ezZs6pSpYree+89jR07VgaDIdsT0PLlyzV16lQFBwfrrbfe0oQJE+Tk5GSlqgGg4Jw5c0bVqlXTk08+qUWLFkmS5c7EwYMHtW7dOq1YsUJ79uyRs7OzJk+erFdffdWaJSOPcP8JNmH//v0yGAwqUaKEDAaDUlJSLEHOZDIpPT1dktSjRw/997//VaNGjTRz5kz9888/1iwbAArM4sWL5ebmpiFDhlhCXMaEwA0aNNDbb7+tP/74Qz/++KOqVq2qESNG6IsvvrBmycgjhDnYhLp160qSDh06JElydHS0bDMajZbRV2azWTVq1NBXX32lxMRE7dixo+CLBQAruHDhgkwmk0qWLCnp+prVGSvemEwmmUwmOTg4qE+fPlqwYIHKly+vr7/+WlevXrVm2cgDhDnYBG9vb/Xo0UOzZ8/W2LFjFRERke1+Gb9CjUajSpQooTNnzhRkmQBgNW3atFF8fLx27dolSXJwcLBsMxqNma7W+fv7a/jw4Tp9+rT27NljlXqRdwhzsAmOjo5688039cADD2jq1KkaMWKENmzYoOTk5Ez7ZZy89u/fr/j4eLVt29Ya5QJAgWvVqpUaNmyo4cOHa8KECTp16pRufiz+xtfFixdXYmJipjsdsE0MgIBNOXnypCZMmKAlS5YoJSVFDRs21OOPP64WLVrI1dVVjo6OCgsL04gRI+Th4aFjx45Zu2QAKDCrVq3S4MGDFR0drccee0x9+/ZV8+bNVbp0aTk7O1ueNY6Ojtarr76qDRs2KDY21spV414R5mATMgY5ODg46OzZs5ZRWTt37lR8fLyMRqM8PDx06dIlSdcf9p00aZIeeughK1cOAAUrLCxMH3zwgX755RdduXJF9erVU7t27VS7dm25urrKxcVFCxcu1Jo1a/T6669r4sSJ1i4Z94gwB5uVmppqWYv13LlzunLlimJjY/XII4+oS5cu8vb2tnaJAFBg0tLSZGdnZ1nK8Pfff9emTZsUFBSkiIgIpaSkZNp/3Lhxevnll1W6dGkrVYy8QphDoZaWlqaQkBBt3LhRrq6ucnBwUKlSpdSwYcNMa7ImJycznxyAIi8lJSXTM3DXrl3T33//rbCwMCUkJCgyMlKurq566KGHVKdOHStWirxEmEOhderUKU2fPl1ffvllpvZixYqpWrVqateunbp27aqWLVvKzc0t069SACgqTp48qbVr1+rIkSNydHSUi4uL6tSpo/bt23OHooggzKHQ6tWrl1asWKHBgwerWbNmsre3V1xcnLZv366NGzfq8uXLKl++vJ577jm9+uqrKlu2rLVLBoACtWTJEr311luKiIiQwWCQi4uLEhISJEnlypXTww8/rD59+qhdu3ZydHRUampqpilLcH8gzKFQOn36tKpWraqRI0dq6tSpWa62nT9/XitXrtTcuXP1119/qX379vrmm29UtWpVK1UMAAUrIiJCjRo1kqenp2bMmCFXV1cVL15cZ86c0c8//6zly5crMTFRnp6eGjp0qEaPHi0PDw9rl418wDxzKJTWrFkjR0dHtW/f3rJ8140qVKigF198UQsXLtRLL72krVu3atKkSZZlvQDgfjd79mwZjUZ9+umnevjhh9WmTRv5+/vr8ccf13//+19dvnxZc+fOla+vr6ZMmaLnn39e0dHR1i4b+YAwh0LJwcFBSUlJcnFxsbzOTvXq1TV9+nS98MILmjdvnsLCwgqyTACwmj///FPly5eXv7+/pP+tgHPjVE4DBw7Uzz//rP79++vnn3/W999/b82SkU8IcyiUmjdvrmLFimncuHE6ceKEDAaDzGZzlitvqampcnZ2VmBgoIxGo4KCgqxUMQAUnNTUVPn5+SksLMyyFmvGOqw3rlctSZUrV9ZXX32lBg0a6L///a/i4+OtUjPyD2EOhVK1atX09NNPa8eOHRo9erQOHDggg8FgOUGZTCaZzWbLFbuEhAQZDAZGbgEoEhwcHNSmTRslJCRoyJAhlnWob/7RazabZTKZ5OrqqmbNmuns2bOKioqyVtnIJ4Q5FErFihXTrFmz9Morr+iXX35Ro0aN1LVrVy1evFhXrlyR0Wi0DIq4cOGC5s2bp5IlS6pTp05WrhwACsZDDz2kjh07auHChXrrrbe0d+/eTD96JclgMMhoNOry5ctKTk6Wg4ODqlevbsWqkR8YzYpCyWQyyWg06uLFi/rxxx/1+eef69SpU5IkFxcXtWzZUk2aNFFYWJh27NihuLg4ffDBBxo5cqSVKweAgnPlyhWNHDlSc+fOlSS1bdtWL7zwgh566CG5ubnp2rVr8vT01Ndff63Ro0erf//+WebuhO0jzKHQMZvN2U78++uvv2r+/PnasWOHLl26JCcnJyUmJqpx48Z688039cgjj1gGTADA/S4tLU329vY6e/asli1bpgULFujQoUOSrj8/FxAQIE9PTx07dkxhYWFq1aqV5s+frwceeMDKlSOvEeZQKJ07d07e3t5KTExUamqq3N3dLduuXr2qffv2SZK8vb3l5uYmLy8va5UKAIVCcnKy1q9fr1WrVungwYOKj4/XlStX5OjoqP79++ull15SxYoVrV0m8gFhDoWG2WzW6tWr9d133+nvv//W1atXVb9+fdWvX1/+/v6qV6+eqlatKldXV2uXCgBWdfHiRUVHR6tUqVKKi4tT6dKlVapUKcv2S5cu6fz585bw5u7uzlKH9zHCHAqNcePGadq0aXJxcVGlSpWUmpqqlJQURUREyGw2q0GDBurZs6eeeeYZlStXztrlAkCBi4yM1DvvvKNNmzbp3LlzKl68uKpUqaKaNWsqICBALVu2VP369S2PnNzqsRXcXwhzKBROnz6tOnXqqF27dpo+fbpq1qypmJgYRUREKCwsTNu3b9eGDRsUGhqqBg0aaOLEiXr44YctAyUA4H4XFRWlJ554Qrt377YMcDAajTpz5owOHTqkxMRE1a5dW71799YLL7ygChUqWLtkFBDCHAqFDz74QJ999pmWLl2qjh07Wh7szRAfH68jR45o6dKlmjFjhry8vLRu3To1bNjQekUDQAEaP368ZsyYoQkTJui1116TJF2+fFlXr17VqVOntHHjRv388886duyYmjVrpo8//litWrXi6lwRQJhDofDss89q06ZN2r9/v7y8vCwnn+xOQkuWLNHQoUNVq1YtVnwAUGTUqVNHfn5+mjt3rsqUKZPl/JicnKyQkBAtWLBAn376qWrUqKHff/9dZcuWtWLVKAjcn0KhUL9+fUVFRemPP/6QdH2iS5PJlOlElfG7o0+fPnryySd14sQJhYSEWKVeAChIFy5ckNlsVnJyssqUKSNJWX7oOjk5qX79+poyZYpmzJihkJAQffLJJ9YoFwWMMIdCISAgQK6urnr33Xf1119/SZLlWbiM5WgyAp50fbmvxMRE1hgEcN8zm80qU6aM6tSpo927d2vPnj2W9pvXq5auzzH3yiuvqG7dugoODtbVq1cLumQUMMIcrM5sNuvBBx/Up59+qtDQUAUEBGjo0KHavHmzrly5YlmORroe8BITE/X333/L2dlZTZs2tXL1AJC/Ms6BgYGBunLlit544w0dOXIky3rV6enpljsY8fHxqlSpki5evCg3Nzdrlo8CYH/nXYD8lXGroG/fvkpLS9P48eM1e/ZsrVixQi1atFCzZs0UEBCgRo0aKTQ0VHPnztXy5cv1yiuvWLlyACg4gwcPVmxsrMaOHat69eppwIAB6tevn9q0aSNnZ2dJ/3scJTg4WAcPHlTXrl2tWTIKCAMgYHU3P8SbkJCgOXPmaMmSJQoODrbcRjAYDLK3t1dqaqoGDhyoDz74QN7e3tYqGwAKTMZ58vLly5o7d66mTJmi6Oho2dnZqXHjxmrVqpXat28vDw8PBQcHa9asWbpy5Yq2bNmievXqWbt85DPCHAqtmJgYHT9+XLt27dIff/yh9PR0Va9eXbVq1dLzzz9v7fIAoMDc/KM3KSlJCxYs0H//+99sR/XXrl1bY8aMUf/+/QuyTFgJYQ5WdfHiRf399986fvy4rl69qoCAANWsWVOlS5e2PAuSITk5WU5OTpbXzJ0EAFJ4eLh+++03HT58WOXKlVPZsmXVunVrVa1a1dqloYAQ5mA169at04cffpjlV2XJkiXVsWNH9enTR927d5eDg4NlGys+AChq1q9fr8OHD+vAgQPy8vJSkyZNVLVqVVWqVEmlSpXKdI5E0USYg1VERESoXbt2SkhI0MCBA9W+fXudPHlS+/fv18GDB3Xo0CElJyerdu3aGjt2rHr27ClHR0euxgEoMi5fvqxJkybp448/lp2dXaZpSEqWLKlWrVrpiSee0KOPPqqSJUtatnGeLHoYzQqr+Oabb3Tp0iXNmTNHTz75ZKZtZ8+e1Z9//qmVK1dq0aJFevrpp3X27Fm99dZbnKAAFBmzZ8/WrFmz9Pjjj+vVV19VhQoVtH//foWEhCg4OFhBQUFatWqV/P399e677+rxxx+XlHUyYdz/uDIHq2jevLmKFSumZcuWqXTp0kpLS8s0Z1KGrVu36vXXX9c///yjL7/8UoMGDbJSxQBQsCpXrqy6detqwYIFKlWqVKZt58+f1/79+7Vy5UrNnTtX6enp+vbbb/XCCy9YqVpYEw8focBdvXpVxYsXV1RUlFxcXCRdnww4I8hlrPggSe3bt9d3330nFxcX/frrr5btAHA/O3bsmP799181aNDAEuRMJpPl3FihQgV169ZNM2fO1K+//qoqVapo9OjRrFddRBHmUODc3NzUuHFjhYSEaPHixZKUZVBDxmuTySR/f3+1adNGx44d05kzZ7iFAOC+ZzabVaJECYWFhUmS0tLSJGVe5tBsNsvR0VFdu3bVJ598okuXLlnWt0bRQpiDVWSsG/jCCy/o1Vdf1b59+5SUlCTpf897pKWlyWg0Kj4+Xo6OjkpKSpKvr681ywaAAlGrVi15e3tr7dq1Wrdunezt7bP86L1xveoHH3xQlStXVnBwsDXKhZUR5mAV3t7eev/991W5cmXNmjVLQ4cO1bRp07Rt2zadOXNGSUlJsre/Pj5n1apV2rZtmx5++GErVw0A+S/jUZLPP/9c7u7u6tatm0aOHKk9e/Zk+dGbmpoqSQoJCVFycrIqVKhgnaJhVQyAQIG6ech8bGysJk2apKVLlyoiIkJlypRR3bp1VaFCBbm4uCgxMVFLly5VlSpVtGLFCtWoUcOK1QNAwUlPT9fChQs1ZswYRUVFqXbt2goMDFTLli1Vu3Zt1axZU0ajUefOndObb76pZcuWaffu3WrUqJG1S0cBI8yhwGUEurNnz6pChQoyGo06fPiwVq9erW3btuno0aOKiIiQJHl6eqphw4b6/PPPVadOHStXDgAFLzo6WrNmzdLSpUt1/Phxubi4yNvbW25ubipZsqSOHTum6OhoPffcc/ryyy+tXS6sgDCHApOWlqadO3dq7ty5On78uAwGg1xcXNS0aVP17t1b/v7+MpvNioiIUGJiok6ePKmaNWuqUqVKsre3ZyJMAEVKxsh+Ozs7JSYmKjQ0VMHBwdq5c6d2796tY8eOqUyZMqpUqZJeeOEFPf3003J1dbV22bACwhwKzLRp0/TBBx/oypUrqlq1quzs7BQSEmLZXrt2bQ0bNkw9e/ZU2bJlrVgpABROJpNJSUlJcnR0VFxcnKKiorhrAcIcCsapU6dUr149NWrUSAsWLJCjo6O8vLwUFRWlVatWadmyZdq2bZuk63PLTZkyRU2aNLFu0QBQgBITExUeHi4fHx8VK1Ys0zaTySSDwWC5O3HznQrWrS7aCHMoEOPGjdM333yjRYsWqWPHjpKynoz+/vtvTZs2TUuXLpWvr69++OEHNW7c2FolA0CBmjx5spYvX64nn3xSzZs3V40aNeTl5ZVpZZyM/8vOOHdGR0fL09PTMvofRRNhDgWiR48eOnDggLZu3SofHx+lpaVZnoPLeCYkw4wZMzRy5Eg9++yzmjdvnhWrBoCCU7FiRZ0/f152dnby8PBQy5YtFRgYqGbNmsnPzy/Lkl4JCQl677339O+//2rOnDlcmSvCiPIoEP7+/vrll1909epVSbL8irxxPdaMK3Wvvfaa/vjjD23ZskUnT56Un5+f1eoGgIJw/PhxxcXFqUWLFurXr582bdqkoKAgrV69Wj4+PmrXrp06deokf39/eXt7q0SJEjp8+LBmz56tdu3aEeSKOMIcCkT79u0lSf3799f06dPVunVrOTo6ZtkvPT1ddnZ2qlGjhtatW2cJfwBwPzt+/LiSkpIUGBio4cOH65FHHlFISIiCgoK0ZcsWLV++XD/88INq166tDh066KGHHtLmzZsVHx+vwYMHW7t8WBm3WVEg0tPTNXr0aH3yySeqWbOmhg8frp49e8rLyyvLvpcuXdKIESO0bt06Xbx40QrVAkDB+umnn9S7d28tXrxYvXv3trSnpqbqzJkzOnjwoP744w/LXJwODg4ym81ycnJSbGysFStHYUCYQ4H65ptv9PHHH+vkyZOqUKGCnnjiCT388MOqVKmS7OzsVKJECc2cOVOfffaZhg0bpunTp1u7ZADId2azWceOHZOzs7OqVKmS7byaCQkJOn78uEJCQjRv3jxt2rRJL7/8sj7//HMrVY3CgjCHAmU2m3XixAnNnj1bixcv1tmzZyVJZcuWlYODgyIjI2UymdS3b19NmTJFFStWtHLFAGBd2QW7V199VbNmzdLevXvl7+9vpcpQWBDmYDUJCQnas2ePVq5cqfPnz+vixYtyd3dX79691aNHDzk7O1u7RAAoNDLmkjt9+rQee+wxXbp0SeHh4dYuC4UAAyBgNa6urmrfvr3at2+v1NRUOTg4WLskACi0Mkasnjt3TqmpqRo2bJiVK0JhwZU5AABsiNls1tmzZ1WyZEnWYoUkwhwAAIBNY5ZBAAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABv2fwYQZJkoNozxAAAAAElFTkSuQmCC" }, - "execution_count": 6, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -300,8 +300,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:56.253735Z", - "start_time": "2023-11-10T17:46:54.395467Z" + "end_time": "2023-11-13T17:24:06.927046Z", + "start_time": "2023-11-13T17:24:06.032255Z" } }, "id": "cbb3c2d9a11b43ac" @@ -320,7 +320,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 29, "outputs": [ { "data": { @@ -354,8 +354,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:56.331972Z", - "start_time": "2023-11-10T17:46:56.263233Z" + "end_time": "2023-11-13T17:24:07.016037Z", + "start_time": "2023-11-13T17:24:06.935911Z" } }, "id": "16f5ec62b6f90570" @@ -378,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 30, "outputs": [], "source": [ "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", @@ -395,8 +395,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:56.335562Z", - "start_time": "2023-11-10T17:46:56.332754Z" + "end_time": "2023-11-13T17:24:07.019984Z", + "start_time": "2023-11-13T17:24:07.014632Z" } }, "id": "f79d7c9a5cca338" @@ -413,14 +413,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 31, "outputs": [ { "data": { "text/plain": "
", "image/png": 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}, - "execution_count": 9, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -429,7 +429,7 @@ "# Initialize register\n", "var = ['B','E','A','J','M']\n", "qr = [QuantumRegister(1, name=v) for v in var]\n", - "qc = QuantumCircuit(*qr, name='Pachinko')\n", + "qc = QuantumCircuit(*qr, name='State preparation')\n", "# Specify control qubits\n", "# P(B)\n", "qc.ry(theta_B, qr[0])\n", @@ -466,8 +466,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:56.625028Z", - "start_time": "2023-11-10T17:46:56.342879Z" + "end_time": "2023-11-13T17:24:07.365475Z", + "start_time": "2023-11-13T17:24:07.025977Z" } }, "id": "85bb861283b06275" @@ -484,13 +484,13 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 32, "outputs": [ { "data": { - "text/plain": "0.8721300000000001" + "text/plain": "0.00527" }, - "execution_count": 10, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -506,8 +506,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:56.863167Z", - "start_time": "2023-11-10T17:46:56.634452Z" + "end_time": "2023-11-13T17:24:08.724581Z", + "start_time": "2023-11-13T17:24:07.365152Z" } }, "id": "5468619791203a79" @@ -524,14 +524,14 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 33, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" + "image/png": 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" }, - "execution_count": 11, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -543,25 +543,11 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-10T17:46:57.022898Z", - "start_time": "2023-11-10T17:46:56.862475Z" + "end_time": "2023-11-13T17:24:08.888941Z", + "start_time": "2023-11-13T17:24:08.724739Z" } }, "id": "2d4094095ef21b20" - }, - { - "cell_type": "code", - "execution_count": 11, - "outputs": [], - "source": [], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-10T17:46:57.028129Z", - "start_time": "2023-11-10T17:46:57.024008Z" - } - }, - "id": "626e57867222c038" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/__init__.py b/qiskit_machine_learning/algorithms/__init__.py index 1c356f1ca..d6566bbef 100644 --- a/qiskit_machine_learning/algorithms/__init__.py +++ b/qiskit_machine_learning/algorithms/__init__.py @@ -56,6 +56,16 @@ NeuralNetworkClassifier VQC +Classifiers ++++++++++++ +Algorithms for inference. + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + QBayesian + Regressors ++++++++++ Algorithms for data regression. @@ -78,6 +88,7 @@ OneHotObjectiveFunction, ) from .classifiers import QSVC, PegasosQSVC, VQC, NeuralNetworkClassifier +from .inference import QBayesian from .regressors import QSVR, VQR, NeuralNetworkRegressor __all__ = [ @@ -94,4 +105,5 @@ "QSVR", "NeuralNetworkRegressor", "VQR", + "QBayesian", ] diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 6739f0465..e6b9f81e0 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -129,8 +129,8 @@ def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: return relative_counts def power_grover( - self, grover_op: GroverOperator, evidence: dict, k: int - ) -> (GroverOperator, set): + self, grover_op: GroverOperator, evidence: dict, k: int, th: float + ) -> (GroverOperator, set): """ Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns a tuple containing the updated quantum circuit and a set of the measured @@ -139,6 +139,7 @@ def power_grover( grover_op (GroverOperator): The Grover operator to be applied. evidence (dict): A dictionary representing the evidence. k (int): The power to which the Grover operator is raised. + th (float): The threshold for accepted evidence Returns: tuple: A tuple containing the updated quantum circuit and a set of the measured evidence qubits. @@ -170,13 +171,15 @@ def power_grover( e_count[evidence_qubits[i]] += e_sample_val else: e_count[evidence_qubits[i]] += -e_sample_val - # Assign to every qubit if it is more often measured 1 -> 1 o/w 0 + # Assign to every evidence qubit if it is measured with high probability (th) 1 o/w 0 e_meas = { - (e_count_key, int(e_count_val >= 0)) for e_count_key, e_count_val in e_count.items() + (e_count_key, int(e_count_val >= th)) for e_count_key, e_count_val in e_count.items() } return qc, e_meas - def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 10) -> dict: + def rejection_sampling( + self, evidence: dict, shots: int = 100000, limit: int = 10, th: float = 0.8 + ) -> dict: """ Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude @@ -185,6 +188,7 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 evidence (dict): A dictionary representing the evidence. shots (int): The number of times the circuit will be executed. limit (int): The maximum number of iterations for the Grover operator. + th (float): The threshold for accepted evidence Returns: dict: A dictionary containing the samples as a dictionary """ @@ -210,7 +214,7 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 # Increment power k += 1 # Create circuit with 2^k times grover operator - qc, meas_e = self.power_grover(grover_op=grover_op, evidence=evidence, k=k) + qc, meas_e = self.power_grover(grover_op=grover_op, evidence=evidence, k=k, th=th) # Test number of if len(e.intersection(meas_e)) > best_inter: best_qc = qc @@ -218,18 +222,20 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 self.converged = True # Create a classical register with the size of the evidence + best_qc_meas = QuantumCircuit(*self.circ.qregs) + best_qc_meas.append(best_qc, self.circ.qregs) measurement_qcr = ClassicalRegister(self.circ.num_qubits - len(evidence)) - best_qc.add_register(measurement_qcr) + best_qc_meas.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them query_qubits = [ (label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if label not in evidence ] - query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1]) + query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1], reverse=True) # Measure query variables and return their count - best_qc.measure([q[2] for q in query_qubits_sorted], measurement_qcr) + best_qc_meas.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit - counts = self.run_circuit(best_qc, shots=shots) + counts = self.run_circuit(best_qc_meas, shots=shots) # Build default string with evidence query_string = '' var_idx_sorted = [ @@ -251,8 +257,9 @@ def rejection_sampling(self, evidence: dict, shots: int = 100000, limit: int = 1 return self.samples def inference( - self, query: dict, evidence: dict = None, shots: int = 100000, limit: int = 10 - ) -> float: + self, query: dict, evidence: dict = None, shots: int = 100000, limit: int = 10, + th: float = 0.8 + ) -> float: """ Performs inference on the query variables given the evidence. It uses rejection sampling if evidence is provided and calculates the probability of the query. @@ -263,13 +270,14 @@ def inference( executed. If you want to indicate no evidence insert an empty list. shots (int): The number of times the circuit will be executed. limit (int): The maximum number of 2^k times the Grover operator is integrated + th (float): The threshold for accepted evidence Returns: float: The probability of the query given the evidence. Raises: ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: - self.rejection_sampling(evidence, shots, limit) + self.rejection_sampling(evidence, shots, limit, th) else: if not self.samples: raise ValueError("Provide evidence or indicate no evidence with empty list") diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 0b222f6fe..1f9ba27e3 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -14,7 +14,7 @@ import unittest from test import QiskitMachineLearningTestCase from qiskit_algorithms.utils import algorithm_globals -from qiskit_machine_learning.algorithms.inference.qbayesian import QBayesian +from qiskit_machine_learning.algorithms import QBayesian from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister @@ -77,7 +77,7 @@ def test_rejection_sampling(self): ] for e, res in zip(test_cases, true_res): samples = self.qbayesian.rejection_sampling(evidence=e) - self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.12) + self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.08) for sample_key, sample_val in samples.items()])) def test_inference(self): @@ -101,12 +101,14 @@ def test_inference(self): # 4. Query marginalized inference res.append(self.qbayesian.inference(query=test_q_4, evidence=test_e_4)) # Correct inference - self.assertTrue(np.all(np.isclose(true_res, res, atol=0.6))) + self.assertTrue(np.all(np.isclose(true_res, res, atol=0.04))) # No change in samples self.assertTrue(samples[0] == samples[1]) def test_parameter(self): """Tests parameter of QBayesian methods""" + # Test set threshold + self.qbayesian.rejection_sampling(evidence={'B': 1}, th=0.9) # Test set limit self.qbayesian.rejection_sampling(evidence={'B': 1}, limit=1) # Test set shots @@ -139,7 +141,7 @@ def test_trivial_circuit(self): qb = QBayesian(circuit=qc) # Inference self.assertTrue( - np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.05)) + np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.02)) ) From 59f5311bd546eaf885eeec882f2d09ff23f8cc41 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 13 Nov 2023 23:20:01 +0100 Subject: [PATCH 20/48] Prepared release --- .../13_quantum_bayesian_inference.ipynb | 77 +++++----- .../algorithms/inference/qbayesian.py | 83 ++++++----- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 44 ++++++ test/algorithms/inference/test_qbayesian.py | 138 ++++++++++-------- 4 files changed, 207 insertions(+), 135 deletions(-) create mode 100644 releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 861423339..980bebc99 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -51,17 +51,20 @@ "source": [ "import matplotlib.pyplot as plt\n", "import networkx as nx\n", + "\n", "# Create a directed graph\n", "G = nx.DiGraph()\n", "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", - "G.add_node('A', pos=(0, 0))\n", - "G.add_node('B', pos=(1, 0))\n", + "G.add_node(\"A\", pos=(0, 0))\n", + "G.add_node(\"B\", pos=(1, 0))\n", "# Add a directed edge from A to B\n", - "G.add_edge('A', 'B')\n", + "G.add_edge(\"A\", \"B\")\n", "# Get the positions of each node\n", - "pos = nx.get_node_attributes(G, 'pos')\n", + "pos = nx.get_node_attributes(G, \"pos\")\n", "# Draw the graph\n", - "nx.draw(G, pos, with_labels=True, node_size=2000, node_color='skyblue', arrowstyle='->', arrowsize=20)\n", + "nx.draw(\n", + " G, pos, with_labels=True, node_size=2000, node_color=\"skyblue\", arrowstyle=\"->\", arrowsize=20\n", + ")\n", "# Show the plot\n", "plt.show()" ] @@ -86,6 +89,7 @@ "source": [ "# Include libraries\n", "import numpy as np\n", + "\n", "# Define rotation angles\n", "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", @@ -129,12 +133,13 @@ "source": [ "from qiskit import QuantumRegister\n", "from qiskit import QuantumCircuit\n", - "# Define quantum registers \n", - "qrA = QuantumRegister(1, name='A')\n", - "qrB = QuantumRegister(1, name='B')\n", + "\n", + "# Define quantum registers\n", + "qrA = QuantumRegister(1, name=\"A\")\n", + "qrB = QuantumRegister(1, name=\"B\")\n", "# Define a 2-qubit quantum circuit\n", "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", - "#Apply the R_Y_theta rotation gate on the first qubit\n", + "# Apply the R_Y_theta rotation gate on the first qubit\n", "qc.ry(theta_A, 0)\n", "# Apply the controlled-R_Y_theta rotation gate\n", "qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB)\n", @@ -144,7 +149,7 @@ "qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB)\n", "# Apply another X gate on the first qubit\n", "qc.x(0)\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" ], "metadata": { "collapsed": false, @@ -183,8 +188,8 @@ "source": [ "from qiskit_machine_learning.algorithms import QBayesian\n", "\n", - "query = {'B': 0}\n", - "evidence = {'A': 1}\n", + "query = {\"B\": 0}\n", + "evidence = {\"A\": 1}\n", "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", @@ -227,24 +232,24 @@ ], "source": [ "# Choose the number of nodes\n", - "n = 10 \n", + "n = 10\n", "# Generate probabilities\n", - "prob = np.random.random_sample(2*(n-1)+1)\n", + "prob = np.random.random_sample(2 * (n - 1) + 1)\n", "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", - "# Define quantum registers \n", + "# Define quantum registers\n", "qr = [QuantumRegister(1, name=i) for i in range(n)]\n", "# Generate circuit\n", "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", - "#Apply the R_Y_theta rotation gate on the first qubit\n", + "# Apply the R_Y_theta rotation gate on the first qubit\n", "qc.ry(theta[0], 0)\n", "# Apply the controlled-R_Y_theta rotations\n", "for i in range(1, n, 1):\n", - " qc.cry(theta_B_A, control_qubit=i-1, target_qubit=i)\n", - " qc.x(i-1)\n", - " qc.cry(theta_B_nA, control_qubit=i-1, target_qubit=i)\n", - " qc.x(i-1)\n", + " qc.cry(theta_B_A, control_qubit=i - 1, target_qubit=i)\n", + " qc.x(i - 1)\n", + " qc.cry(theta_B_nA, control_qubit=i - 1, target_qubit=i)\n", + " qc.x(i - 1)\n", "# Draw circuit\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)" + "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" ], "metadata": { "collapsed": false, @@ -289,7 +294,7 @@ "source": [ "from qiskit.visualization import plot_histogram\n", "\n", - "evidence = {str(i): 0 for i in range(n-1)}\n", + "evidence = {str(i): 0 for i in range(n - 1)}\n", "# Initialize quantum bayesian\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", @@ -339,17 +344,21 @@ "# Add nodes\n", "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", "# Add edges\n", - "G.add_edges_from([(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"),\n", - " (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")])\n", + "G.add_edges_from(\n", + " [(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"), (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")]\n", + ")\n", "# Manually set positions\n", - "pos = {\"Burglary\": (0, 1), \"Earthquake\": (1, 1),\n", - " \"Alarm\": (0.5, 0.5),\n", - " \"JohnCalls\": (0, 0), \"MaryCalls\": (1, 0)}\n", + "pos = {\n", + " \"Burglary\": (0, 1),\n", + " \"Earthquake\": (1, 1),\n", + " \"Alarm\": (0.5, 0.5),\n", + " \"JohnCalls\": (0, 0),\n", + " \"MaryCalls\": (1, 0),\n", + "}\n", "# Draw the network\n", "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", - "plt.show()\n", - " " + "plt.show()" ], "metadata": { "collapsed": false, @@ -427,9 +436,9 @@ ], "source": [ "# Initialize register\n", - "var = ['B','E','A','J','M']\n", + "var = [\"B\", \"E\", \"A\", \"J\", \"M\"]\n", "qr = [QuantumRegister(1, name=v) for v in var]\n", - "qc = QuantumCircuit(*qr, name='State preparation')\n", + "qc = QuantumCircuit(*qr, name=\"State preparation\")\n", "# Specify control qubits\n", "# P(B)\n", "qc.ry(theta_B, qr[0])\n", @@ -461,7 +470,7 @@ "qc.cry(theta_M_nA, qr[2], qr[4])\n", "qc.x(qr[2])\n", "# Draw circuit\n", - "qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1)\n" + "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" ], "metadata": { "collapsed": false, @@ -496,8 +505,8 @@ } ], "source": [ - "query = {'B': 1}\n", - "evidence = {'J':1}\n", + "query = {\"B\": 1}\n", + "evidence = {\"J\": 1}\n", "# Initialize quantum bayesian inference framework\n", "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index e6b9f81e0..372f01752 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -9,14 +9,13 @@ # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. +"""Quantum Bayesian Inference""" from qiskit import QuantumCircuit, transpile, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator from qiskit_aer import AerSimulator -"""Quantum Bayesian Inference""" - class QBayesian: r""" @@ -25,8 +24,6 @@ class QBayesian: **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. - - Usage: ------ To use the `QBayesian` class, instantiate it with a quantum circuit that represents the @@ -73,7 +70,7 @@ def __init__(self, circuit: QuantumCircuit): self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} # Label of register mapped to its qubit index bottom up in significance self.label2qidx = { - qrg.name: self.circ.num_qubits-idx-1 for idx, qrg in enumerate(self.circ.qregs) + qrg.name: self.circ.num_qubits - idx - 1 for idx, qrg in enumerate(self.circ.qregs) } # Samples from rejection sampling self.samples = {} @@ -85,21 +82,21 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: Constructs a Grover operator based on the provided evidence. The evidence is used to determine the "good states" that the Grover operator will amplify. Args: - evidence (dict): A dictionary representing the evidence with keys as variable labels and - values as states. + evidence (dict): A dictionary representing the evidence with keys as variable labels + and values as states. Returns: GroverOperator: The constructed Grover operator. """ # Evidence to reversed qubit index sorted by index num_qubits = self.circ.num_qubits e2idx = sorted( - [(self.label2qidx[e_key], e_val) - for e_key, e_val in evidence.items()], key=lambda x: x[0] + [(self.label2qidx[e_key], e_val) for e_key, e_val in evidence.items()], + key=lambda x: x[0], ) # Binary format of good states num_evd = len(e2idx) bin_str = [ - format(i, f'0{(num_qubits - num_evd)}b') for i in range(2 ** (num_qubits - num_evd)) + format(i, f"0{(num_qubits - num_evd)}b") for i in range(2 ** (num_qubits - num_evd)) ] # Get good states good_states = [] @@ -109,12 +106,12 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: good_states.append(b) # Get statevector by transform good states w.r.t its idx to 1 and o/w to 0 oracle = Statevector( - [int(format(i, f'0{num_qubits}b') in good_states) for i in range(2 ** num_qubits)] + [int(format(i, f"0{num_qubits}b") in good_states) for i in range(2**num_qubits)] ) return GroverOperator(oracle, state_preparation=self.circ) def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: - """ Run the quantum circuit for the number of shots on the Aer simulator backend. """ + """Run the quantum circuit for the number of shots on the Aer simulator backend.""" # Get the Aer simulator backend simulator_backend = AerSimulator() # Transpile the circuit for the given backend @@ -129,8 +126,8 @@ def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: return relative_counts def power_grover( - self, grover_op: GroverOperator, evidence: dict, k: int, th: float - ) -> (GroverOperator, set): + self, grover_op: GroverOperator, evidence: dict, k: int, threshold: float + ) -> (GroverOperator, set): """ Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns a tuple containing the updated quantum circuit and a set of the measured @@ -139,7 +136,7 @@ def power_grover( grover_op (GroverOperator): The Grover operator to be applied. evidence (dict): A dictionary representing the evidence. k (int): The power to which the Grover operator is raised. - th (float): The threshold for accepted evidence + threshold (float): The threshold for accepted evidence Returns: tuple: A tuple containing the updated quantum circuit and a set of the measured evidence qubits. @@ -150,7 +147,7 @@ def power_grover( # Apply grover operator 2^k times qc_grover = QuantumCircuit(*self.circ.qregs) qc_grover.append(grover_op, self.circ.qregs) - qc_grover = qc_grover.power(2 ** k) + qc_grover = qc_grover.power(2**k) qc.append(qc_grover, self.circ.qregs) # Add quantum circuit for measuring qc_measure = QuantumCircuit(*self.circ.qregs) @@ -160,9 +157,9 @@ def power_grover( qc_measure.add_register(measurement_ecr) # Map the evidence qubits to the classical bits and measure them evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] - qc_measure.measure([q for q in evidence_qubits], measurement_ecr) + qc_measure.measure(evidence_qubits, measurement_ecr) # Run the circuit with the Grover operator and measurements - e_samples = self.run_circuit(qc_measure, shots=1024*self.circ.num_qubits) + e_samples = self.run_circuit(qc_measure, shots=1024 * self.circ.num_qubits) e_count = {self.label2qubit[e]: 0 for e in evidence} for e_sample_key, e_sample_val in e_samples.items(): # Go through reverse binary that matches order of qubits @@ -173,13 +170,14 @@ def power_grover( e_count[evidence_qubits[i]] += -e_sample_val # Assign to every evidence qubit if it is measured with high probability (th) 1 o/w 0 e_meas = { - (e_count_key, int(e_count_val >= th)) for e_count_key, e_count_val in e_count.items() + (e_count_key, int(e_count_val >= threshold)) + for e_count_key, e_count_val in e_count.items() } return qc, e_meas def rejection_sampling( - self, evidence: dict, shots: int = 100000, limit: int = 10, th: float = 0.8 - ) -> dict: + self, evidence: dict, shots: int = 100000, limit: int = 10, threshold: float = 0.8 + ) -> dict: """ Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude @@ -188,7 +186,7 @@ def rejection_sampling( evidence (dict): A dictionary representing the evidence. shots (int): The number of times the circuit will be executed. limit (int): The maximum number of iterations for the Grover operator. - th (float): The threshold for accepted evidence + threshold (float): The threshold for accepted evidence Returns: dict: A dictionary containing the samples as a dictionary """ @@ -205,20 +203,22 @@ def rejection_sampling( # Get grover operator if evidence not empty grover_op = self.get_grover_op(evidence) # Amplitude amplification - e, meas_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} + true_e, meas_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} best_qc, best_inter = QuantumCircuit(), 0 self.converged = False k = -1 # If the measurement of the evidence qubits matches the evidence stop - while (e != meas_e) and (k < limit): + while (true_e != meas_e) and (k < limit): # Increment power k += 1 # Create circuit with 2^k times grover operator - qc, meas_e = self.power_grover(grover_op=grover_op, evidence=evidence, k=k, th=th) + qc, meas_e = self.power_grover( + grover_op=grover_op, evidence=evidence, k=k, threshold=threshold + ) # Test number of - if len(e.intersection(meas_e)) > best_inter: + if len(true_e.intersection(meas_e)) > best_inter: best_qc = qc - if e == meas_e: + if true_e == meas_e: self.converged = True # Create a classical register with the size of the evidence @@ -228,8 +228,9 @@ def rejection_sampling( best_qc_meas.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them query_qubits = [ - (label, self.label2qidx[label], qubit) for label, qubit in self.label2qubit.items() if - label not in evidence + (label, self.label2qidx[label], qubit) + for label, qubit in self.label2qubit.items() + if label not in evidence ] query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1], reverse=True) # Measure query variables and return their count @@ -237,29 +238,31 @@ def rejection_sampling( # Run circuit counts = self.run_circuit(best_qc_meas, shots=shots) # Build default string with evidence - query_string = '' - var_idx_sorted = [ - label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1]) - ] + query_string = "" + var_idx_sorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1])] for var in var_idx_sorted: if var in evidence: query_string += str(evidence[var]) else: - query_string += 'q' + query_string += "q" # Retrieve valid samples self.samples = {} # Replace placeholder q with query variables from samples for key, val in counts.items(): query = query_string for char in key: - query = query.replace('q', char, 1) + query = query.replace("q", char, 1) self.samples[query] = val return self.samples def inference( - self, query: dict, evidence: dict = None, shots: int = 100000, limit: int = 10, - th: float = 0.8 - ) -> float: + self, + query: dict, + evidence: dict = None, + shots: int = 100000, + limit: int = 10, + threshold: float = 0.8, + ) -> float: """ Performs inference on the query variables given the evidence. It uses rejection sampling if evidence is provided and calculates the probability of the query. @@ -270,14 +273,14 @@ def inference( executed. If you want to indicate no evidence insert an empty list. shots (int): The number of times the circuit will be executed. limit (int): The maximum number of 2^k times the Grover operator is integrated - th (float): The threshold for accepted evidence + threshold (float): The threshold for accepted evidence Returns: float: The probability of the query given the evidence. Raises: ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: - self.rejection_sampling(evidence, shots, limit, th) + self.rejection_sampling(evidence, shots, limit, threshold) else: if not self.samples: raise ValueError("Provide evidence or indicate no evidence with empty list") diff --git a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml new file mode 100644 index 000000000..60c5a7185 --- /dev/null +++ b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -0,0 +1,44 @@ +--- +prelude: > + The Qiskit Machine Learning library introduces the `QBayesian` class, + implementing the Quantum Bayesian Inference algorithm. This new feature + enhances the library's capabilities in quantum machine learning, + particularly in the area of probabilistic reasoning and inference + on quantum computers. + +features: + - | + Introduction of the `QBayesian` class in the Qiskit Machine Learning library. + This class implements Quantum Bayesian Inference, allowing users to perform + probabilistic reasoning with quantum circuits. The implementation is based on the + algorithm described in the paper "Quantum inference on Bayesian networks" + by Low, Yoder, and Chuang. + + - | + The `QBayesian` class supports various functionalities including: + - Initialization with a quantum circuit representing a Bayesian network. + - Rejection sampling for estimating probabilities given evidence, with + Grover's algorithm-based amplification. + - Approximate Bayesian inference using rejection sampling, + with Grover's algorithm-based amplification. + - | + The `13_quantum_bayesian_inference` notebook describes a tutorial for the + usage of the `QBayesian` class + +issues: + - | + Users should ensure that each register in the quantum circuit passed to + `QBayesian` is mapped to exactly one qubit. The class raises a `ValueError` + if this condition is not met. + +upgrade: + - | + Users looking to leverage advanced probabilistic inference techniques in + quantum computing can now use the `QBayesian` class. To use this feature, + ensure that the latest version of the Qiskit Machine Learning library is installed. + +other: + - | + The `QBayesian` class is a significant addition for researchers and practitioners + working in quantum machine learning, particularly in the domain of Bayesian inference. + It opens up new possibilities for complex probabilistic modeling on quantum computers. diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 1f9ba27e3..6057afe83 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -10,13 +10,16 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -import numpy as np +""" Test Quantum Bayesian Inference """ + import unittest from test import QiskitMachineLearningTestCase + +import numpy as np from qiskit_algorithms.utils import algorithm_globals -from qiskit_machine_learning.algorithms import QBayesian from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister +from qiskit_machine_learning.algorithms import QBayesian class TestQBayesianInference(QiskitMachineLearningTestCase): @@ -26,66 +29,80 @@ def setUp(self): super().setUp() algorithm_globals.random_seed = 10598 # Probabilities - theta_A = 2 * np.arcsin(np.sqrt(0.25)) - theta_B_nA = 2 * np.arcsin(np.sqrt(0.6)) - theta_B_A = 2 * np.arcsin(np.sqrt(0.7)) - theta_C_nBnA = 2 * np.arcsin(np.sqrt(0.1)) - theta_C_nBA = 2 * np.arcsin(np.sqrt(0.55)) - theta_C_BnA = 2 * np.arcsin(np.sqrt(0.7)) - theta_C_BA = 2 * np.arcsin(np.sqrt(0.9)) + theta_a = 2 * np.arcsin(np.sqrt(0.25)) + theta_b_na = 2 * np.arcsin(np.sqrt(0.6)) + theta_b_a = 2 * np.arcsin(np.sqrt(0.7)) + theta_c_nbna = 2 * np.arcsin(np.sqrt(0.1)) + theta_c_nba = 2 * np.arcsin(np.sqrt(0.55)) + theta_c_bna = 2 * np.arcsin(np.sqrt(0.7)) + theta_c_ba = 2 * np.arcsin(np.sqrt(0.9)) # Random variables - qrA = QuantumRegister(1, name='A') - qrB = QuantumRegister(1, name='B') - qrC = QuantumRegister(1, name='C') + qr_a = QuantumRegister(1, name="A") + qr_b = QuantumRegister(1, name="B") + qr_c = QuantumRegister(1, name="C") # Define a 3-qubit quantum circuit - qcA = QuantumCircuit(qrA, qrB, qrC, name="Bayes net") + qc = QuantumCircuit(qr_a, qr_b, qr_c, name="Bayes net") # P(A) - qcA.ry(theta_A, 0) + qc.ry(theta_a, 0) # P(B|-A) - qcA.x(0) - qcA.cry(theta_B_nA, qrA, qrB) - qcA.x(0) + qc.x(0) + qc.cry(theta_b_na, qr_a, qr_b) + qc.x(0) # P(B|A) - qcA.cry(theta_B_A, qrA, qrB) + qc.cry(theta_b_a, qr_a, qr_b) # P(C|-B,-A) - qcA.x(0) - qcA.x(1) - qcA.mcry(theta_C_nBnA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(0) - qcA.x(1) + qc.x(0) + qc.x(1) + qc.mcry(theta_c_nbna, [qr_a[0], qr_b[0]], qr_c[0]) + qc.x(0) + qc.x(1) # P(C|-B,A) - qcA.x(1) - qcA.mcry(theta_C_nBA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(1) + qc.x(1) + qc.mcry(theta_c_nba, [qr_a[0], qr_b[0]], qr_c[0]) + qc.x(1) # P(C|B,-A) - qcA.x(0) - qcA.mcry(theta_C_BnA, [qrA[0], qrB[0]], qrC[0]) - qcA.x(0) + qc.x(0) + qc.mcry(theta_c_bna, [qr_a[0], qr_b[0]], qr_c[0]) + qc.x(0) # P(C|B,A) - qcA.mcry(theta_C_BA, [qrA[0], qrB[0]], qrC[0]) + qc.mcry(theta_c_ba, [qr_a[0], qr_b[0]], qr_c[0]) # Quantum Bayesian inference - self.qbayesian = QBayesian(qcA) + self.qbayesian = QBayesian(qc) def test_rejection_sampling(self): """Test rejection sampling with different amount of evidence""" - test_cases = [{'A': 0, 'B': 0}, {'A': 0}, {}] + test_cases = [{"A": 0, "B": 0}, {"A": 0}, {}] true_res = [ - {'000': 0.9, '100': 0.1}, - {'000': 0.36, '100': 0.04, '010': 0.18, '110': 0.42}, - {'000': 0.27, '001': 0.03375, '010': 0.135, '011': 0.0175, - '100': 0.03, '101': 0.04125, '110': 0.315, '111': 0.1575} + {"000": 0.9, "100": 0.1}, + {"000": 0.36, "100": 0.04, "010": 0.18, "110": 0.42}, + { + "000": 0.27, + "001": 0.03375, + "010": 0.135, + "011": 0.0175, + "100": 0.03, + "101": 0.04125, + "110": 0.315, + "111": 0.1575, + }, ] - for e, res in zip(test_cases, true_res): - samples = self.qbayesian.rejection_sampling(evidence=e) - self.assertTrue(np.all([np.isclose(res[sample_key], sample_val, atol=0.08) - for sample_key, sample_val in samples.items()])) + for evd, res in zip(test_cases, true_res): + samples = self.qbayesian.rejection_sampling(evidence=evd) + self.assertTrue( + np.all( + [ + np.isclose(res[sample_key], sample_val, atol=0.08) + for sample_key, sample_val in samples.items() + ] + ) + ) def test_inference(self): """Test inference with different amount of evidence""" - test_q_1, test_e_1 = ({'B': 1}, {'A': 1, 'C': 1}) - test_q_2 = {'B': 0} + test_q_1, test_e_1 = ({"B": 1}, {"A": 1, "C": 1}) + test_q_2 = {"B": 0} test_q_3 = {} - test_q_4, test_e_4 = ({'B': 1}, {'A': 0}) + test_q_4, test_e_4 = ({"B": 1}, {"A": 0}) true_res = [0.79, 0.21, 1, 0.6] res = [] samples = [] @@ -108,40 +125,39 @@ def test_inference(self): def test_parameter(self): """Tests parameter of QBayesian methods""" # Test set threshold - self.qbayesian.rejection_sampling(evidence={'B': 1}, th=0.9) + self.qbayesian.rejection_sampling(evidence={"B": 1}, threshold=0.9) # Test set limit - self.qbayesian.rejection_sampling(evidence={'B': 1}, limit=1) + self.qbayesian.rejection_sampling(evidence={"B": 1}, limit=1) # Test set shots - self.qbayesian.inference(query={'B': 1}, evidence={'A': 0, 'C': 0}, shots=10) + self.qbayesian.inference(query={"B": 1}, evidence={"A": 0, "C": 0}, shots=10) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="No ValueError in constructor with invalid input."): - QBayesian(QuantumCircuit(QuantumRegister(2, 'qr'))) + QBayesian(QuantumCircuit(QuantumRegister(2, "qr"))) # Test invalid inference without evidence or generated samples with self.assertRaises(ValueError, msg="No ValueError in inference with invalid input."): - QBayesian(QuantumCircuit(QuantumRegister(1, 'qr'))).inference({'A': 0}) + QBayesian(QuantumCircuit(QuantumRegister(1, "qr"))).inference({"A": 0}) def test_trivial_circuit(self): """Tests trivial quantum circuit""" # Define rotation angles - theta_A = 2 * np.arcsin(np.sqrt(0.2)) - theta_B_A = 2 * np.arcsin(np.sqrt(0.9)) - theta_B_nA = 2 * np.arcsin(np.sqrt(0.3)) + theta_a = 2 * np.arcsin(np.sqrt(0.2)) + theta_b_a = 2 * np.arcsin(np.sqrt(0.9)) + theta_b_na = 2 * np.arcsin(np.sqrt(0.3)) # Define quantum registers - qrA = QuantumRegister(1, name='A') - qrB = QuantumRegister(1, name='B') + qr_a = QuantumRegister(1, name="A") + qr_b = QuantumRegister(1, name="B") # Define a 2-qubit quantum circuit - qc = QuantumCircuit(qrA, qrB, name="Bayes net small") - qc.ry(theta_A, 0) - qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB) + qc = QuantumCircuit(qr_a, qr_b, name="Bayes net small") + qc.ry(theta_a, 0) + qc.cry(theta_b_a, control_qubit=qr_a, target_qubit=qr_b) qc.x(0) - qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB) + qc.cry(theta_b_na, control_qubit=qr_a, target_qubit=qr_b) qc.x(0) - qc.draw('mpl', style='bw', plot_barriers=False, justify='none', fold=-1) - # Initialize quantum bayesian - qb = QBayesian(circuit=qc) + qc.draw("mpl", style="bw", plot_barriers=False, justify="none", fold=-1) # Inference self.assertTrue( - np.all(np.isclose(0.1, qb.inference(query={'B': 0}, evidence={'A': 1}), atol=0.02)) + np.all(np.isclose(0.1, QBayesian(circuit=qc) + .inference(query={"B": 0}, evidence={"A": 1}), atol=0.02)) ) From 2765b1bb893ecf9fb58d6a4fed146a9f3002e5ae Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 13 Nov 2023 23:38:53 +0100 Subject: [PATCH 21/48] Made trivial test less strict --- test/algorithms/inference/test_qbayesian.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 6057afe83..53190a392 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -157,7 +157,7 @@ def test_trivial_circuit(self): # Inference self.assertTrue( np.all(np.isclose(0.1, QBayesian(circuit=qc) - .inference(query={"B": 0}, evidence={"A": 1}), atol=0.02)) + .inference(query={"B": 0}, evidence={"A": 1}), atol=0.04)) ) From cea8b11dac7e41bc0378400a507108c900c88501 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Wed, 15 Nov 2023 14:25:39 +0100 Subject: [PATCH 22/48] Fixed format errors --- docs/tutorials/07_pegasos_qsvc.ipynb | 14 +++++++++-- .../algorithms/inference/qbayesian.py | 23 +++++++++++-------- test/algorithms/inference/test_qbayesian.py | 11 ++++++--- 3 files changed, 33 insertions(+), 15 deletions(-) diff --git a/docs/tutorials/07_pegasos_qsvc.ipynb b/docs/tutorials/07_pegasos_qsvc.ipynb index 3ca8db2d9..c829d43bf 100644 --- a/docs/tutorials/07_pegasos_qsvc.ipynb +++ b/docs/tutorials/07_pegasos_qsvc.ipynb @@ -26,7 +26,12 @@ "cell_type": "code", "execution_count": 1, "id": "impressed-laser", - "metadata": {}, + "metadata": { + "ExecuteTime": { + "end_time": "2023-11-06T20:46:25.509287Z", + "start_time": "2023-11-06T20:46:23.936897Z" + } + }, "outputs": [], "source": [ "from sklearn.datasets import make_blobs\n", @@ -47,7 +52,12 @@ "cell_type": "code", "execution_count": 2, "id": "adolescent-composer", - "metadata": {}, + "metadata": { + "ExecuteTime": { + "end_time": "2023-11-06T20:46:25.560893Z", + "start_time": "2023-11-06T20:46:25.511175Z" + } + }, "outputs": [], "source": [ "import numpy as np\n", diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 372f01752..76ed3437b 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -15,6 +15,7 @@ from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator from qiskit_aer import AerSimulator +from typing import Tuple class QBayesian: @@ -24,6 +25,7 @@ class QBayesian: **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. + Usage: ------ To use the `QBayesian` class, instantiate it with a quantum circuit that represents the @@ -36,7 +38,7 @@ class QBayesian: # Define a quantum circuit qc = QuantumCircuit(...) - # Initialize the QBayesian class with the circuit + # Initialize the framework qb = QBayesian(qc) # Perform inference @@ -64,7 +66,7 @@ def __init__(self, circuit: QuantumCircuit): for qrg in circuit.qregs: if qrg.size > 1: raise ValueError("Every register needs to be mapped to exactly one unique qubit") - # Initialize QBayesian + # Initialize parameter self.circ = circuit # Label of register mapped to its qubit self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} @@ -73,9 +75,9 @@ def __init__(self, circuit: QuantumCircuit): qrg.name: self.circ.num_qubits - idx - 1 for idx, qrg in enumerate(self.circ.qregs) } # Samples from rejection sampling - self.samples = {} + self.samples = dict() # True if rejection sampling converged after limit - self.converged = bool + self.converged = bool() def get_grover_op(self, evidence: dict) -> GroverOperator: """ @@ -104,7 +106,7 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: for e_idx, e_val in e2idx: b = b[:e_idx] + str(e_val) + b[e_idx:] good_states.append(b) - # Get statevector by transform good states w.r.t its idx to 1 and o/w to 0 + # Get statevector by transform good states w.r.t its index to 1 and o/w to 0 oracle = Statevector( [int(format(i, f"0{num_qubits}b") in good_states) for i in range(2**num_qubits)] ) @@ -127,7 +129,7 @@ def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: def power_grover( self, grover_op: GroverOperator, evidence: dict, k: int, threshold: float - ) -> (GroverOperator, set): + ) -> Tuple[GroverOperator, set]: """ Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns a tuple containing the updated quantum circuit and a set of the measured @@ -144,7 +146,7 @@ def power_grover( # Create circuit qc = QuantumCircuit(*self.circ.qregs) qc.append(self.circ, self.circ.qregs) - # Apply grover operator 2^k times + # Apply Grover operator 2^k times qc_grover = QuantumCircuit(*self.circ.qregs) qc_grover.append(grover_op, self.circ.qregs) qc_grover = qc_grover.power(2**k) @@ -200,10 +202,11 @@ def rejection_sampling( # Run circuit self.samples = self.run_circuit(qc, shots=shots) return self.samples - # Get grover operator if evidence not empty + # Get Grover operator if evidence not empty grover_op = self.get_grover_op(evidence) # Amplitude amplification - true_e, meas_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()}, {} + true_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} + meas_e = dict() best_qc, best_inter = QuantumCircuit(), 0 self.converged = False k = -1 @@ -211,7 +214,7 @@ def rejection_sampling( while (true_e != meas_e) and (k < limit): # Increment power k += 1 - # Create circuit with 2^k times grover operator + # Create circuit with 2^k times Grover operator qc, meas_e = self.power_grover( grover_op=grover_op, evidence=evidence, k=k, threshold=threshold ) diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 53190a392..e32aa2a21 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -123,7 +123,7 @@ def test_inference(self): self.assertTrue(samples[0] == samples[1]) def test_parameter(self): - """Tests parameter of QBayesian methods""" + """Tests parameter of methods""" # Test set threshold self.qbayesian.rejection_sampling(evidence={"B": 1}, threshold=0.9) # Test set limit @@ -156,8 +156,13 @@ def test_trivial_circuit(self): qc.draw("mpl", style="bw", plot_barriers=False, justify="none", fold=-1) # Inference self.assertTrue( - np.all(np.isclose(0.1, QBayesian(circuit=qc) - .inference(query={"B": 0}, evidence={"A": 1}), atol=0.04)) + np.all( + np.isclose( + 0.1, + QBayesian(circuit=qc).inference(query={"B": 0}, evidence={"A": 1}), + atol=0.04, + ) + ) ) From f624c468ed8a2caaa47744908fa2d276a9abfc4f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Wed, 15 Nov 2023 14:25:56 +0100 Subject: [PATCH 23/48] Updated pylint --- .pylintdict | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.pylintdict b/.pylintdict index c86aed7c8..ea9ce51a2 100644 --- a/.pylintdict +++ b/.pylintdict @@ -88,8 +88,10 @@ gaussian gellmann getter gpu +guang guzik hamiltonian +hao hashable havlíček hilbert @@ -188,6 +190,8 @@ qae qarg qargs qasm +qb +qbayesian qc qgan qgans @@ -276,6 +280,7 @@ vz wikipedia williams wrt +yoder zoufal zsh θ From d4eeba85c46f2cc3daa57eae68358284a6c92dc4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Wed, 15 Nov 2023 15:50:25 +0100 Subject: [PATCH 24/48] Included types for dict and set for format --- qiskit_machine_learning/algorithms/inference/qbayesian.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 76ed3437b..46453c086 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -15,7 +15,7 @@ from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator from qiskit_aer import AerSimulator -from typing import Tuple +from typing import Tuple, Dict, Set class QBayesian: @@ -75,7 +75,7 @@ def __init__(self, circuit: QuantumCircuit): qrg.name: self.circ.num_qubits - idx - 1 for idx, qrg in enumerate(self.circ.qregs) } # Samples from rejection sampling - self.samples = dict() + self.samples: Dict[str, int] = {} # True if rejection sampling converged after limit self.converged = bool() @@ -206,7 +206,7 @@ def rejection_sampling( grover_op = self.get_grover_op(evidence) # Amplitude amplification true_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} - meas_e = dict() + meas_e: Set[Tuple[str, int]] = set() best_qc, best_inter = QuantumCircuit(), 0 self.converged = False k = -1 From b39e00a569587f28e677411d229f992d2e4467b4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Wed, 15 Nov 2023 16:24:01 +0100 Subject: [PATCH 25/48] Fixed spelling error from an unchanged file --- .pylintdict | 6 ++++++ qiskit_machine_learning/algorithms/inference/qbayesian.py | 2 +- 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/.pylintdict b/.pylintdict index ea9ce51a2..cb8dbc3b2 100644 --- a/.pylintdict +++ b/.pylintdict @@ -18,6 +18,7 @@ autosummary backend backends backpropagation +bayesian benchmarking bergholm bitstring @@ -88,6 +89,7 @@ gaussian gellmann getter gpu +grover guang guzik hamiltonian @@ -106,6 +108,7 @@ inlier inplace instantiation instantiations +isaac isometry iten iterable @@ -124,6 +127,7 @@ langle lukin macos makefile +mary matmul matplotlib maxiter @@ -235,6 +239,7 @@ stdlib stdlib stdout str +subclasses subcircuits submodules subobjects @@ -248,6 +253,7 @@ temme tensored terra th +theodore toctree todo traceback diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 46453c086..c192e0bf3 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -11,11 +11,11 @@ # that they have been altered from the originals. """Quantum Bayesian Inference""" +from typing import Tuple, Dict, Set from qiskit import QuantumCircuit, transpile, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator from qiskit_aer import AerSimulator -from typing import Tuple, Dict, Set class QBayesian: From 56d8fcf5e3f92083a24461e46c300ab072f1d359 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 24 Nov 2023 11:56:27 +0100 Subject: [PATCH 26/48] Fixed tutorial and code based on feedback --- .pylintdict | 10 + .../13_quantum_bayesian_inference.ipynb | 656 ++++++++++++------ .../algorithms/inference/qbayesian.py | 241 ++++--- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 29 +- test/algorithms/inference/test_qbayesian.py | 9 +- 5 files changed, 576 insertions(+), 369 deletions(-) diff --git a/.pylintdict b/.pylintdict index cb8dbc3b2..2fc620de4 100644 --- a/.pylintdict +++ b/.pylintdict @@ -1,3 +1,4 @@ +acyclic adam adjoint aer @@ -18,14 +19,17 @@ autosummary backend backends backpropagation +bayes bayesian benchmarking bergholm bitstring bitstrings bivariate +bloch bool boolean +borujeni cargs carlo cbit @@ -82,6 +86,7 @@ farrokh fidelities fidelityquantumkernel formatter +frac frontend func gambetta @@ -108,6 +113,7 @@ inlier inplace instantiation instantiations +interdependencies isaac isometry iten @@ -145,6 +151,7 @@ multioutput mxd mypy nat +nbsphinx ndarray nielsen nn @@ -196,6 +203,7 @@ qargs qasm qb qbayesian +qbi qc qgan qgans @@ -209,6 +217,7 @@ qubits rangle rbf readme +recalibration regressor regressors regs @@ -230,6 +239,7 @@ shalev shende shwartz sigmoid +sima sklearn softmax sparsearray diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 980bebc99..e9ed1f6dc 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -5,10 +5,15 @@ "source": [ "# Quantum Bayesian Inference with Qiskit\n", "\n", - "##### Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. Quantum Bayesian Inference provides a method to speed up the sampling process. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. This method efficiently utilizes the structure of Bayesian networks to produce quantum states that represent classical probability distributions.\n", + "## Overview\n", + "This notebook demonstrates a quantum Bayesian inference (QBI) implementations provided in `qiskit-machine-learning`, and how it can be integrated into basic quantum machine learning (QML) workflows.\n", "\n", - "##### This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", - "\n" + "The tutorial is structured as follows:\n", + "\n", + "1. [Introduction](#1.-Introduction)\n", + "2. [How to Instantiate QBI](#2.-How-to-Instantiate-QBIs)\n", + "3. [How to Run Rejection Sampling](#3.-How-to-Run-an-Rejection-Sampling)\n", + "4. [How to Run an Inference](#4.-How-to-Run-an-Inference)" ], "metadata": { "collapsed": false @@ -18,31 +23,110 @@ { "cell_type": "markdown", "source": [ - "# Step 1: Creating Rotations for Bayesian Network\n", + "\n", + "## 1. Introduction\n", "\n", - "In the first example we consider a simple Bayesian network that is only based on two nodes." + "### 1.1. Quantum vs. Classical Bayesian Inference\n", + "\n", + "Bayesian networks, or belief networks, are graphical models that illustrate probabilistic relationships between variables using nodes (representing variables) and edges (indicating conditional dependencies) in a directed acyclic graph. Each node is associated with conditional probability tables (CPTs) that detail the influence of parent nodes on their children. \n", + "\n", + "In these networks, Bayesian inference is key for updating probabilities. It employs Bayes' theorem to revise the likelihood of hypotheses based on new data, considering the network's variable interdependencies. For instance, in a network assessing diseases based on symptoms, observing new symptoms allows for recalculating disease probabilities. This recalibration combines the disease's prior probability with the observed symptom likelihood, leading to an updated, more precise disease probability. Thus, Bayesian inference is a dynamic process of adjusting our understanding of one variable in light of new information about others, facilitating informed, evidence-based decisions.\n", + "\n", + "Exact inference on Bayesian networks is \\#P-hard. That is why usually approximate inference is used to sample from the distribution on query variables given evidence variables. QBI efficiently utilizes the structure of Bayesian networks represented by a quantum circuit that represent the probability distributions. By employing a quantum version of rejection sampling and leveraging amplitude amplification, quantum computation achieves a significant speedup, making it possible to obtain samples much faster. \n", + "\n", + "This tutorial will guide you through the process of using the QBayesian class to perform such inference tasks. This inference algorithm implements the algorithm from the paper \"Quantum inference on Bayesian networks\" by Low, Guang Hao et al. This leads to a speedup per sample from $O(nmP(e)^{-1})$ to $O(n2^{m}P(e)^{-\\frac{1}{2}})$, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence.\n", + "\n", + "### 1.2. Implementation in `qiskit-machine-learning`\n", + "\n", + "The QBI in `qiskit-machine-learning` can be used for different quantum circuits representing Bayesian networks with. The implementation is based on the Sampler primitive from [qiskit primitives](https://qiskit.org/documentation/apidoc/primitives.html). The primitive is the entry point to run QBI on either a simulator or real quantum hardware. QBI takes in an optional instance of its corresponding primitive, which can be any subclass of `BaseSampler`.\n", + "\n", + "The `qiskit.primitives` module provides a reference implementation for the `Sampler` class to run statevector simulations. By default, if no instance is passed to a QBI class, an instance of the corresponding reference primitive of `Sampler` is created automatically by QBI.\n", + "For more information about primitives please refer to the [primitives documentation](https://qiskit.org/documentation/apidoc/primitives.html).\n", + "\n", + "The `QBayesian` class is used for QBI in `qiskit-machine-learning`. It is initialized with a quantum circuit that represents a Bayesian network. This enables the execution of quantum rejection sampling and inference.\n" + ], + "metadata": { + "collapsed": false + }, + "id": "3237c8b584b541bd" + }, + { + "cell_type": "markdown", + "source": [ + "***\n", + "\n", + "Let's now look into specific examples for the `QBayesian` implementations. But first, let's set the algorithmic seed to ensure that the results don't change between runs." + ], + "metadata": { + "collapsed": false + }, + "id": "bafaeda078302d7f" + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "## 2. How to Instantiate QBI" + ], + "metadata": { + "collapsed": false + }, + "id": "36c0c73ab1fe5686" + }, + { + "cell_type": "markdown", + "source": [ + "### 2.1. Create Rotations for the Bayesian Networks\n", + "In quantum computing, the rotation matrix around the y-axis, denoted as $R_y(\\theta)$, is used to rotate the state of a qubit around the y-axis of the Bloch sphere by an angle $\\theta$. This approach allows for precise control over the quantum state of a qubit, enabling the encoding of specific probabilities in quantum algorithms. When this rotation is applied to a qubit initially in the $|0\\rangle$ state, the resulting state $|\\psi\\rangle$ is:\n", + "$$ |\\psi\\rangle = R_y(\\theta)|0\\rangle = \\begin{pmatrix} \\cos\\left(\\frac{\\theta}{2}\\right) \\\\ \\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} $$\n", + "\n", + "where\n", + "\n", + "* $R_y(\\theta) = \\begin{pmatrix} \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\\\ \\sin\\left(\\frac{\\theta}{2}\\right) & \\cos\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}$\n", + "\n", + "\n", + "This state is a superposition of $|0\\rangle$ and $|1\\rangle$ with respective amplitudes $\\cos\\left(\\frac{\\theta}{2}\\right) $ and $\\sin\\left(\\frac{\\theta}{2}\\right) $. To set a specific probability $p$ for measuring the qubit in the $|1\\rangle$ state, you can determine $\\theta$ using $\\arcsin$:\n", + "$$ (\\sin^2\\left(\\frac{\\theta}{2}\\right) = p) \\Leftrightarrow (\\theta = 2\\arcsin\\left(\\sqrt{p}\\right)) $$\n", + "\n", + "The counter probability $q = 1 - p$, which is the probability of measuring the qubit in the $|0\\rangle$ state, is given by:\n", + "$$ q = \\cos^2\\left(\\frac{\\theta}{2}\\right) $$\n", + "\n", + "This approach can be extended for conditional probabilities. For example, with the Bayesian network shown above, you can use the following formula to calculate the joint probability distribution:\n", + "$$(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(R_y\\otimes{I})|00\\rangle$$" ], "metadata": { "collapsed": false }, "id": "6adf88f1d249b336" }, + { + "cell_type": "markdown", + "source": [ + "#### 2.1.1. Two Node Bayesian Network Example\n", + "\n", + "In the first example we consider a simple Bayesian network that is only based on two nodes." + ], + "metadata": { + "collapsed": false + }, + "id": "f0be387a44da5bac" + }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 49, "id": "initial_id", "metadata": { "collapsed": true, "ExecuteTime": { - "end_time": "2023-11-13T17:24:05.571706Z", - "start_time": "2023-11-13T17:24:05.504882Z" + "end_time": "2023-11-24T10:51:29.146074Z", + "start_time": "2023-11-24T10:51:29.080310Z" } }, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" @@ -55,10 +139,10 @@ "# Create a directed graph\n", "G = nx.DiGraph()\n", "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", - "G.add_node(\"A\", pos=(0, 0))\n", - "G.add_node(\"B\", pos=(1, 0))\n", + "G.add_node(\"X\", pos=(0, 0))\n", + "G.add_node(\"Y\", pos=(1, 0))\n", "# Add a directed edge from A to B\n", - "G.add_edge(\"A\", \"B\")\n", + "G.add_edge(\"X\", \"Y\")\n", "# Get the positions of each node\n", "pos = nx.get_node_attributes(G, \"pos\")\n", "# Draw the graph\n", @@ -72,10 +156,12 @@ { "cell_type": "markdown", "source": [ + "\n", "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", - "$$P(A)=0.2$$\n", - "$$P(B|A)=0.9$$\n", - "$$P(B|-A)=0.3$$" + "$$P(X)=0.2$$\n", + "$$P(Y|X)=0.9$$\n", + "$$P(Y|-X)=0.3$$\n", + "The corresponding rotation angles are:" ], "metadata": { "collapsed": false @@ -84,22 +170,22 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 50, "outputs": [], "source": [ "# Include libraries\n", "import numpy as np\n", "\n", "# Define rotation angles\n", - "theta_A = 2 * np.arcsin(np.sqrt(0.2))\n", - "theta_B_A = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_B_nA = 2 * np.arcsin(np.sqrt(0.3))" + "theta_X = 2 * np.arcsin(np.sqrt(0.2))\n", + "theta_Y_X = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_Y_nX = 2 * np.arcsin(np.sqrt(0.3))" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:05.577922Z", - "start_time": "2023-11-13T17:24:05.571589Z" + "end_time": "2023-11-24T10:51:29.149471Z", + "start_time": "2023-11-24T10:51:29.121013Z" } }, "id": "326c1d2e72f41202" @@ -107,25 +193,146 @@ { "cell_type": "markdown", "source": [ - "# Step 2: Create a Quantum Circuit for Bayesian Network\n", + "#### 2.1.2. Burglary Alarm Example\n", "\n", + "Now consider a more complex network. Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." + ], + "metadata": { + "collapsed": false + }, + "id": "e1dd146c9d2bdad3" + }, + { + "cell_type": "code", + "execution_count": 51, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Create a directed graph\n", + "G = nx.DiGraph()\n", + "# Add nodes\n", + "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", + "# Add edges\n", + "G.add_edges_from(\n", + " [(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"), (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")]\n", + ")\n", + "# Manually set positions\n", + "pos = {\n", + " \"Burglary\": (0, 1),\n", + " \"Earthquake\": (1, 1),\n", + " \"Alarm\": (0.5, 0.5),\n", + " \"JohnCalls\": (0, 0),\n", + " \"MaryCalls\": (1, 0),\n", + "}\n", + "# Draw the network\n", + "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", + "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", + "plt.show()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T10:51:29.262231Z", + "start_time": "2023-11-24T10:51:29.125917Z" + } + }, + "id": "e4e5d93f2afa6aee" + }, + { + "cell_type": "markdown", + "source": [ + "The Bayesian Network for this scenario involves the following variables:\n", + "\n", + "Burglary (B): Whether a burglary has occurred.\n", + "Earthquake (E): Whether an earthquake has occurred.\n", + "Alarm (A): Whether the alarm goes off.\n", + "John Calls (J): Whether John calls you.\n", + "Mary Calls (M): Whether Mary calls you.\n", + "\n", + "Use this as conditional probability tables:\n", + "$$P(B)=0.001$$\n", + "$$P(E)=0.002$$\n", + "$$P(A|-B,-E) = 0.001$$\n", + "$$P(A|-B,E) = 0.29$$\n", + "$$P(A|B,-E) = 0.94$$\n", + "$$P(A|B,E) = 0.95$$\n", + "$$P(J|-A) = 0.05$$\n", + "$$P(J|A) = 0.9$$\n", + "$$P(M|-A) = 0.9$$\n", + "$$P(M|A) = 0.3$$\n", + "Then we get:\n" + ], + "metadata": { + "collapsed": false + }, + "id": "587dc2c38a0a3ca9" + }, + { + "cell_type": "code", + "execution_count": 52, + "outputs": [], + "source": [ + "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_E = 2 * np.arcsin(np.sqrt(0.002))\n", + "theta_A_nBnE = 2 * np.arcsin(np.sqrt(0.001))\n", + "theta_A_nBE = 2 * np.arcsin(np.sqrt(0.29))\n", + "theta_A_BnE = 2 * np.arcsin(np.sqrt(0.94))\n", + "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", + "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", + "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_M_nA = 2 * np.arcsin(np.sqrt(0.9))\n", + "theta_M_A = 2 * np.arcsin(np.sqrt(0.3))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T10:51:29.264208Z", + "start_time": "2023-11-24T10:51:29.256015Z" + } + }, + "id": "a815411b4f10c78c" + }, + { + "cell_type": "markdown", + "source": [ + "### 2.2. Create a Quantum Circuit for the Bayesian Networks\n", "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." ], "metadata": { "collapsed": false }, + "id": "473ea24e63019832" + }, + { + "cell_type": "markdown", + "source": [ + "#### 2.2.1 Two Node Bayesian Network Example" + ], + "metadata": { + "collapsed": false + }, "id": "33797564f68ae67" }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 53, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 25, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -135,27 +342,27 @@ "from qiskit import QuantumCircuit\n", "\n", "# Define quantum registers\n", - "qrA = QuantumRegister(1, name=\"A\")\n", - "qrB = QuantumRegister(1, name=\"B\")\n", + "qrX = QuantumRegister(1, name=\"X\")\n", + "qrY = QuantumRegister(1, name=\"Y\")\n", "# Define a 2-qubit quantum circuit\n", - "qc = QuantumCircuit(qrA, qrB, name=\"Bayes net small\")\n", + "qc_2n = QuantumCircuit(qrX, qrY, name=\"Bayes net small\")\n", "# Apply the R_Y_theta rotation gate on the first qubit\n", - "qc.ry(theta_A, 0)\n", + "qc_2n.ry(theta_X, 0)\n", "# Apply the controlled-R_Y_theta rotation gate\n", - "qc.cry(theta_B_A, control_qubit=qrA, target_qubit=qrB)\n", + "qc_2n.cry(theta_Y_X, control_qubit=qrX, target_qubit=qrY)\n", "# Apply the X gate on the first qubit\n", - "qc.x(0)\n", + "qc_2n.x(0)\n", "# Apply the controlled-R_Y_theta rotation gate\n", - "qc.cry(theta_B_nA, control_qubit=qrA, target_qubit=qrB)\n", + "qc_2n.cry(theta_Y_nX, control_qubit=qrX, target_qubit=qrY)\n", "# Apply another X gate on the first qubit\n", - "qc.x(0)\n", - "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" + "qc_2n.x(0)\n", + "qc_2n.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:05.659173Z", - "start_time": "2023-11-13T17:24:05.583828Z" + "end_time": "2023-11-24T10:51:29.380180Z", + "start_time": "2023-11-24T10:51:29.268991Z" } }, "id": "4f99dbe56bc6910a" @@ -163,328 +370,309 @@ { "cell_type": "markdown", "source": [ - "# Step 3: Perform Inference\n", - "\n", - "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the `inference` method to estimate probabilities given evidence." + "#### 2.2.2. Burglary Alarm Example" ], "metadata": { "collapsed": false }, - "id": "5d22c72ca6352a56" + "id": "7596c28a61daad7d" }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 54, "outputs": [ { "data": { - "text/plain": "0.12058" + "text/plain": "
", + "image/png": 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}, - "execution_count": 26, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from qiskit_machine_learning.algorithms import QBayesian\n", - "\n", - "query = {\"B\": 0}\n", - "evidence = {\"A\": 1}\n", - "# Initialize quantum bayesian inference framework\n", - "qbayesian = QBayesian(circuit=qc)\n", - "# Inference\n", - "qbayesian.inference(query=query, evidence=evidence)" + "# Initialize register\n", + "var = [\"B\", \"E\", \"A\", \"J\", \"M\"]\n", + "qr = [QuantumRegister(1, name=v) for v in var]\n", + "qc_ba = QuantumCircuit(*qr, name=\"State preparation\")\n", + "# Specify control qubits\n", + "# P(B)\n", + "qc_ba.ry(theta_B, qr[0])\n", + "# P(E)\n", + "qc_ba.ry(theta_E, qr[1])\n", + "# P(A|B,E)\n", + "qc_ba.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", + "# P(A|-B,E)\n", + "qc_ba.x(qr[0])\n", + "qc_ba.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc_ba.x(qr[0])\n", + "# P(A|B,-E)\n", + "qc_ba.x(qr[1])\n", + "qc_ba.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc_ba.x(qr[1])\n", + "# P(A|-B,-E)\n", + "qc_ba.x(qr[0])\n", + "qc_ba.x(qr[1])\n", + "qc_ba.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", + "qc_ba.x(qr[0])\n", + "qc_ba.x(qr[1])\n", + "# P(J|A)\n", + "qc_ba.cry(theta_J_A, qr[2], qr[3])\n", + "# P(M|A)\n", + "qc_ba.cry(theta_M_A, qr[2], qr[4])\n", + "# P(J|-A) + P(M|-A)\n", + "qc_ba.x(qr[2])\n", + "qc_ba.cry(theta_J_nA, qr[2], qr[3])\n", + "qc_ba.cry(theta_M_nA, qr[2], qr[4])\n", + "qc_ba.x(qr[2])\n", + "# Draw circuit\n", + "qc_ba.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:05.757915Z", - "start_time": "2023-11-13T17:24:05.666180Z" + "end_time": "2023-11-24T10:51:29.788086Z", + "start_time": "2023-11-24T10:51:29.391611Z" } }, - "id": "841bce19ea097bf1" + "id": "79045cc1a7706f87" + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "## 3. How to Run Rejection Sampling" + ], + "metadata": { + "collapsed": false + }, + "id": "b8cc65c8d0c64c91" }, { "cell_type": "markdown", "source": [ - "# Step 4: Generalize the approach for n nodes\n", + "### 3.1. Set up\n", + "\n", + "Rejection sampling is a basic technique used in probabilistic computing for generating observations from a distribution. It's particularly useful when direct sampling from the desired distribution is difficult. The core idea is to use a simpler distribution (referred to as the proposal distribution) from which we can easily sample, and then to \"reject\" or \"accept\" these samples based on a certain criterion (evidence) so that the accepted samples follow the desired target distribution. \n", + "\n", + "Quantum rejection sampling adapts the classical rejection sampling method to the quantum computing context, utilizing quantum algorithms and states to perform efficient sampling. Once the state is prepared by the given quantum circuit representing the Bayesian network, it is measured, resulting in the collapse to one of its possible outcomes. This step is analogous to drawing a sample in classical rejection sampling. However, quantum rejection sampling primarily focuses on post-selection, where only specific measurement outcomes that meet desired criteria, here evidence, are retained, and others are disregarded.\n", + "\n", + "In this implementation, Grover's algorithm is employed for amplitude amplification. This step is designed to increase the probability amplitudes of the desired outcomes, thereby reducing the number of samples needed. The efficiency of quantum rejection sampling lies in its utilization of quantum parallelism, which allows for the simultaneous evaluation of multiple probabilities, and quantum interference, which can be used to increase the likelihood of obtaining desired outcomes.\n", "\n", - "Now we generalize the approach for n nodes in a chain with random probabilities." + "Quantum rejection sampling is particularly beneficial in complex or high-dimensional probability distribution scenarios, where classical computers face challenges. Its applications extend to quantum machine learning, probabilistic modeling, and other areas of quantum computing. \n", + "\n", + "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the rejection sampling method to estimate probabilities given evidence." + ], + "metadata": { + "collapsed": false + }, + "id": "eff9038bd1a6a91e" + }, + { + "cell_type": "markdown", + "source": [ + "#### 3.1.1 Two Node Bayesian Network Example\n", + "If we want to carry out a rejection sampling with X=1 as evidence, we can do this in the following way:" ], "metadata": { "collapsed": false }, - "id": "79a2c40d290870" + "id": "c3fd5b7532b845c4" }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 55, "outputs": [ { "data": { - "text/plain": "
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Oc/Hx8WrdunWFPnPjjTfqxhtvdPaUAAAA+BOnN0DMmDFDK1asKLPPt99+q0ceecTZUwAAAKAcToe5RYsWae/evWX2+fnnn7V48WJnTwEAAIByVOlz5v7s4sWLDt1LBwAAAOdUKmmZTKYS2202m5KTkxUTE8OGBwAAgGpUoZU5s9ksi8Vif37ctGnT7D9f+T8PDw+1atVKu3fv1rBhw6qlcAAAAFRwZa5nz5721bgtW7YoICCgxOfKWSwWNWjQQH379tXo0aOrpFAAAAAUV6Ewt2nTJvt/m81m/eMf/9DUqVOruiYAAAA4yOl75qxWa1XWAQAAACdU625WAAAAVC+HV+YeeeQRmUwmzZgxQ35+fg4/DNhkMunf//630wUCAACgdCabzWZzpKPZbJbJZNL+/fvVtm1bmc2OLeqZTCYVFBRUqkh3kJ2dLV9fX2VlZcnHx8fV5QDA39Loea6uAPjDgvHVO76j2cPhlbnff/9dktSsWbMiPwMAAMB1HA5zLVu2LPNnAAAAXH1sgAAAADAwh1fmkpKSnD5JQECA058FAABA6RwOc4GBgaW+i7UsJpNJ+fn5Ff4cAAAAyudwmBsxYoRTYc5ZO3bsUFRUlH744Qfl5eWpQ4cOmjBhgoYMGVKhcU6cOKGZM2fq22+/VXJysmrXrq22bdtqxIgRevzxx6upegAAgKvD4TC3aNGiaiyjqI0bNyo8PFze3t4aNmyY6tatq2XLlmno0KFKTk7WxIkTHRpn7969CgsL0+nTpzVo0CDdd999ysnJ0f79+7Vy5UrCHAAAMDyHnzN3teTn56t9+/Y6duyYfvzxR3Xu3FmSlJWVpZCQEB05ckTx8fHl7qbNzs5Whw4ddOHCBa1bt04dO3Ysdh4PD8ffZsZz5gDA9XjOHNyJuzxnzu12s27YsEGJiYkaPny4PchJkq+vr6ZMmaJLly5p8eLF5Y7z3nvvKSkpSbNmzSoW5CRVKMgBAAC4K7d7ndemTZskSWFhYcWOhYeHS5I2b95c7jhLly6VyWRSZGSkDh48qDVr1ujChQtq3769br/9dtWoUcPhmgAAANxVhe6ZM5lMeu655+Tn5+fwPXQVDXMJCQmSpDZt2hQ75u/vrzp16tj7lObSpUv65Zdf1KhRI7399tuKioqS1Wq1Hw8KCtLy5cvVoUOHUsfIzc1Vbm6u/efs7GxJUl5envLy8iRdfsWZxWJRQUFBkfEL2/Pz83XlVWyLxSKz2Vxqe+G4hQpXD/+8G7i0dk9PT1mt1iKvTzOZTPLw8Ci1vbTamRNzYk7MyR3nJF29jXhAea7G98kRbvc6r6ysLEmXL6uWxMfHx96nNJmZmSooKNCpU6f0r3/9S3PmzNHDDz+svLw8zZ8/X6+88ooGDx6sAwcOyNvbu8QxZs6cqenTpxdrX7NmjWrVqiXp8vPzgoODtW/fviLP4WvXrp3at2+v7du36+TJk/b2zp07q2XLltqyZYvOnj1rb+/evbsaN26sNWvWFPmH69Onj2rWrKlVq1YVqSEiIkIXLlzQxo0b7W0eHh4aNGiQMjIyFBcXZ2+vW7eu+vbtq+TkZO3du9fe3qhRI/Xo0UMJCQk6ePCgvZ05MSfmxJzceU4S9yzDfVT392nXrl0O1eF2GyDCwsK0du1aJSQkqHXr1sWON2vWTDk5OWUGupSUFHvofOaZZzRv3rwix4cOHaro6Gh9/PHHeuihh0oco6SVuRYtWigjI8N+E6Kr/0L9K/7VzZyYE3NiTmXNacxbrMzBfcx/unq/T5mZmWrYsGG5GyDcbhdA4YpcaWEtOztb9evXd2gMSbrzzjuLHb/zzjsVHR2tnTt3lhrmvLy85OXlVazd09NTnp6eRdosFossFkuxvqVtsiit/c/jOtNuNptlNhff11Jae2m1MyfmVNF25sScpOqfE+BOXPV9KnY+h3qV4euvv9Zdd92lgIAA+fr6KiAgQHfffbeWL1/u1HiF98qVdF9cWlqacnJySryf7kq1a9e2r8zVq1ev2PHCtstL9gAAAMbldJjLz8/XkCFDdN9992nlypVKS0tTrVq1lJaWphUrVigyMlJDhgyp8Ku8evXqJenyvWl/FhsbW6RPWfr27StJ+u2334odK2wLDAysUG0AAADuxukwN3PmTH355Ze67bbbtHXrVl28eFGpqam6ePGitmzZotDQUC1btkyzZs2q0Lj9+vVTUFCQlixZUuTmwaysLM2YMUM1atTQiBEj7O2pqak6cOBAscuyjz32mCRp1qxZOnPmjL09LS1Nb731lsxmsyIjIys+cQAAADfi9AaIoKAgeXt7a9++fSVe083Ly1PHjh2Vm5urw4cPV2js0l7ndfToUc2dO7fI67xGjRqlxYsXa+HChRo1alSRcSZOnKg33nhDLVq00ODBg5WXl6dvvvlGJ06c0IwZMzR58mSHa+INEADgerwBAu7E8G+ASE1N1eDBg8u8qXXw4MFKTU2t8Nh9+vTRtm3bdOutt2rp0qV6//335efnp88//9zh97JK0uuvv66FCxfan4u3ZMkStW3bVl999VWFghwAAIC7cno3a4sWLZSTk1Nmn3PnzikgIMCp8UNCQhQTE1Nuv0WLFpX5AONRo0YVW7EDAAD4q3B6Ze7RRx9VdHR0qStvx48f19KlS/Xoo486XRwAAADK5vDK3JVPJpakIUOG6Pvvv1dwcLDGjx+v0NBQ+fn5KT09XVu3btVbb72l0NBQ3X///VVeNAAAAC5zeAOE2WyWyVT8yds2m63U9sLPVfTxJO6IDRAA4HpsgIA7cZcNEA6vzI0YMaLE0AYAAADXcTjMlbXJAAAAAK5R6dd5AQAAwHUIcwAAAAbm9HPmJOns2bN65513tG7dOqWkpCg3N7dYH5PJpMTExMqcBgAAAKVwOsydPHlSPXr0UGJionx8fOw7Li5duqQLFy5Ikpo2bSpPT88qKxYAAABFOX2Zddq0aUpMTNT//u//6vTp05KkZ599VufOndNPP/2kkJAQBQYG6tdff62yYgEAAFCU02Fu1apV6tevnx566KFijyzp0qWLYmJidOTIEU2fPr3SRQIAAKBkToe51NRUBQcH23+2WCz2y6uSVL9+fQ0cOFDR0dGVqxAAAAClcjrM+fr6Ki8vz/5z/fr1dezYsSJ9fHx8lJ6e7nx1AAAAKJPTYS4oKEhHjhyx/xwcHKy1a9fq1KlTkqQLFy5o5cqVCggIqHSRAAAAKJnTYS4sLEzr16/X+fPnJUljx47ViRMn1KlTJ91///268cYblZiYqFGjRlVVrQAAAPgTp8PcY489pgULFtjD3L333qvXXntN586d07Jly5SWlqYJEyZo0qRJVVYsAAAAijLZbDZbVQ5YUFCgjIwMNW7cuNguVyMrfI5eVlaWfHx8XF0OAPwtjZ7n6gqAPywYX73jO5o9KvUGiJJYLBb5+flV9bAAAAAoQaXDXGpqqj7//HPt2bNHWVlZ8vX1VXBwsIYNG6YmTZpURY0AAAAoRaXC3LvvvqtJkyYpNzdXV16t/eSTT/TCCy9o7ty5GjduXKWLBAAAQMmcDnOff/65nnrqKV1zzTV64YUXdNttt8nPz0/p6enasmWL3nrrLfvxIUOGVGXNAAAA+D9Ob4C46aabdOzYMe3du1dNmzYtdvzYsWMKDg5WQECAdu3aVelCXY0NEADgemyAgDtxlw0QTj+aZP/+/RoyZEiJQU6Smjdvrvvvv1/79+939hQAAAAoh9Nhrl69eqpdu3aZferUqaN69eo5ewoAAACUw+kwd+edd2rlypXKz88v8XheXp5Wrlypu+66y+niAAAAUDanw9ycOXNUu3ZthYWF6ccffyxyLC4uTmFhYapbt65mzZpV6SIBAABQMod3swYFBRVru3Tpknbv3q1bb71VHh4euuaaa5SRkWFfrWvSpIluuukmJSYmVl3FAAAAsHM4zFmt1mKv5/L09FRAQECRtj9viLBarZUoDwAAAGVxOMwdOXKkGssAAACAM5y+Zw4AAACuV+l3s0pSfn6+Dh48qOzsbPn4+Khdu3by8KiSoQEAAFCGSq3MZWZmavTo0fL19VXHjh0VGhqqjh07ql69ehozZoxOnTpVVXUCAACgBE4vn2VmZqpbt246dOiQGjRooNtuu01NmjRRWlqadu7cqQ8//FCbN29WXFycGjRoUJU1AwAA4P84vTL38ssv69ChQ5o0aZKOHj2q1atXa+HChYqJidHRo0f13HPPKSEhQa+++mpV1gsAAIArmGw2m82ZDwYFBSkwMFAbNmwotU/fvn115MgRHT582OkC3YWjL7sFAFSf0fNcXQHwhwXjq3d8R7OH0ytzKSkp6t69e5l9unfvrpSUFGdPAQAAgHI4HeZ8fX119OjRMvscPXpUvr6+zp4CAAAA5XA6zPXq1UtffPGF1q1bV+Lx9evX64svvlDv3r2dPQUAAADK4fRu1qioKH333XcKDw9XRESEevXqJT8/P6Wnp2vTpk2KiYlRrVq1NHXq1KqsFwAAAFdwOszdcMMNio2N1ahRo/Tdd9/pu+++k8lkUuF+imuvvVaLFi3SDTfcUGXFAgAAoKhKvaYhNDRUCQkJ+v7777Vnzx77GyCCg4N16623ymQyVVWdAAAAKIHTYe6RRx5Rhw4d9Oyzzyo0NFShoaFVWRcAAAAc4PQGiCVLlujEiRNVWQsAAAAqyOkwd+211yo1NbUqawEAAEAFOR3mHnnkEX333Xc6fvx4VdYDAACACnD6nrnIyEht3LhRPXr00H/913+pS5cu8vPzK3HTQ0BAQKWKBAAAQMmcDnNBQUH2R5E8/fTTpfYzmUzKz8939jQAAAAog9NhbsSIETx6BAAAwMWcDnOLFi2qwjIAAADgDKc3QAAAAMD1KvUGCEnKzc3VqlWrtGfPHmVlZcnX11fBwcGKiIiQl5dXVdQIAACAUlQqzK1YsUJjxozRyZMn7e9klS5vemjcuLE++OADDR48uNJFAgAAoGROh7n169crMjJSFotFjzzyiG677Tb5+fkpPT1dW7Zs0SeffKJ7771XsbGx6tu3b1XWDAAAgP9jsl25pFYBoaGh2rdvn3744QfdeOONxY7v27dPt956qzp37qytW7dWulBXy87Olq+vr7KysuTj4+PqcgDgb2n0PFdXAPxhwfjqHd/R7OH0Bog9e/Zo6NChJQY5SerYsaOGDBmi3bt3O3sKAAAAlMPpMFerVi01atSozD6NGzdWrVq1nD0FAAAAyuF0mOvfv7/WrVtXZp9169ZpwIABzp4CAAAA5XA6zM2dO1cnTpzQiBEjlJycXORYcnKyHn74YWVkZGju3LmVLhIAAAAlc3o368MPP6z69evr008/1eeff66AgAD7btakpCQVFBSoY8eOeuihh4p8zmQyaf369ZUuHAAAAJUIc5s2bbL/d35+vg4fPqzDhw8X6fPzzz8X+xzvcwUAAKg6Toc5q9ValXUAAADACbybFQAAwMCqLMwlJSVpy5YtVTUcAAAAHFBlYW7hwoXq06dPVQ0HAAAAB3CZFQAAwMDcNszt2LFDERERqlevnmrXrq1u3bopOjra6fFOnz6tZs2ayWQy6fbbb6/CSgEAAFzH6d2s1Wnjxo0KDw+Xt7e3hg0bprp162rZsmUaOnSokpOTNXHixAqP+eSTTyorK6saqgUAAHCdKluZ8/X1VUBAQKXHyc/P1+jRo2U2m7VlyxZ98MEHev311/Xzzz+rbdu2mjJlio4ePVqhMZctW6YlS5Zo9uzZla4PAADAnVRZmBs/frx+//33So+zYcMGJSYmavjw4ercubO93dfXV1OmTNGlS5e0ePFih8c7efKkHn/8cT388MMaNGhQpesDAABwJ253z1zhmyXCwsKKHQsPD5ckbd682eHxHnvsMVksFr311ltVUh8AAIA7cfieucJnyIWEhMjb27tCz5Tr2bOnw30TEhIkSW3atCl2zN/fX3Xq1LH3Kc8nn3yir776SsuXL1f9+vUrdM9cbm6ucnNz7T9nZ2dLkvLy8pSXlydJMpvNslgsKigoKPJGjML2/Px82Ww2e7vFYpHZbC61vXDcQh4el/958vPzHWr39PSU1WpVQUGBvc1kMsnDw6PU9tJqZ07MiTkxJ3eck8QrIeE+rsb3yREOh7nevXvLZDJp//79atu2rf1nR1w5ofIUBi5fX98Sj/v4+DgUylJSUvT000/rgQce0F133eXw+QvNnDlT06dPL9a+Zs0a1apVS5IUEBCg4OBg7du3T0lJSfY+7dq1U/v27bV9+3adPHnS3t65c2e1bNlSW7Zs0dmzZ+3t3bt3V+PGjbVmzZoi/3B9+vRRzZo1tWrVqiI1RERE6MKFC9q4caO9zcPDQ4MGDVJGRobi4uLs7XXr1lXfvn2VnJysvXv32tsbNWqkHj16KCEhQQcPHrS3MyfmxJyYkzvPSfIR4C6q+/u0a9cuh+ow2a78U6kM06ZNk8lk0lNPPaUGDRrYf3ZEVFSUQ/2ky5dX165dq4SEBLVu3brY8WbNmiknJ6fcQBcREaFdu3bp119/1TXXXCNJOnLkiFq1aqXw8HCtXr26zM+XtDLXokULZWRkyMfn8i8TV/+F+lf8q5s5MSfmxJzKmtOYt1iZg/uY/3T1fp8yMzPVsGFDZWVl2bNHSRxemZs2bVqZP1eVwhW50sJadna26tevX+YYixcvVkxMjL744gt7kKsoLy8veXl5FWv39PSUp6dnkTaLxSKLxVKs7x+XBRxr//O4zrSbzWaZzcVvhSytvbTamRNzqmg7c2JOUvXPCXAnrvo+FTufQ72uosJ75Uq6Ly4tLU05OTkl3k93pT179kiS7r//fplMJvv/WrVqJUmKjY2VyWQqslsWAADAiJx+aPDZs2d18uRJtWjRoshfUEuXLtWKFSvk7e2tJ554QjfddFOFxu3Vq5dmzpypNWvWaNiwYUWOxcbG2vuUpXv37srJySnWnpOTo6VLl6p58+YKDw+vkufiAQAAuJLD98z92eOPP65PPvlE6enp9g0B77//vp588kn7fRE1a9bUrl271L59e4fHzc/PV7t27XT8+HH9+OOP9tWzrKwshYSE6MiRIzp48KACAwMlSampqcrKylKTJk1K3TRRqCL3zP1Zdna2fH19y71uDQCoPqPnuboC4A8Lxlfv+I5mD6cvs27evFn9+/e3BzlJmjVrlpo1a6YtW7YoOjpaNptNr732WoXG9fDw0Icffiir1aqePXtqzJgxmjhxojp16qT4+HjNmDHDHuQkafLkybruuuv09ddfOzsVAAAAw3L6MmtqamqRF9bv379fycnJmjNnjkJDQyVJX375ZYWeR1eoT58+2rZtm6KiorR06VLl5eWpQ4cOmj17toYOHepsyQAAAH85Toe53Nxc1ahRw/7z5s2bZTKZiry5ISgoSCtWrHBq/JCQEMXExJTbb9GiRVq0aJFDYwYGBsrJq8oAAABuyenLrM2bN9e+ffvsP3/77bdq0KCBOnbsaG87deqU6tSpU7kKAQAAUCqnV+YGDhyod999V//85z/l7e2t1atXa8SIEUX6xMfHs2MUAACgGjkd5iZPnqyVK1fqjTfekCQ1adJE//rXv+zHT5w4oe+//15PPvlk5asEAABAiZwOc/7+/vr111+1fv16SVLPnj2LbJvNyMjQa6+9pvDw8MpXCQAAgBI5Heaky8+Ru+OOO0o8dv311+v666+vzPAAAAAoh9u9zgsAAACOq9TKXEFBgaKjo7Vu3TqlpKQoNze3WB+TyWS/FAsAAICq5XSYO3funMLCwvTjjz/KZrPJZDIVeYZb4c8mk6lKCgUAAEBxTl9mfeWVVxQXF6fp06crIyNDNptN06ZNU2pqqpYuXaqgoCDdf//9Ja7WAQAAoGo4Hea++uordevWTS+++KIaNGhgb/fz89P999+vjRs3at26dRV+NysAAAAc53SYS0pKUrdu3f4YyGwusgrXvHlzDRo0SIsXL65chQAAACiV02Gudu3aMpv/+Livr69SU1OL9PH391dSUpLz1QEAAKBMToe5li1bFglqN954ozZs2GBfnbPZbFq/fr2aNGlS+SoBAABQIqfDXL9+/bRx40bl5+dLkkaOHKmkpCR1795dkyZNUmhoqPbu3avIyMgqKxYAAABFOf1oktGjR6thw4Y6efKkmjRpokceeUR79uzRe++9p71790qSIiMjNW3atCoqFQAAAH9msl35cLgqcPLkSR0+fFgtW7aUv79/VQ7tUtnZ2fL19VVWVlaRd9ACAK6e0fNcXQHwhwXjq3d8R7NHpd4AUZJGjRqpUaNGVT0sAAAASsC7WQEAAAzM6ZW5oKAgh/qZTCYlJiY6exoAAACUwekwZ7VaS3zvalZWls6cOSNJatKkiWrUqOF0cQAAACib02HuyJEjZR6bMGGC0tPTtXbtWmdPAQAAgHJUyz1zgYGBWrp0qU6fPq0XXnihOk4BAAAAVeMGCE9PTw0YMEDR0dHVdQoAAIC/vWrdzXr+/HllZmZW5ykAAAD+1qotzG3dulWfffaZ2rVrV12nAAAA+NtzegNE3759S2zPz8/X8ePH7Rskpk6d6uwpAAAAUA6nw9ymTZtKbDeZTKpfv77CwsI0YcIEDRgwwNlTAAAAoByVes4cAAAAXKvS72Y9ceKEjh8/LqvVqmbNmsnf378q6gIAAIADnNoAkZubqzlz5qhNmzZq0qSJbrnlFoWEhKhZs2a65ppr9Oyzz5b5UGEAAABUjQqHueTkZHXp0kWTJ09WYmKimjRpopCQEIWEhKhJkybKzMzUW2+9pVtuuUXr1q2zfy41NZVnzgEAAFSxCoW5vLw8RURE6D//+Y8eeOAB7d+/X8eOHVNcXJzi4uJ07Ngx7d+/Xw8++KAyMzN1991368iRI0pMTFRoaKgOHDhQXfMAAAD4W6rQPXPz58/Xr7/+qqioKEVFRZXYp127dvr444/Vtm1bRUVF6cEHH9SRI0eUkZGhm2++uUqKBgAAwGUVWpmLjo5W69atHXp23Isvvqg2bdooLi5OFy9eVGxsrAYNGuR0oQAAACiuQmHut99+U1hYmEwmU7l9TSaTve9PP/2k3r17O1sjAAAASlGhMJeTkyNfX1+H+/v4+MjDw0OtW7eucGEAAAAoX4XCXOPGjXXo0CGH+ycmJqpx48YVLgoAAACOqVCY6969u2JiYpSWllZu37S0NH333XcKDQ11ujgAAACUrUJh7rHHHlNOTo7uueceZWRklNrv1KlTuueee3T+/HmNHTu20kUCAACgZBV6NEmfPn00evRoLViwQNddd53Gjh2rvn37qkWLFpIuP1B4/fr1WrBggTIyMjRmzBg2PgAAAFSjCr+b9b333pOPj4/efPNNzZw5UzNnzixy3GazyWw265///GexYwAAAKhaFQ5zFotFr732msaMGaNFixYpLi7Ofg+dv7+/evTooZEjR6pNmzZVXiwAAACKqnCYK9SmTRu9+uqrVVkLAAAAKqhCGyAAAADgXghzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAzMbcPcjh07FBERoXr16ql27drq1q2boqOjHfqszWZTTEyMHn/8cXXs2FG+vr6qVauWOnXqpBkzZujixYvVXD0AAMDV4eHqAkqyceNGhYeHy9vbW8OGDVPdunW1bNkyDR06VMnJyZo4cWKZn8/NzVVERIS8vLzUu3dvhYeH6+LFi4qNjdULL7yg5cuXa9OmTapVq9ZVmhEAAED1MNlsNpuri7hSfn6+2rdvr2PHjunHH39U586dJUlZWVkKCQnRkSNHFB8fr5YtW5Y6Rl5enubMmaNx48apfv36RdojIyO1cuVKzZkzR5MmTXK4ruzsbPn6+iorK0s+Pj5Ozw8A4LzR81xdAfCHBeOrd3xHs4fbXWbdsGGDEhMTNXz4cHuQkyRfX19NmTJFly5d0uLFi8scw9PTUy+88EKRIFfYPnnyZEnS5s2bq7x2AACAq83twtymTZskSWFhYcWOhYeHS6pcEPP09JQkeXi45RVmAACACnG7RJOQkCBJatOmTbFj/v7+qlOnjr2PMz766CNJJYfFK+Xm5io3N9f+c3Z2tqTLl2rz8vIkSWazWRaLRQUFBbJarfa+he35+fm68iq2xWKR2Wwutb1w3EKFgTM/P9+hdk9PT1mtVhUUFNjbTCaTPDw8Sm0vrXbmxJyYE3NyxzlJJgHu4mp8nxzhdmEuKytL0uXLqiXx8fGx96momJgYzZ8/X9ddd53+3//7f2X2nTlzpqZPn16sfc2aNfaNEwEBAQoODta+ffuUlJRk79OuXTu1b99e27dv18mTJ+3tnTt3VsuWLbVlyxadPXvW3t69e3c1btxYa9asKfIP16dPH9WsWVOrVq0qUkNERIQuXLigjRs32ts8PDw0aNAgZWRkKC4uzt5et25d9e3bV8nJydq7d6+9vVGjRurRo4cSEhJ08OBBeztzYk7MiTm585wk7lmG+6ju79OuXbscqsPtNkCEhYVp7dq1SkhIUOvWrYsdb9asmXJycioc6Hbs2KF+/frJw8NDW7du1Q033FBm/5JW5lq0aKGMjAz7TYiu/gv1r/hXN3NiTsyJOZU1pzFvsTIH9zH/6er9PmVmZqphw4blboBwu5W5whW50sJadnZ2sY0N5dm5c6fCwsJkNpsVGxtbbpCTJC8vL3l5eRVr9/T0tN93V8hischisRTrW9p9eaW1/3lcZ9rNZrPM5uK3QpbWXlrtzIk5VbSdOTEnqfrnBLgTV32fip3PoV5XUeG9ciXdF5eWlqacnJwS76crzc6dOzVgwABZrVbFxsaqS5cuVVYrAACAq7ldmOvVq5eky/em/VlsbGyRPuUpDHIFBQVavXq1unbtWnWFAgAAuAG3C3P9+vVTUFCQlixZUuTmwaysLM2YMUM1atTQiBEj7O2pqak6cOBAscuyu3bt0oABA5Sfn6+YmBh17979ak0BAADgqnG7e+Y8PDz04YcfKjw8XD179izyOq+jR49q7ty5CgwMtPefPHmyFi9erIULF2rUqFGSpMzMTA0YMEBnzpzR7bffrrVr12rt2rVFzlOvXj2NHz/+6k0MAACgGrhdmJMub03ftm2boqKitHTpUuXl5alDhw6aPXu2hg4dWu7ns7Ozdfr0aUnS6tWrtXr16mJ9WrZsSZgDAACG53aPJnFXvJsVAFyPd7PCnfBuVgAAAFQaYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzMHtvPvuuwoMDJS3t7e6du2q7du3l9r3119/VWRkpAIDA2UymTRv3rxifbZs2aLBgweradOmMplMWr58ebE+6enpGjVqlJo2bapatWrp9ttvV0JCQhXOCgCA6kGYg1tZunSpJkyYoKioKO3evVudOnVSeHi4Tpw4UWL/8+fPKygoSLNmzZK/v3+Jfc6dO6dOnTrp3XffLfG4zWbT3XffrcOHD+ubb77Rnj171LJlS/Xv31/nzp2rsrkBAFAdeJ2Xg3id19XRtWtXdenSRe+8844kyWq1qkWLFnrqqaf0/PPPl/nZwMBAjR8/vsx37ppMJn399de6++677W3x8fFq166d/vOf/+iGG26wn9ff318zZszQo48+Wul5AagavM4L7oTXeQF/cunSJe3atUv9+/e3t5nNZvXv319xcXHVdt7c3FxJkre3d5Hzenl5adu2bdV2XgAAqgJhDm4jIyNDBQUF8vPzK9Lu5+entLS0ajtv+/btFRAQoMmTJ+v06dO6dOmSZs+erWPHjik1NbXazgsAQFUgzOFvz9PTU1999ZXi4+PVoEED1apVSxs3btTAgQNlNvMVAQC4Nw9XFwAUuuaaa2SxWJSenl6kPT09vdTNDVXl5ptv1t69e5WVlaVLly6pUaNG6tq1q2655ZZqPS8AAJXFsgPcRo0aNXTzzTdr/fr19jar1ar169ere/fuV6UGX19fNWrUSAkJCdq5c6fuuuuuq3JeAACcxcoc3MqECRM0cuRI3XLLLQoJCdG8efN07tw5/eMf/5AkjRgxQs2aNdPMmTMlXd408dtvv9n/+/jx49q7d6/q1Kmj1q1bS5JycnJ06NAh+zl+//137d27Vw0aNFBAQIAk6YsvvlCjRo0UEBCgX375Rc8884zuvvtuhYWFXc3pAwBQYYQ5uJWhQ4fq5MmTmjp1qtLS0tS5c2etXr3avikiKSmpyH1sKSkpCg4Otv88d+5czZ07V7169dKmTZskSTt37lSfPn3sfSZMmCBJGjlypBYtWiRJSk1N1YQJE5Senq4mTZpoxIgReumll6p5tgAAVB7PmXMQz5kDANfjOXNwJzxnDgAAAJVGmAMAADAwwhwAAICBEeYAAAAMjN2sboabe+FOqvvmXgBA5bEyBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADMxtw9yOHTsUERGhevXqqXbt2urWrZuio6MrNEZubq7+9a9/qU2bNvL29lbTpk01ZswYnThxopqqBgAAuLo8XF1ASTZu3Kjw8HB5e3tr2LBhqlu3rpYtW6ahQ4cqOTlZEydOLHcMq9Wqu+66S7GxserWrZsiIyOVkJCgDz/8UOvXr9ePP/6oRo0aXYXZAAAAVB+3W5nLz8/X6NGjZTabtWXLFn3wwQd6/fXX9fPPP6tt27aaMmWKjh49Wu44ixcvVmxsrB544AH98MMPmjVrlpYtW6b33ntPhw8f1osvvngVZgMAAFC93C7MbdiwQYmJiRo+fLg6d+5sb/f19dWUKVN06dIlLV68uNxxFixYIEmaOXOmTCaTvX3s2LEKCgrSp59+qgsXLlR5/QAAAFeT24W5TZs2SZLCwsKKHQsPD5ckbd68ucwxLl68qJ9++knt2rVTy5YtixwzmUwaMGCAzp07p507d1ZN0QAAAC7idmEuISFBktSmTZtix/z9/VWnTh17n9IkJibKarWWOMaVY5c3DgAAgLtzuw0QWVlZki5fVi2Jj4+PvU9lxriyX0lyc3OVm5tbbMzMzEzl5eVJksxmsywWiwoKCmS1Wu19C9vz8/Nls9ns7RaLRWazudT2vLw8XbroWebcgKvp1Km8Ij97eFz+lZGfn1+k3dPTU1arVQUFBfY2k8kkDw+PUttL+95U5ffJkdqZk7HmdOmiSYC7OHOmer9PmZmZklTku1MStwtz7mLmzJmaPn16sfZWrVq5oBrANf53sqsrAAD3dbV+R549e7bUBSrJDcNcYbGlrZplZ2erfv36lR7jyn4lmTx5siZMmGD/2Wq1KjMzUw0bNiyyoQLuJzs7Wy1atFBycrJ9FRYAcBm/I43DZrPp7Nmzatq0aZn93C7MXXk/280331zkWFpamnJychQSElLmGEFBQTKbzaXeE1fWfXmFvLy85OXlVaStXr165ZUPN+Lj48MvKgAoBb8jjaGshadCbrcBolevXpKkNWvWFDsWGxtbpE9patasqZCQEB08eLDYM+lsNpvWrl2r2rVr65ZbbqmiqgEAAFzD7cJcv379FBQUpCVLlmjv3r329qysLM2YMUM1atTQiBEj7O2pqak6cOBAsUuqY8aMkXT5cumVNw7Onz9fhw8f1oMPPqiaNWtW72QAAACqmduFOQ8PD3344YeyWq3q2bOnxowZo4kTJ6pTp06Kj4/XjBkzFBgYaO8/efJkXXfddfr666+LjDNy5EiFh4frs88+U48ePfT888/rvvvu07hx49SqVSu98sorV3lmuFq8vLwUFRVV7DI5AIDfkX9FJlt5+11dZPv27YqKitIPP/ygvLw8dejQQRMmTNDQoUOL9Bs1apQWL16shQsXatSoUUWO5ebmatasWfr444+VnJysBg0a6I477tArr7wiPz+/qzgbAACA6uG2YQ4AAADlc7vLrAAAAHAcYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEORie1Wp1dQkAALgMYQ6GZzb/8f/GBDsAKK6goMDVJaAaEeZgWOnp6Zo4caJiY2N15swZSX8EO5vNRrAD8LdX+HvQYrFIcvx3Iy+HMhZe5wXDioqK0ssvv6zAwEBdf/316t27t3r16qWOHTsWeYG01WqVzWaTxWLRpk2bdPHiRd1+++0urBwAro73339fmzZt0ogRI9SrVy/VqVPHfqww1F15dQPGRJiDYQUHB+u3337TTTfdpN27dysvL08tW7bUrbfeqj59+ujWW29V+/bt7f3Pnz+vBx54QN9++63OnTsnb29vF1YPANWvVatWOnr0qLy8vNSpUyeFhYUpIiJCXbt2lclksvfLz8+Xh4eHzp8/rw8++ECdOnVSnz59XFg5KoIwB0NKTk5Wz5491bBhQ8XFxWnXrl1atWqVVqxYoX379slsNuuGG25Qz5491bNnT4WHh+vgwYO688471aVLF61YscLVUwCAavXrr7+qQ4cOuvnmm1W/fn2tW7dOklS7dm3deuutioiIUFhYWJE/erdt26aePXuqR48e2rZtm6tKRwV5uLoAwBmpqanKzs5Wr1695OnpqS5duigkJERPPvmkdu/erW+++UYxMTF699139dFHH+mWW26Rp6en0tPTNWbMGFeXDwDV7pdffpEkDR8+XM8++6zi4+O1fPlyffbZZ1qzZo3WrFkjf39/9e7dWwMHDtQdd9yh7du3S5ImT57sytJRQazMwZAOHTqk5557TpGRkRo+fHix43l5eUpJSdHWrVu1cuVKrVu3TqdPn1a9evWUmZnpgooB4Or64IMP9Nhjj+m7777TwIEDixzbsWOHPvvsM3355Zc6duyYJKlNmzbKzs7WhQsX7JvKYAyEORhWVlaW8vPz1bBhw1L7WK1Wmc1mzZ8/X48//rgef/xxvfvuu1exSgC4+mw2m3766SdFR0friSee0LXXXmtvv/JeuYsXL2r9+vX64osvtHz5cmVnZ+uJJ57Q22+/7arS4QTCHAznz7+MpMvPUDKZTKXuyvqv//ovzZ07Vzt37tRNN910NcoEAJfLyclRjRo1VKNGjWLH/vy79Mknn9R7772n3bt3q3PnzlexSlQWYQ6GVPhLKC0tTY0bNy4S4goKCmQ2m+2/pI4dO6ZBgwYpJSVFJ0+edFXJAOB2Cn+XJiYmaujQocrKylJCQoKry0IFsQEChpKfn6/vv/9eH330keLj42U2m1WzZk116tRJkZGR6tGjh/3hmIW8vb01atQoNW3a1EVVA4B7Kvyjd//+/dq9e7cmTZrk4orgDFbmYChz587Vyy+/rLNnz6p169ayWCw6ePCg/Xj79u01evRoPfDAA/L397e3X7p0SR4eHjwcE8DfSkm3pZQkPT1dq1ev1uDBg9WgQYOrUBmqEmEOhvH777+rQ4cOuummm7R48WLVqFFDfn5+SktL08qVK/XFF19o06ZNkqS+fftqzpw53B8H4G/lwoULSkpKUkBAgGrWrFmhzxYUFBS7sgFjIMzBMKZOnar58+dryZIl6tevn6Tif3X+8ssvmjt3rqKjo9WyZUt9+umnuvnmmx3+6xQAjGzWrFlatmyZ7r33XnXr1k3t2rWTn59fmSHt5MmTql+/vjw8uPPKqAhzMIzIyEjt3btXGzduVEBAgP31M4Uvjr7yl9Vbb72lZ599ViNHjtTChQtdWDUAXD3NmzdXSkqKLBaLfH191aNHD4WFhalr164KCgoq9iinc+fOadq0aTp16pQWLFjAypxBEcNhGMHBwfr666+Vk5MjSfa/Ik0mk/0XUOEK3DPPPKOtW7dqw4YNOnz4sIKCglxWNwBcDfHx8crKylL37t01fPhwrV27VnFxcfr2228VEBCg3r17q3///goODlazZs1Ur149/ec//9GCBQvUu3dvgpyBEeZgGIUvfX7wwQf1+uuvKzQ0tMRnJxXe99GuXTvFxMTYwx8A/JXFx8fr4sWLCgsL0xNPPKE77rhDBw8eVFxcnDZs2KBly5bp008/1fXXX6++ffvq9ttv1/r165Wdna3Ro0e7unxUApdZYRgFBQV67rnn9MYbb6h9+/Z64okndN9998nPz69Y39OnT2v8+PGKiYnRiRMnXFAtAFxdX375pYYMGaLPP/9cQ4YMsbfn5eXp6NGj+vnnn7V161Zt2rRJ+/fvl6enp2w2m7y8vHjNocER5mA48+fP12uvvabDhw+radOmuueeezRw4EC1aNFCFotF9erV09tvv6158+Zp3Lhxev31111dMgBUO5vNpgMHDsjb21utWrUqcePXuXPnFB8fr4MHD2rhwoVau3atnnzySf33f/+3i6pGVSDMwXBsNpsOHTqkBQsW6PPPP7e/JLpx48by9PRUamqqrFarHnjgAc2ePVvNmzd3ccUA4FolBbunn35a77zzjnbt2qXg4GAXVYaqQJiDoZ07d07bt2/XihUrlJKSohMnTsjHx0dDhgxRZGSkvL29XV0iALgNq9Uqs9msI0eO6K677tLp06eVlJTk6rJQSWyAgKHVrl1bffr0UZ8+fZSXlydPT09XlwQAbqvwLTjHjx9XXl6exo0b5+KKUBVYmQMA4G/GZrPp2LFjatCggWrXru3qclBJhDkAAAAD463jAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABvb/AXPtFa/oODGjAAAAAElFTkSuQmCC" }, - "execution_count": 27, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# Choose the number of nodes\n", - "n = 10\n", - "# Generate probabilities\n", - "prob = np.random.random_sample(2 * (n - 1) + 1)\n", - "theta = [2 * np.arcsin(np.sqrt(p)) for p in prob]\n", - "# Define quantum registers\n", - "qr = [QuantumRegister(1, name=i) for i in range(n)]\n", - "# Generate circuit\n", - "qc = QuantumCircuit(*qr, name=\"Bayes net\")\n", - "# Apply the R_Y_theta rotation gate on the first qubit\n", - "qc.ry(theta[0], 0)\n", - "# Apply the controlled-R_Y_theta rotations\n", - "for i in range(1, n, 1):\n", - " qc.cry(theta_B_A, control_qubit=i - 1, target_qubit=i)\n", - " qc.x(i - 1)\n", - " qc.cry(theta_B_nA, control_qubit=i - 1, target_qubit=i)\n", - " qc.x(i - 1)\n", - "# Draw circuit\n", - "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" + "from qiskit_machine_learning.algorithms import QBayesian\n", + "from qiskit.visualization import plot_histogram\n", + "\n", + "evidence = {\"X\": 1}\n", + "# Initialize QBayesian\n", + "qb_2n = QBayesian(circuit=qc_2n)\n", + "# Sampling\n", + "samples = qb_2n.rejection_sampling(evidence=evidence)\n", + "plot_histogram(samples)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:06.018169Z", - "start_time": "2023-11-13T17:24:05.762992Z" + "end_time": "2023-11-24T10:51:29.892049Z", + "start_time": "2023-11-24T10:51:29.787284Z" } }, - "id": "3764be5e0ce2db02" + "id": "1e602fda98a6356d" }, { "cell_type": "markdown", "source": [ - "We could also do inference with this model, but the chosen probabilities are random, as is the result." + "We can also set the threshold to accept the evidence. For example, if set to 0.9, this means that each evidence qubit must be equal to the value of the evidence variable at least 90% of the time in order to be accepted. Sometimes we can also improve our result by setting the threshold for acceptance of the evidence higher:" ], "metadata": { "collapsed": false }, - "id": "9ded5b8b18eb4256" + "id": "166108a390743bd4" }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 56, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'0000000000': 0.27594, '1000000000': 0.72406}\n" - ] - }, { "data": { "text/plain": "
", - "image/png": 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PSctgMGTbbjabFRERoXXr1jHgAQAAIB/d1ZU5o9EoOzs7y/xx7733nuX1jX/s7e1VpUoV7du3T0899VS+FA4AAIC7vDLXpk0by9W47du3y8fHJ9t55ezs7FSyZEl16NBBgwcPzpNCAQAAkNVdhblt27ZZ/m40GvXcc89p3LhxeV0TAAAAcijXz8yZTKa8rAMAAAC5kK+jWQEAAJC/cnxlbtCgQTIYDJo4caK8vLxyPBmwwWDQd999l+sCAQAAcGsGs9lszsmORqNRBoNBR48eVfXq1WU05uyinsFgUHp6+j0VWRjEx8fLw8NDcXFxcnd3t3Y5AFAkDf7M2hUA/zN7RP4eP6fZI8dX5k6dOiVJ8vb2zvQaAAAA1pPjMOfr63vb1wAAACh4DIAAAACwYTm+MhceHp7rD/Hx8cn1ewEAAHBrOQ5zlStXvuVarLdjMBiUlpZ21+8DAADAneU4zA0YMCBXYQ4AAAD5J8dhbv78+flYBgAAAHKDARAAAAA2jDAHAABgw1jOCwAAwIaxnFcOsZwXAFgfy3mhMGE5LwAAANwzlvMCAACwYQyAAAAAsGH3HOZ++eUXPfbYY/Lx8ZGHh4d8fHz0+OOPa8WKFXlQHgAAAG4nx7dZb5aWlqZ+/fpp+fLlMpvNsre3V6lSpRQVFaWVK1dq1apV6tGjhxYtWiR7+1x/DAAAAG4j11fmJk2apJ9++kkPPvig/vjjDyUlJSkyMlJJSUnavn27WrdureXLl2vy5Ml5WS8AAABukOOpSW7m5+cnZ2dnHTp0KNsrb6mpqapfv76Sk5N18uTJey7U2piaBACsj6lJUJgUlqlJcn1lLjIyUt27d7/lLVQHBwd1795dkZGRuf0IAAAA3EGuw1ylSpV09erV2+6TkJAgHx+f3H4EAAAA7iDXYe6FF17Q0qVLb3nl7dy5c1qyZIleeOGFXBcHAACA28vxMNPw8PBMr3v37q2dO3fK399fI0aMUOvWreXl5aULFy7ojz/+0IwZM9S6dWv16tUrz4sGAADAdXe9NuvNzGbzLdsz3peWlnaPZVofAyAAwPoYAIHCpLAMgMjxlbkBAwZkG9oAAABgPTkOc/Pnz8/HMgAAAJAbrM0KAABgwwhzAAAANuyeFk29cuWKZs2apd9++03nz59XcnJyln0MBoPCwsLu5WMAAABwC7kOc9HR0WrZsqXCwsLk7u5uGXGRkpKixMRESVKFChXk4OCQZ8UCAAAgs1zfZn3vvfcUFham//73v7p06ZIkaeTIkUpISNDu3bsVEBCgypUr68iRI3lWLAAAADLLdZhbu3atOnbsqKeffjrLlCVNmzbVunXrdPr0aU2YMOGeiwQAAED2ch3mIiMj5e/vb3ltZ2dnub0qSZ6ennr44Ye1dOnSe6sQAAAAt5TrMOfh4aHU1FTLa09PT509ezbTPu7u7rpw4ULuqwMAAMBt5TrM+fn56fTp05bX/v7+2rRpk/79919JUmJiolatWiUfH597LhIAAADZy3WYCwwM1ObNm3Xt2jVJ0tChQ3Xx4kU1aNBAvXr1Ut26dRUWFqaBAwfmVa0AAAC4Sa7D3IsvvqjZs2dbwtyTTz6pjz/+WAkJCVq+fLmioqI0atQovfnmm3lWLAAAADIzmM1mc14eMD09XTExMSpbtmyWUa62LGMevbi4OLm7u1u7HAAokgZ/Zu0KgP+ZPSJ/j5/T7HFPK0Bkx87OTl5eXnl9WAAAAGTjnsNcZGSkFi9erP379ysuLk4eHh7y9/fXU089pfLly+dFjQAAALiFewpzX3zxhd58800lJyfrxru1Cxcu1DvvvKNp06Zp2LBh91wkAAAAspfrMLd48WK98sorKl26tN555x09+OCD8vLy0oULF7R9+3bNmDHDsr137955WTMAAAD+X64HQDRq1Ehnz57VgQMHVKFChSzbz549K39/f/n4+Gjv3r33XKi1MQACAKyPARAoTArLAIhcT01y9OhR9e7dO9sgJ0kVK1ZUr169dPTo0dx+BAAAAO4g12GuRIkScnV1ve0+bm5uKlGiRG4/AgAAAHeQ6zD36KOPatWqVUpLS8t2e2pqqlatWqXHHnss18UBAADg9nId5qZOnSpXV1cFBgZq165dmbYFBQUpMDBQxYsX1+TJk++5SAAAAGQvx6NZ/fz8srSlpKRo3759atWqlezt7VW6dGnFxMRYrtaVL19ejRo1UlhYWN5VDAAAAIschzmTyZRleS4HBwf5+Phkart5QITJZLqH8gAAAHA7OQ5zp0+fzscyAAAAkBu5fmYOAAAA1pcnYS4tLU1HjhxRUFCQjhw5cssRrncjODhYXbt2tUyB0rx5cy1dujTXx7t06ZK8vb1lMBj00EMP3XN9AAAAhcE9hbnY2FgNHjxYHh4eql+/vlq3bq369eurRIkSGjJkiP79999cHXfr1q1q1aqVduzYod69e+vFF19UVFSU+vTpo+nTp+fqmC+//LLi4uJy9V4AAIDCKtdhLjY2Vs2bN9d3332nYsWKqXPnzhowYIACAwNVrFgxzZkzRy1btlRsbOxdHTctLU2DBw+W0WjU9u3b9e2332r69Ok6ePCgqlevrrFjx+rMmTN3dczly5dr0aJFmjJlyl29DwAAoLDLdZj74IMPdOLECb355ps6c+aM1q9fr3nz5mndunU6c+aMRo8erdDQUH300Ud3ddwtW7YoLCxM/fr1U8OGDS3tHh4eGjt2rFJSUrRgwYIcHy86OlovvfSSnnnmGXXr1u2uagEAACjsch3mfv31V7Vr105TpkzJsqyXi4uLJk2apHbt2umXX365q+Nu27ZNkhQYGJhlW5cuXSRJv//+e46P9+KLL8rOzk4zZsy4qzoAAABsQY6nJrnZ+fPn1bdv39vu06JFC/355593ddzQ0FBJUrVq1bJsK1eunNzc3Cz73MnChQv1888/a8WKFfL09LyrZ+aSk5OVnJxseR0fHy/p+jJlqampkiSj0Sg7Ozulp6dnmk8voz0tLU1ms9nSbmdnJ6PReMv2jONmsLe//q/n5gElt2p3cHCQyWRSenq6pc1gMMje3v6W7beqnT7RJ/pEnwpjn6TM850C1lQQ36ecyHWY8/DwuOOza2fOnJGHh8ddHTcjcN3qfe7u7jkKZefPn9err76qvn375mp92EmTJmnChAlZ2jdu3CgXFxdJko+Pj/z9/XXo0CGFh4db9qlRo4Zq1qypPXv2KDo62tLesGFD+fr6avv27bpy5YqlvUWLFipbtqw2btyY6V9c+/btVaxYMa1duzZTDV27dlViYqK2bt1qabO3t1e3bt0UExOjoKAgS3vx4sXVoUMHRURE6MCBA5b2MmXKqGXLlgoNDVVISIilnT7RJ/pEnwpznyR3AYVFfn+f9u7dm6M6DOYbfyrdhd69e+vXX3/VmjVr1KlTpyzbN2/erK5du+rxxx/XkiVLcnzcwMBAbdq0SaGhoapatWqW7d7e3rp69eodA13Xrl21d+9eHTlyRKVLl5Z0feLjKlWqqEuXLlq/fv1t35/dlblKlSopJiZG7u7XTybW/oV6P/7qpk/0iT7Rp9v1acgMrsyh8Pjm1fz9PsXGxqpUqVKKi4uzZI/s5PrK3Pjx47VmzRp16dJFXbt2Vdu2beXl5aULFy5o27ZtWrdunVxcXDRu3Li7Om7GFblbhbX4+Hh5enre9hgLFizQunXrtGzZMkuQu1tOTk5ycnLK0u7g4CAHB4dMbXZ2drKzs8uy7/9uC+Ss/ebj5qbdaDTKaMz6KOSt2m9VO32iT3fbTp/ok5T/fQIKE2t9n7Lsl6O9slGnTh1t2LBBAwcO1Jo1a7RmzRoZDAbLL68HHnhA8+fPV506de7quBnPyoWGhqpx48aZtkVFRenq1asKCAi47TH2798vSerVq1e22zds2CCDwaAGDRpkugwKAABga3Id5iSpdevWCg0N1c6dO7V//37Fx8fL3d1d/v7+atWqlQyGu78c3rZtW02aNEkbN27UU089lWnbhg0bLPvcTosWLXT16tUs7VevXtWSJUtUsWJFdenSRT4+PnddHwAAQGGS62fmBg0apHr16mnkyJF5WlBaWppq1Kihc+fOadeuXZa55uLi4hQQEKDTp08rJCRElStXliRFRkYqLi5O5cuXv+Ngi7t5Zu5m8fHx8vDwuON9awBA/hn8mbUrAP5n9oj8PX5Os0eu55lbtGiRLl68mNu335K9vb3mzJkjk8mkNm3aaMiQIXr99dfVoEEDHT9+XBMnTrQEOUkaM2aMatWqddfz2QEAANwPcn2b9YEHHlBkZGRe1mLRvn177dixQ+PHj9eSJUuUmpqqevXqacqUKerTp0++fCYAAIAtyvVt1unTp2vy5Mk6cOCAvL2987quQofbrABgfdxmRWFSWG6z5vrKXI8ePbR161a1bNlSb731lpo2bSovL69sBz0w0AAAACB/5DrM+fn5WaYiefXVV2+5n8FgyPFyFAAAALg7uQ5zAwYMyNXUIwAAAMg7uQ5z8+fPz8MyAAAAkBu5npoEAAAA1ndPK0BI1xekX7t2rfbv36+4uDh5eHjI399fXbt2zXZtUwAAAOSdewpzK1eu1JAhQxQdHa0bZzgxGAwqW7asvv32W3Xv3v2eiwQAAED2ch3mNm/erB49esjOzk6DBg3Sgw8+KC8vL124cEHbt2/XwoUL9eSTT2rDhg3q0KFDXtYMAACA/5frSYNbt26tQ4cO6c8//1TdunWzbD906JBatWqlhg0b6o8//rjnQq2NSYMBwPqYNBiFSWGZNDjXAyD279+vPn36ZBvkJKl+/frq3bu39u3bl9uPAAAAwB3kOsy5uLioTJkyt92nbNmycnFxye1HAAAA4A5yHeY6deqk33777bb7/Pbbb+rcuXNuPwIAAAB3kOswN23aNF28eFEDBgxQREREpm0RERF65plnFBMTo2nTpt1zkQAAAMherkezPvPMM/L09NQPP/ygxYsXy8fHxzKaNTw8XOnp6apfv76efvrpTO8zGAzavHnzPRcOAACAewhz27Zts/w9LS1NJ0+e1MmTJzPtc/DgwSzvYz1XAACAvJPrMGcymfKyDgAAAOQCa7MCAADYsDwLc+Hh4dq+fXteHQ4AAAA5kGdhbt68eWrfvn1eHQ4AAAA5wG1WAAAAG0aYAwAAsGGEOQAAABuWZ2HOw8NDPj4+eXU4AAAA5ECehbkRI0bo1KlTeXU4AAAA5AC3WQEAAGxYjleAyJhDLiAgQM7Oznc1p1ybNm3uvjIAAADcUY7DXLt27WQwGHT06FFVr17d8jon0tPTc10gAAAAbi3HYW7cuHEyGAwqXbp0ptcAAACwnhyHuffee++2rwEAAFDwGAABAABgw3Id5q5cuaKTJ08qNTU1U/uSJUvUv39/Pf/889q3b989FwgAAIBby/Ft1pu99dZbWrhwoS5cuCAHBwdJ0ldffaWXX35ZZrNZkrR48WLt3btXNWvWzJtqAQAAkEmur8z9/vvv6tSpk1xcXCxtkydPlre3t7Zv366lS5fKbDbr448/zpNCUXR88cUXqly5spydndWsWTPt2bPnlvvOnj1bDz74oDw9PeXp6alOnTpl2d9gMGT75+b/NtesWaNmzZqpWLFi8vT01OOPP54f3QMAIE/lOsxFRkaqSpUqltdHjx5VRESEXn31VbVu3Vo9e/bUo48+elfz0QFLlizRqFGjNH78eO3bt08NGjRQly5ddPHixWz337Ztm/r27autW7cqKChIlSpVUmBgoM6dO2fZJzIyMtOfuXPnymAwqEePHpZ9li9frmeeeUbPPfecDh48qJ07d6pfv3753l8AAO5Vrm+zJicny9HR0fL6999/l8FgUGBgoKXNz89PK1euvLcKUaR88sknGjx4sJ577jlJ0tdff601a9Zo7ty5evvtt7Ps/8MPP2R6PWfOHC1fvlybN2/WgAEDJEnlypXLtM+vv/6q9u3by8/PT5KUlpam1157TR9//LGef/55y361a9fO074BAJAfcn1lrmLFijp06JDl9erVq1WyZEnVr1/f0vbvv//Kzc3t3ipEkZGSkqK9e/eqU6dOljaj0ahOnTopKCgoR8e4du2aUlNTVbJkyWy3X7hwQWvWrMkU2vbt26dz587JaDTK399f5cuX18MPP6zDhw/fW4cAACgAuQ5zDz/8sDZu3Kg33nhD//nPf7R+/Xp179490z7Hjx+Xj4/PPReJoiEmJkbp6eny8vLK1O7l5aWoqKgcHWP06NGqUKFCpkB4owULFqh48eJ68sknLW0nT56UdH3uxP/85z9avXq1PD091a5dO8XGxuayNwAAFIxch7kxY8bIx8dHn3zyiSZOnCgvLy+9//77lu0XL17Uzp07WZcVBWby5MlavHixfvnlFzk7O2e7z9y5c9W/f/9M200mkyTpnXfeUY8ePdS4cWPNmzdPBoNBy5YtK5DaAQDIrVw/M1euXDkdOXJEmzdvliS1adNG7u7ulu0xMTH6+OOP1aVLl3uvEkVC6dKlZWdnpwsXLmRqv3DhQpbn3m42bdo0TZ48Wb/99lumW/03+uOPPxQSEqIlS5Zkai9fvrykzM/IOTk5yc/PT+Hh4bnpCgAABSbXYU6SihUrpkceeSTbbbVr1+YBctwVR0dHNW7cWJs3b7ZMC2IymbR582a9/PLLt3zf1KlT9dFHH2nDhg1q0qTJLff77rvv1LhxYzVo0CBTe+PGjeXk5KSQkBC1bt1akpSamqrTp0/L19f33jsGAEA+uqcwB+S1UaNG6dlnn1WTJk0UEBCgzz77TAkJCZbRrQMGDJC3t7cmTZokSZoyZYrGjRunRYsWqXLlypZn69zc3DINvomPj9eyZcs0ffr0LJ/p7u6uF198UePHj1elSpXk6+trmYOuV69e+d1lAADuyT2FufT0dC1dulS//fabzp8/r+Tk5Cz7GAwGy61Y4E769Omj6OhojRs3TlFRUWrYsKHWr19vGRQRHh4uo/F/j3p+9dVXSklJUc+ePTMdZ/z48XrvvfcsrxcvXiyz2ay+fftm+7kff/yx7O3t9cwzzygxMVHNmjXTli1b5OnpmfedBAAgDxnMGWtv3aWEhAQFBgZq165dMpvNMhgMuvFQGa8NBoPS09PzrGBriY+Pl4eHh+Li4jI9GwgAKDiDP7N2BcD/zB6Rv8fPafbI9WjWDz/8UEFBQZowYYJiYmJkNpv13nvvKTIyUkuWLJGfn5969eqV7dU6AAAA5I1ch7mff/5ZzZs313/+859ME7R6eXmpV69e2rp1q3777TfWZgUAAMhHuQ5z4eHhat68+f8OZDRmugpXsWJFdevWTQsWLLi3CgEAAHBLuQ5zrq6umR5E9/DwUGRkZKZ9ypUrxzxdAAAA+SjXYc7X1zdTUKtbt662bNliuTpnNpu1efNmy4SsAAAAyHu5DnMdO3bU1q1blZaWJkl69tlnFR4erhYtWujNN99U69atdeDAAfXo0SPPigUAAEBmuZ5nbvDgwSpVqpSio6NVvnx5DRo0SPv379eXX36pAwcOSJJ69OiRaa4vAAAA5K1czzN3K9HR0Tp58qR8fX3vuJ6mLWGeOQCwPuaZQ2FSWOaZy/PlvMqUKaMyZcrk9WGLDE5UKEzy+0QFALh3uX5mDgAAANaX6ytzfn5+OdrPYDAoLCwstx8DAACA28h1mDOZTDIYDFna4+LidPnyZUlS+fLl5ejomOviAAAAcHu5DnOnT5++7bZRo0bpwoUL2rRpU24/AgAAAHeQL8/MVa5cWUuWLNGlS5f0zjvv5MdHAAAAQPk4AMLBwUGdO3fW0qVL8+sjAAAAirx8Hc167do1xcbG5udHAAAAFGn5Fub++OMP/fjjj6pRo0Z+fQQAAECRl+sBEB06dMi2PS0tTefOnbMMkBg3blxuPwIAAAB3kOswt23btmzbDQaDPD09FRgYqFGjRqlz5865/QgAAADcwT3NMwcAAADruue1WS9evKhz587JZDLJ29tb5cqVy4u6AAAAkAO5GgCRnJysqVOnqlq1aipfvryaNGmigIAAeXt7q3Tp0ho5cuRtJxUGAABA3rjrMBcREaGmTZtqzJgxCgsLU/ny5RUQEKCAgACVL19esbGxmjFjhpo0aaLffvvN8r7IyEjmnAMAAMhjdxXmUlNT1bVrVx0+fFh9+/bV0aNHdfbsWQUFBSkoKEhnz57V0aNH1b9/f8XGxurxxx/X6dOnFRYWptatW+vYsWP51Q8AAIAi6a6emfvmm2905MgRjR8/XuPHj892nxo1auj7779X9erVNX78ePXv31+nT59WTEyMGjdunCdFAwAA4Lq7ujK3dOlSVa1aNUdzx/3nP/9RtWrVFBQUpKSkJG3YsEHdunXLdaEAAADI6q7C3D///KPAwEAZDIY77mswGCz77t69W+3atcttjQAAALiFuwpzV69elYeHR473d3d3l729vapWrXrXhQEAAODO7irMlS1bVidOnMjx/mFhYSpbtuxdFwUAAICcuasw16JFC61bt05RUVF33DcqKkpr1qxR69atc10cAAAAbu+uwtyLL76oq1ev6oknnlBMTMwt9/v333/1xBNP6Nq1axo6dOg9FwkAAIDs3dXUJO3bt9fgwYM1e/Zs1apVS0OHDlWHDh1UqVIlSdcnFN68ebNmz56tmJgYDRkyhIEPAAAA+eiu12b98ssv5e7urk8//VSTJk3SpEmTMm03m80yGo164403smwDAABA3rrrMGdnZ6ePP/5YQ4YM0fz58xUUFGR5hq5cuXJq2bKlnn32WVWrVi3PiwUAAEBmdx3mMlSrVk0fffRRXtYCAACAu3RXAyAAAABQuBDmAAAAbBhhDgAAwIYR5gAAAGxYoQ1zwcHB6tq1q0qUKCFXV1c1b95cS5cuzdF7zWaz1q1bp5deekn169eXh4eHXFxc1KBBA02cOFFJSUn5XD0AAEDByPVo1vy0detWdenSRc7OznrqqadUvHhxLV++XH369FFERIRef/31274/OTlZXbt2lZOTk9q1a6cuXbooKSlJGzZs0DvvvKMVK1Zo27ZtcnFxKaAeAQAA5I9CF+bS0tI0ePBgGY1Gbd++XQ0bNpQkjRs3TgEBARo7dqx69uwpX1/fWx7Dzs5OH374oYYNGyZPT09Le2pqqnr06KFVq1bpiy++0Jtvvpnf3QEAAMhXhe4265YtWxQWFqZ+/fpZgpwkeXh4aOzYsUpJSdGCBQtuewwHBwe98847mYJcRvuYMWMkSb///nue1w4AAFDQCl2Y27ZtmyQpMDAwy7YuXbpIurcg5uDgIEmyty90FyUBAADuWqFLNKGhoZKU7XJg5cqVk5ubm2Wf3Jg7d66k7MPijZKTk5WcnGx5HR8fL+n6rdrU1FRJktFolJ2dndLT02UymSz7ZrSnpaXJbDZb2u3s7GQ0Gm/Zfv24DrnuG5DXMv5bz5DxIygtLS1Tu4ODg0wmk9LT0y1tBoNB9vb2t2y/1fcmb79Pd66dPtlWnySDgMKiIL5POVHowlxcXJyk67dVs+Pu7m7Z526tW7dO33zzjWrVqqXnn3/+tvtOmjRJEyZMyNK+ceNGy8AJHx8f+fv769ChQwoPD7fsU6NGDdWsWVN79uxRdHS0pb1hw4by9fXV9u3bdeXKFUt7ixYtVLZsWW3cuFFSt1z1DcgPa9euzfS6a9euSkxM1NatWy1t9vb26tatm2JiYhQUFGRpL168uDp06KCIiAgdOHDA0l6mTBm1bNlSoaGhCgkJsbTnx/fpxhNh+/btVaxYMfpk432S3AUUFvn9fdq7d2+O6jCYb/ypVAgEBgZq06ZNCg0NVdWqVbNs9/b21tWrV+860AUHB6tjx46yt7fXH3/8oTp16tx2/+yuzFWqVEkxMTFyd79+MsmPX6jDvuDKHAqPL4dzZY4+Fa4+DZnBlTkUHt+8mr/fp9jYWJUqVUpxcXGW7JGdQndlLuOK3K3CWnx8fJaBDXfy119/KTAwUEajURs2bLhjkJMkJycnOTk5ZWl3cHCwPHeXwc7OTnZ2dln2vdVzebdqv/m4gLXd6r/J7NqNRqOMxqyP4d6q/Vbfm/z+PtEn2+4TUJhY6/uU5fNytFcBynhWLrvn4qKionT16tVsn6e7lb/++kudO3eWyWTShg0b1LRp0zyrFQAAwNoKXZhr27atJP3/82OZbdiwIdM+d5IR5NLT07V+/Xo1a9Ys7woFAAAoBApdmOvYsaP8/Py0aNGiTA8PxsXFaeLEiXJ0dNSAAQMs7ZGRkTp27FiW27J79+5V586dlZaWpnXr1qlFixYF1QUAAIACU+iembO3t9ecOXPUpUsXtWnTJtNyXmfOnNG0adNUuXJly/5jxozRggULNG/ePA0cOFCSFBsbq86dO+vy5ct66KGHtGnTJm3atCnT55QoUUIjRowouI4BAADkg0IX5qTrQ9N37Nih8ePHa8mSJUpNTVW9evU0ZcoU9enT547vj4+P16VLlyRJ69ev1/r167Ps4+vrS5gDAAA2r1CGOUkKCAjQunXr7rjf/PnzNX/+/ExtlStXViGbcQUAACBfFLpn5gAAAJBzhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYU2zAUHB6tr164qUaKEXF1d1bx5cy1duvSujpGcnKz3339f1apVk7OzsypUqKAhQ4bo4sWL+VQ1AABAwbK3dgHZ2bp1q7p06SJnZ2c99dRTKl68uJYvX64+ffooIiJCr7/++h2PYTKZ9Nhjj2nDhg1q3ry5evToodDQUM2ZM0ebN2/Wrl27VKZMmQLoDQAAQP4pdFfm0tLSNHjwYBmNRm3fvl3ffvutpk+froMHD6p69eoaO3aszpw5c8fjLFiwQBs2bFDfvn31559/avLkyVq+fLm+/PJLnTx5Uv/5z38KoDcAAAD5q9CFuS1btigsLEz9+vVTw4YNLe0eHh4aO3asUlJStGDBgjseZ/bs2ZKkSZMmyWAwWNqHDh0qPz8//fDDD0pMTMzz+gEAAApSoQtz27ZtkyQFBgZm2dalSxdJ0u+//37bYyQlJWn37t2qUaOGfH19M20zGAzq3LmzEhIS9Ndff+VN0QAAAFZS6MJcaGioJKlatWpZtpUrV05ubm6WfW4lLCxMJpMp22PceOw7HQcAAKCwK3QDIOLi4iRdv62aHXd3d8s+93KMG/fLTnJyspKTk7McMzY2VqmpqZIko9EoOzs7paeny2QyWfbNaE9LS5PZbLa029nZyWg03rI9NTVVKUkOt+0bUJD+/Tc102t7++unjLS0tEztDg4OMplMSk9Pt7QZDAbZ29vfsv1W35u8/D7lpHb6ZFt9SkkyCCgsLl/O3+9TbGysJGX67mSn0IW5wmLSpEmaMGFClvYqVapYoRrAOv47xtoVAEDhVVDnyCtXrtzyApVUCMNcRrG3umoWHx8vT0/Pez7GjftlZ8yYMRo1apTltclkUmxsrEqVKpVpQAUKn/j4eFWqVEkRERGWq7AAgOs4R9oOs9msK1euqEKFCrfdr9CFuRufZ2vcuHGmbVFRUbp69aoCAgJueww/Pz8ZjcZbPhN3u+fyMjg5OcnJySlTW4kSJe5UPgoRd3d3TlQAcAucI23D7S48ZSh0AyDatm0rSdq4cWOWbRs2bMi0z60UK1ZMAQEBCgkJyTInndls1qZNm+Tq6qomTZrkUdUAAADWUejCXMeOHeXn56dFixbpwIEDlva4uDhNnDhRjo6OGjBggKU9MjJSx44dy3JLdciQIZKu3y698cHBb775RidPnlT//v1VrFix/O0MAABAPit0Yc7e3l5z5syRyWRSmzZtNGTIEL3++utq0KCBjh8/rokTJ6py5cqW/ceMGaNatWrpl19+yXScZ599Vl26dNGPP/6oli1b6u2331bPnj01bNgwValSRR9++GEB9wwFxcnJSePHj89ymxwAwDnyfmQw32m8q5Xs2bNH48eP159//qnU1FTVq1dPo0aNUp8+fTLtN3DgQC1YsEDz5s3TwIEDM21LTk7W5MmT9f333ysiIkIlS5bUI488og8//FBeXl4F2BsAAID8UWjDHAAAAO6s0N1mBQAAQM4R5gAAAGwYYQ4AAMCGEeYAAABsGGEOAADAhhHmgP+XMbDbbDaLQd4AAFtBmEORlxHcDAaD5X8z/g4AuO7GH7np6elWrAQ3Y545QNfX/T19+rTCwsJUsmRJtWnTRlWrVlXp0qVlNF7/zWM2mwl5AIq0pKQkOTs7W7sM3MTe2gUA1hQeHq5PP/1Un3/+eZZbq76+vnrkkUfUr18/tWjRgiAHoMg6deqUli5dqsOHDys6Olr169dX48aNVbNmTfn6+qpEiRKSJJPJZPkBjILDlTkUacOHD9fcuXP12GOP6emnn1bZsmW1e/du7du3T8HBwfrnn38kSd26ddO7776rgIAATlYAipQff/xRH3zwgY4dO6ZixYopMTHRsq1ixYrq1KmT+vbtq86dO1uxyqKNMIciKzk5WSVLllSfPn00d+7cLNuPHTumrVu3atGiRdq5c6dq1aqlBQsWqEmTJlaoFgAKXnJysmrUqCEnJye988476tatm86fP6/Dhw/r8OHD2rFjh/766y8lJSWpR48eeu+991S7dm1+9BYwbrOiyNq0aZPS09PVpk0bSZlHsRqNRtWsWVM1a9bUwIEDNW/ePI0aNUpDhgzR6tWrVaFCBWuWDgAF4scff1RkZKTmzZunfv36SZJKlSqlevXqyWQy6eTJk9q5c6cWLlyon376SWfOnNHy5ctVsWJFK1detBCbUWTZ2dnJbDYrOjpa0vXRWQaDwfJr0mQyyWQyqVixYho2bJhGjRqlAwcO6NChQ9YsGwAKzM6dO1W2bFk1bdpU0vXzYsYPX6PRqKpVq+rZZ5/VTz/9pPfff1/79u3TsGHDrFx10UOYQ5HVvHlzOTo66scff1RoaKjs7e0zDXLICHYZQ/B79+4tFxcX7dq1y1olA0CB8vX1VXR0tM6ePSsp61ROGcHOw8ND//nPf9StWzcFBwcrPDzcajUXRYQ5FElms1menp6aMWOGDhw4oHbt2unrr7/WqVOnLOEt42SV8frMmTNKS0vj9gGAIqNFixZKSUnR1KlTFR0dLTs7u0xBTrp+rsw4T7Zq1UpXr17ViRMnrFZzUUSYQ5GUcTLq2bOnxo4dq9jYWL3xxht6+eWX9c033ygoKMjyS9TR0VGnT5/W3LlzZWdnp169elmzdAAoECaTSR07dtQ777yjDRs2qFmzZpo1a5aOHz9umXcz41xqZ2cnSYqKilJqaioDxQoYo1kBSdu3b9fXX3+tTZs2KTY2VhUrVlT16tXl6OgoNzc3BQcHKyoqSiNHjtRHH31k7XIBoMCcP39eU6dO1axZs2Q0GtWiRQt16NBBjRo1Uq1atVS1alUlJSXp+++/1zvvvKMWLVro119/tXbZRQphDkVOdis5mM1mRUREaP/+/dq9e7f27t2ro0eP6uzZs3J1dZWPj4/eeecdPf7443JxcbFS5QBgPbt27dK3336r9evXKyoqSsWLF1fJkiXl4OAgJycnHTlyRE2aNNGsWbMUEBBg7XKLFMIciqRr167J3t5eZ86cUbFixTI9B5eYmKiLFy/KwcFBycnJio2NVePGja1YLQAUrOx+9JpMJsXExCg0NFR79+7Vrl27FBwcrH///Vd16tRRtWrVNGnSJHl5eVmp6qKLMIciJTk5Wb///rtmzZqlXbt2yc3NTUajUZUrV9bDDz+sp556St7e3tYuEwCsymQy6fz584qNjVVUVJRq166d6UdvcnKyJMnJyUlRUVFyc3OTm5ubJNaxtgbCHIqUzz77TBMmTFBycrIaNmxoWb7rwoULkq5PFtyrVy+99NJLat26teWExIkJQFFx4sQJffnll1qwYIESEhKUkpIig8GgevXqqU+fPurfv798fHwyvYcAZ12EORQZSUlJqlChgurUqaOlS5fK3d1drq6ukqTdu3dr2bJlltnOK1SooEmTJumZZ56xctUAUHBSUlLUrVs3bdmyRS1btlSrVq0UExOj4OBghYSEKCUlRZLUo0cPvf7662revLmVK4ZEmEMRsnDhQg0ZMkQLFy7Uk08+KSnrr8n09HTNnTtX06ZNU2hoqObMmaNBgwZZq2QAKFDfffedhg0bpvfee09jxozJtG3Pnj1as2aNli9frn/++Ufe3t6aNWuWHnvsMStViwzMM4ciIyQkREaj0bKuampqqiXImUwmpaeny87OToMHD9ZXX31lmVT40qVL1iwbAArM0qVL1bBhQz311FOSpLS0NMuEwAEBAZowYYJ2796tmTNnKj09XYMGDdL69eutWTJEmEMR0rJlS127dk1HjhyRJDk4OFi2GY1Gy6SXZrNZHTp00Lhx43T06FEdOHDAGuUCQIFKSkpSamqqEhMTVa5cOUnXnxfOODdmrFft6uqq4cOHa+bMmbp06ZIWLlwo6X8rQqDgEeZQZDRq1Ei1a9fWsGHD9MUXX+jff//Ndr+0tDRJkoeHh0wmk+Li4gqyTACwCmdnZzVq1EiHDx+2rEGdEeSk6z96jUajZT3WHj16qGvXrtq/f79Onz7NAAgrIsyhyPDy8tKECRNUvHhxvf322xo9erT+/PNPyy2EDBnzyx08eFBGo1EdOnSwUsUAULCeeeYZeXh4qE+fPvrmm28UFRWVZR+TySSDwaCUlBSVKVNGMTExKlu2rBWqRQYGQKDICQoK0ocffqh169ZJkpo3b65HH31UjRo1ssxkvmrVKn366afq2bOn5RYCABQFM2bM0NixY2U0GvXEE0/oqaeekr+/v0qUKKFixYpZ9tu1a5cGDx6sChUqaMOGDVasGIQ5FBlpaWmW2wTHjx/XmjVrtHLlSgUHB+vatWuys7OTs7OzEhISJElPP/203n33XVWrVs3KlQNAwQoKCtLEiRO1adMmpaWlqXHjxnrwwQdVpUoVOTs7S5KmT5+u8+fPa8mSJerSpYuVKy7aCHMo0q5du6Y///xT+/fvV0xMjOLj45Wenq6ePXuqTZs2lpMWABQFqampcnBwkNlsVmhoqLZu3arNmzcrODhYUVFRlpUfJMnT01Nffvml+vTpY8WKIRHmUATExsbqr7/+UlBQkDw9PeXk5CRvb281btxY5cuXt+yXnJwsJycnK1YKANZ37do1ubi4WF7HxcXpyJEjioiIUHJyss6dO6eqVauqZcuWLH9YSBDmcF/bsWOHRo8eraCgIEnXh9mbzWa5uLiodu3a6tSpk7p27aqAgAA5OjoqJSVFjo6OVq4aAApWUFCQfv75Z8XExMjR0VGenp5q1KiROnbsqFKlSlm7PNwBYQ73raSkJDVs2FDR0dGaMGGCypYtKzs7O0VFRem3337Tpk2bdO3aNVWrVk3Dhg3T8OHDZW9vb+2yAaDApKWlafLkyRo3bpwkqUSJEkpOTlZiYqIkydfXV4888oj69u2r5s2by2g0Wm7FovAgzOG+NWfOHL322muaNWuWnnvuuSzbT506pWXLlmnevHkKCQlRv379NHPmTHl6elqhWgAoeD/88IOee+45de3aVePGjZPJZFKxYsV09OhRLV68WCtWrJDJZJKvr69GjBih1157zdolIxuEOdy3+vTpo/3792vNmjWqVq1atr8mTSaT9u7dqw8++ECrV6/WZ599pldffdVKFQNAwWrZsqXs7e317bffqmbNmlm2x8fHa+7cufriiy90+vRpvfbaa/rggw8yTVEC62PSYNyX0tLSVLp0aZ0/f96yLE12twWMRqOaNm2q+fPnq3Hjxpo5c6auXbtW0OUCQIGLjY3VqVOn5Ovrq+rVq1tWdpD+t161u7u7RowYoSVLlqhZs2b65JNP9Pvvv1u5ctyMMIf7jtlslr29vVq1aqVr165p1KhRunTpkqT/naBulJaWppIlS6pNmzaKjo5WSEiINcoGgAJlNptVvnx5nTx5UkajUQaDwbIk143rVUvXl0NcuHChHBwcLLdeUXgQ5nDfyTgZtW3bVm3atNF3332nMWPG6PTp05lOUOnp6Zbgl5ycLIPBIJPJxCTBAIqEUqVKqUOHDgoKCtJ7772n2NhYSVl/9Gb83dvbWw0aNNCBAwcsa1ijcCDM4b7l7e2txYsX67HHHtO3334rPz8/9enTRytXrlRKSors7OwstxS2bt2qJUuWqE2bNnJzc7Ny5QBQMAYNGiRfX19NmTJF7777rk6cOJHlqlzG30NDQ5WamiovLy+mcCpkGACB+1Z6errs7Ox06tQpzZ8/X1999ZViYmIkScWLF1erVq1UrVo1HTx4UDt37lTlypU1f/58tWrVysqVA0DBCQ0N1ciRI7V27VpJUrdu3TRo0CC1bdtWjo6OSkxMlKenp1588UXNnz9fy5cv12OPPWblqnEjwhzuS2az2XK7NUNqaqqWLl2qH374QcHBwUpISJC9vb1SU1PVvXt3vfnmm2ratKmVKgaAgpeWliZ7e3uFhIRo0aJFWrRokcLCwiRJLi4u8vf3l8lk0j///KO4uDgNGjRIc+bMsXLVuBlhDvclk8mkiIgI+fr66vLlyzIajXJ3d7dsj42N1eHDh+Xp6Wn54+rqmm0IBICiIi4uTmvXrtW6desUEhKihIQExcbG6oEHHtBzzz2n3r178yhKIUSYw30lMTFRn3zyiTZs2KC///5bjo6OatCggRo2bKjGjRurXr168vPzk7Ozs7VLBYACd+MP1iNHjshkMsnV1VWJiYny9vZWiRIlLPvGxMTo8uXLqlKlipKSkuTq6mqlqnEnhDncN1JSUtSvXz/9/PPPql27tlxdXWUymXT58mWFh4fL3t5eTZs2Vf/+/fX0008z6SWAIsdsNmvfvn169dVXdejQISUkJKhEiRLy9fVV3bp11aJFC7Vo0UJ169ZlyS4bQpjDfeO7777T8OHDNXz4cE2YMEFubm6KiorSuXPndPz4cW3ZskUbN25URESE2rdvr0mTJikgIIBbqwCKjDVr1mjIkCFKSEjQo48+KqPRaHkm7u+//1Z6eroaNWqkAQMGaNCgQXJxcbF2ycgBwhzuG23btlVqaqp++OEHValSxTKaNUNsbKz279+vefPmadGiRWrWrJnWrl3LWqwAiozWrVvr8uXL+vzzz9WhQwdJ0uXLl3XlyhWFhoZq9erVWrFihU6fPq1HHnlEH3/8sWrUqGHlqnEnhDncF+Lj49WmTRt5eHhkWWrm5itvJpNJ06ZN09tvv61XXnlFM2bMKOhyAaDARUZGqkqVKnrzzTf1/vvvS1KWuxLXrl3TgQMHNGvWLC1evFiPP/64li1blumHMQofJg2GzTObzXJzc1OtWrX0999/6/Dhw5Z2k8lkOVllrDtoNBo1atQoNWjQQHv37lVcXJw1yweAAnHixAk5OjrKzs7ulo+WuLi4qGXLlvr22281YsQIrVixQqtXry7gSnG3CHOweQaDQUaj0XL74I033tDJkyct7ZIyLSAtXV93sFq1aoqMjJSTk5O1SgeAAlOrVi1VqFBBK1asUEREhGUJw5vXWTWZTHJzc9Pw4cPl4uKiHTt2WKli5BRhDveN4cOH66233tLGjRvVqFEjvfXWW/rzzz+VlJRkCXY3Dsk/evSoatSowTQlAIqE0qVL6+GHH9ahQ4c0duxYnT9/Xkaj0fKj9+Y1WZOSklS2bFldunTJWiUjh+ytXQCQFzKei3v99ddVrFgxTZ06VdOmTdOPP/6o5s2bq2nTpmrWrJlq1Kih3bt365NPPtGJEyc0depUa5cOAAVm4sSJSkxM1Lfffqvly5dr8ODB6tmzp1q2bJnlubhNmzYpPDxc3bp1s1K1yCkGQOC+cPMgh3Pnzmnu3Ln6+eefdfDgwSz7lyhRQm+88YbGjh1bkGUCgNWYTCYZjUadPXtWX375pT799FMlJyfL2dlZjRs3VosWLdSuXTslJSVp+/btmj17tmrXrq3g4GBrl447IMzhvmUymRQdHa2QkBDt3r1be/bskaurq6pXr64WLVqoffv21i4RAKwmNjZWc+fO1aJFi3TgwIEs2x977DG98cYbatWqVcEXh7tCmIPNO3jwoEJDQ3X8+HHLQIhq1aqpbNmyWUZsJScnM+ABQJGSceci48pcdk6cOKEtW7YoPDxcvr6+Klu2rDp37sykwTaCMAeblZaWpm+//Vbvv/++Ll68mGlbuXLl1KVLF/Xt21eBgYGZtt3uhAYA95v09HQtWLBA//zzj06cOKEHHnhATZo0UfXq1eXj46OSJUtmO48cq+PYDsIcbNaSJUs0ePBgVatWTS+88IIaNGig/fv368CBA9q7d68OHTokk8mkFi1aaNy4cercuTMhDkCRsm/fPr3//vtauXKlnJyclJycbNlWtmxZtWvXTr169VL37t3l6OgoiRBniwhzsFnNmjWTyWTSokWLVK1atUzbTp06pe3bt+unn37SmjVr5OHhodmzZ6tnz55WqhYACl737t21c+dOvfjiixo4cKDS09N16NAh/fPPPwoKCtKePXsUHx+v9u3ba8KECWrdujVhzgYR5mCTLl68qJo1a2rAgAH67LPPJF2/lXDjRMEZbStWrNArr7wik8mk5cuX8zAvgCIhIiJCvr6+evvttzVx4sQs28PDw7Vnzx4tW7ZMy5YtU9myZbV06VK1adPGCtXiXnDPCTYpLi5Obm5uOnfunKTroe3GyS8zlvKys7NTjx499Mknn+jixYvatm2bZTsA3M82b94sJycnNW7cWNL154VvXA3Hx8dHPXv21Lx58zR37lwlJyfrpZde0oULF6xZNnKBMAebVK1aNfn4+GjTpk3aunVrtmsNGo1Gy0mrV69e8vPz0549e5SWlsYtBAD3vVKlSslsNuvUqVOS/hfmbl6v2sXFRQMHDtTIkSN19OhRHTlyxJplIxcIc7BZU6dOldFo1EMPPaSPPvpIx44dU2pqqiRZTlYZr0NCQmRnZydnZ2fZ27PwCYD7X7NmzVSsWDHNnTtXR44ckb29faa7F9L1c2VaWpokqW3btnJ1dWWSYBtEmIPNCggI0Icffig3NzdNmDBBL730kmbOnKmdO3cqIiJC6enpcnR0VGpqqr7//nuFhYWpX79+1i4bAPKdyWRS2bJlNXPmTIWEhKh58+b68MMP9ffff1vuTtx8h+LUqVNKSEhQvXr1rFQ1cosBELB5R48e1YwZM7R69WqdP39e5cqVU506deTh4SFXV1edOXNG27dvV9euXbV69WprlwsABebKlSv64osv9NFHHykhIUFNmjRRp06d1LRpU9WuXVs1atSQJO3YsUMjRoxQZGSk5Vlk2A7CHGzWjc9+REVF6cCBA9q1a5d2796to0ePKjw8XJLk7e2t3r1766233pKXl5c1SwYAqwgJCdFXX32lX3/9VWfOnFHx4sXl5eUlJycneXh4aO/evSpZsqTGjRunoUOHWrtc3CXCHGxGRnhLTU2V0WhUdHS0UlJS5OPjY9knJSVFkZGRltsI4eHhatKkidzc3KxYOQAUnFutchMbG6uwsDD99ddfljnmzpw5Iz8/P3l7e2vChAkKCAjIdjUIFG6EOdiUY8eO6auvvtLq1avl5OQks9ms8uXLq0OHDnrqqadUtWpVa5cIAFYXExOjhIQEnT59Wj4+PqpSpYplW0pKilJSUuTm5qaLFy8qJSVFFStWtGK1uFeEOdiMrVu36rXXXtPhw4f1wAMPqHr16jp06FCm5zseeughDRs2TJ07d5aTkxPrsAIoUv79918tX75cn3zyic6ePav09HSlp6frgQceUM+ePdWvXz/VqlXL2mUijxHmYDPatm2rsLAwzZkzR+3atZOdnZ0cHBz0999/a9myZVq8eLFOnDghFxcXjR49Wu+++661SwaAAjVy5Eh99dVX8vb21oMPPihHR0ft3r1bYWFhunbtmiSpffv2Gj16tDp16mSZj5O5N20bYQ424ezZs6pSpYree+89jR07VgaDIdsT0PLlyzV16lQFBwfrrbfe0oQJE+Tk5GSlqgGg4Jw5c0bVqlXTk08+qUWLFkmS5c7EwYMHtW7dOq1YsUJ79uyRs7OzJk+erFdffdWaJSOPcP8JNmH//v0yGAwqUaKEDAaDUlJSLEHOZDIpPT1dktSjRw/997//VaNGjTRz5kz9888/1iwbAArM4sWL5ebmpiFDhlhCXMaEwA0aNNDbb7+tP/74Qz/++KOqVq2qESNG6IsvvrBmycgjhDnYhLp160qSDh06JElydHS0bDMajZbRV2azWTVq1NBXX32lxMRE7dixo+CLBQAruHDhgkwmk0qWLCnp+prVGSvemEwmmUwmOTg4qE+fPlqwYIHKly+vr7/+WlevXrVm2cgDhDnYBG9vb/Xo0UOzZ8/W2LFjFRERke1+Gb9CjUajSpQooTNnzhRkmQBgNW3atFF8fLx27dolSXJwcLBsMxqNma7W+fv7a/jw4Tp9+rT27NljlXqRdwhzsAmOjo5688039cADD2jq1KkaMWKENmzYoOTk5Ez7ZZy89u/fr/j4eLVt29Ya5QJAgWvVqpUaNmyo4cOHa8KECTp16pRufiz+xtfFixdXYmJipjsdsE0MgIBNOXnypCZMmKAlS5YoJSVFDRs21OOPP64WLVrI1dVVjo6OCgsL04gRI+Th4aFjx45Zu2QAKDCrVq3S4MGDFR0drccee0x9+/ZV8+bNVbp0aTk7O1ueNY6Ojtarr76qDRs2KDY21spV414R5mATMgY5ODg46OzZs5ZRWTt37lR8fLyMRqM8PDx06dIlSdcf9p00aZIeeughK1cOAAUrLCxMH3zwgX755RdduXJF9erVU7t27VS7dm25urrKxcVFCxcu1Jo1a/T6669r4sSJ1i4Z94gwB5uVmppqWYv13LlzunLlimJjY/XII4+oS5cu8vb2tnaJAFBg0tLSZGdnZ1nK8Pfff9emTZsUFBSkiIgIpaSkZNp/3Lhxevnll1W6dGkrVYy8QphDoZaWlqaQkBBt3LhRrq6ucnBwUKlSpdSwYcNMa7ImJycznxyAIi8lJSXTM3DXrl3T33//rbCwMCUkJCgyMlKurq566KGHVKdOHStWirxEmEOhderUKU2fPl1ffvllpvZixYqpWrVqateunbp27aqWLVvKzc0t069SACgqTp48qbVr1+rIkSNydHSUi4uL6tSpo/bt23OHooggzKHQ6tWrl1asWKHBgwerWbNmsre3V1xcnLZv366NGzfq8uXLKl++vJ577jm9+uqrKlu2rLVLBoACtWTJEr311luKiIiQwWCQi4uLEhISJEnlypXTww8/rD59+qhdu3ZydHRUampqpilLcH8gzKFQOn36tKpWraqRI0dq6tSpWa62nT9/XitXrtTcuXP1119/qX379vrmm29UtWpVK1UMAAUrIiJCjRo1kqenp2bMmCFXV1cVL15cZ86c0c8//6zly5crMTFRnp6eGjp0qEaPHi0PDw9rl418wDxzKJTWrFkjR0dHtW/f3rJ8140qVKigF198UQsXLtRLL72krVu3atKkSZZlvQDgfjd79mwZjUZ9+umnevjhh9WmTRv5+/vr8ccf13//+19dvnxZc+fOla+vr6ZMmaLnn39e0dHR1i4b+YAwh0LJwcFBSUlJcnFxsbzOTvXq1TV9+nS98MILmjdvnsLCwgqyTACwmj///FPly5eXv7+/pP+tgHPjVE4DBw7Uzz//rP79++vnn3/W999/b82SkU8IcyiUmjdvrmLFimncuHE6ceKEDAaDzGZzlitvqampcnZ2VmBgoIxGo4KCgqxUMQAUnNTUVPn5+SksLMyyFmvGOqw3rlctSZUrV9ZXX32lBg0a6L///a/i4+OtUjPyD2EOhVK1atX09NNPa8eOHRo9erQOHDggg8FgOUGZTCaZzWbLFbuEhAQZDAZGbgEoEhwcHNSmTRslJCRoyJAhlnWob/7RazabZTKZ5OrqqmbNmuns2bOKioqyVtnIJ4Q5FErFihXTrFmz9Morr+iXX35Ro0aN1LVrVy1evFhXrlyR0Wi0DIq4cOGC5s2bp5IlS6pTp05WrhwACsZDDz2kjh07auHChXrrrbe0d+/eTD96JclgMMhoNOry5ctKTk6Wg4ODqlevbsWqkR8YzYpCyWQyyWg06uLFi/rxxx/1+eef69SpU5IkFxcXtWzZUk2aNFFYWJh27NihuLg4ffDBBxo5cqSVKweAgnPlyhWNHDlSc+fOlSS1bdtWL7zwgh566CG5ubnp2rVr8vT01Ndff63Ro0erf//+WebuhO0jzKHQMZvN2U78++uvv2r+/PnasWOHLl26JCcnJyUmJqpx48Z688039cgjj1gGTADA/S4tLU329vY6e/asli1bpgULFujQoUOSrj8/FxAQIE9PTx07dkxhYWFq1aqV5s+frwceeMDKlSOvEeZQKJ07d07e3t5KTExUamqq3N3dLduuXr2qffv2SZK8vb3l5uYmLy8va5UKAIVCcnKy1q9fr1WrVungwYOKj4/XlStX5OjoqP79++ull15SxYoVrV0m8gFhDoWG2WzW6tWr9d133+nvv//W1atXVb9+fdWvX1/+/v6qV6+eqlatKldXV2uXCgBWdfHiRUVHR6tUqVKKi4tT6dKlVapUKcv2S5cu6fz585bw5u7uzlKH9zHCHAqNcePGadq0aXJxcVGlSpWUmpqqlJQURUREyGw2q0GDBurZs6eeeeYZlStXztrlAkCBi4yM1DvvvKNNmzbp3LlzKl68uKpUqaKaNWsqICBALVu2VP369S2PnNzqsRXcXwhzKBROnz6tOnXqqF27dpo+fbpq1qypmJgYRUREKCwsTNu3b9eGDRsUGhqqBg0aaOLEiXr44YctAyUA4H4XFRWlJ554Qrt377YMcDAajTpz5owOHTqkxMRE1a5dW71799YLL7ygChUqWLtkFBDCHAqFDz74QJ999pmWLl2qjh07Wh7szRAfH68jR45o6dKlmjFjhry8vLRu3To1bNjQekUDQAEaP368ZsyYoQkTJui1116TJF2+fFlXr17VqVOntHHjRv388886duyYmjVrpo8//litWrXi6lwRQJhDofDss89q06ZN2r9/v7y8vCwnn+xOQkuWLNHQoUNVq1YtVnwAUGTUqVNHfn5+mjt3rsqUKZPl/JicnKyQkBAtWLBAn376qWrUqKHff/9dZcuWtWLVKAjcn0KhUL9+fUVFRemPP/6QdH2iS5PJlOlElfG7o0+fPnryySd14sQJhYSEWKVeAChIFy5ckNlsVnJyssqUKSNJWX7oOjk5qX79+poyZYpmzJihkJAQffLJJ9YoFwWMMIdCISAgQK6urnr33Xf1119/SZLlWbiM5WgyAp50fbmvxMRE1hgEcN8zm80qU6aM6tSpo927d2vPnj2W9pvXq5auzzH3yiuvqG7dugoODtbVq1cLumQUMMIcrM5sNuvBBx/Up59+qtDQUAUEBGjo0KHavHmzrly5YlmORroe8BITE/X333/L2dlZTZs2tXL1AJC/Ms6BgYGBunLlit544w0dOXIky3rV6enpljsY8fHxqlSpki5evCg3Nzdrlo8CYH/nXYD8lXGroG/fvkpLS9P48eM1e/ZsrVixQi1atFCzZs0UEBCgRo0aKTQ0VHPnztXy5cv1yiuvWLlyACg4gwcPVmxsrMaOHat69eppwIAB6tevn9q0aSNnZ2dJ/3scJTg4WAcPHlTXrl2tWTIKCAMgYHU3P8SbkJCgOXPmaMmSJQoODrbcRjAYDLK3t1dqaqoGDhyoDz74QN7e3tYqGwAKTMZ58vLly5o7d66mTJmi6Oho2dnZqXHjxmrVqpXat28vDw8PBQcHa9asWbpy5Yq2bNmievXqWbt85DPCHAqtmJgYHT9+XLt27dIff/yh9PR0Va9eXbVq1dLzzz9v7fIAoMDc/KM3KSlJCxYs0H//+99sR/XXrl1bY8aMUf/+/QuyTFgJYQ5WdfHiRf399986fvy4rl69qoCAANWsWVOlS5e2PAuSITk5WU5OTpbXzJ0EAFJ4eLh+++03HT58WOXKlVPZsmXVunVrVa1a1dqloYAQ5mA169at04cffpjlV2XJkiXVsWNH9enTR927d5eDg4NlGys+AChq1q9fr8OHD+vAgQPy8vJSkyZNVLVqVVWqVEmlSpXKdI5E0USYg1VERESoXbt2SkhI0MCBA9W+fXudPHlS+/fv18GDB3Xo0CElJyerdu3aGjt2rHr27ClHR0euxgEoMi5fvqxJkybp448/lp2dXaZpSEqWLKlWrVrpiSee0KOPPqqSJUtatnGeLHoYzQqr+Oabb3Tp0iXNmTNHTz75ZKZtZ8+e1Z9//qmVK1dq0aJFevrpp3X27Fm99dZbnKAAFBmzZ8/WrFmz9Pjjj+vVV19VhQoVtH//foWEhCg4OFhBQUFatWqV/P399e677+rxxx+XlHUyYdz/uDIHq2jevLmKFSumZcuWqXTp0kpLS8s0Z1KGrVu36vXXX9c///yjL7/8UoMGDbJSxQBQsCpXrqy6detqwYIFKlWqVKZt58+f1/79+7Vy5UrNnTtX6enp+vbbb/XCCy9YqVpYEw8focBdvXpVxYsXV1RUlFxcXCRdnww4I8hlrPggSe3bt9d3330nFxcX/frrr5btAHA/O3bsmP799181aNDAEuRMJpPl3FihQgV169ZNM2fO1K+//qoqVapo9OjRrFddRBHmUODc3NzUuHFjhYSEaPHixZKUZVBDxmuTySR/f3+1adNGx44d05kzZ7iFAOC+ZzabVaJECYWFhUmS0tLSJGVe5tBsNsvR0VFdu3bVJ598okuXLlnWt0bRQpiDVWSsG/jCCy/o1Vdf1b59+5SUlCTpf897pKWlyWg0Kj4+Xo6OjkpKSpKvr681ywaAAlGrVi15e3tr7dq1Wrdunezt7bP86L1xveoHH3xQlStXVnBwsDXKhZUR5mAV3t7eev/991W5cmXNmjVLQ4cO1bRp07Rt2zadOXNGSUlJsre/Pj5n1apV2rZtmx5++GErVw0A+S/jUZLPP/9c7u7u6tatm0aOHKk9e/Zk+dGbmpoqSQoJCVFycrIqVKhgnaJhVQyAQIG6ech8bGysJk2apKVLlyoiIkJlypRR3bp1VaFCBbm4uCgxMVFLly5VlSpVtGLFCtWoUcOK1QNAwUlPT9fChQs1ZswYRUVFqXbt2goMDFTLli1Vu3Zt1axZU0ajUefOndObb76pZcuWaffu3WrUqJG1S0cBI8yhwGUEurNnz6pChQoyGo06fPiwVq9erW3btuno0aOKiIiQJHl6eqphw4b6/PPPVadOHStXDgAFLzo6WrNmzdLSpUt1/Phxubi4yNvbW25ubipZsqSOHTum6OhoPffcc/ryyy+tXS6sgDCHApOWlqadO3dq7ty5On78uAwGg1xcXNS0aVP17t1b/v7+MpvNioiIUGJiok6ePKmaNWuqUqVKsre3ZyJMAEVKxsh+Ozs7JSYmKjQ0VMHBwdq5c6d2796tY8eOqUyZMqpUqZJeeOEFPf3003J1dbV22bACwhwKzLRp0/TBBx/oypUrqlq1quzs7BQSEmLZXrt2bQ0bNkw9e/ZU2bJlrVgpABROJpNJSUlJcnR0VFxcnKKiorhrAcIcCsapU6dUr149NWrUSAsWLJCjo6O8vLwUFRWlVatWadmyZdq2bZuk63PLTZkyRU2aNLFu0QBQgBITExUeHi4fHx8VK1Ys0zaTySSDwWC5O3HznQrWrS7aCHMoEOPGjdM333yjRYsWqWPHjpKynoz+/vtvTZs2TUuXLpWvr69++OEHNW7c2FolA0CBmjx5spYvX64nn3xSzZs3V40aNeTl5ZVpZZyM/8vOOHdGR0fL09PTMvofRRNhDgWiR48eOnDggLZu3SofHx+lpaVZnoPLeCYkw4wZMzRy5Eg9++yzmjdvnhWrBoCCU7FiRZ0/f152dnby8PBQy5YtFRgYqGbNmsnPzy/Lkl4JCQl677339O+//2rOnDlcmSvCiPIoEP7+/vrll1909epVSbL8irxxPdaMK3Wvvfaa/vjjD23ZskUnT56Un5+f1eoGgIJw/PhxxcXFqUWLFurXr582bdqkoKAgrV69Wj4+PmrXrp06deokf39/eXt7q0SJEjp8+LBmz56tdu3aEeSKOMIcCkT79u0lSf3799f06dPVunVrOTo6ZtkvPT1ddnZ2qlGjhtatW2cJfwBwPzt+/LiSkpIUGBio4cOH65FHHlFISIiCgoK0ZcsWLV++XD/88INq166tDh066KGHHtLmzZsVHx+vwYMHW7t8WBm3WVEg0tPTNXr0aH3yySeqWbOmhg8frp49e8rLyyvLvpcuXdKIESO0bt06Xbx40QrVAkDB+umnn9S7d28tXrxYvXv3trSnpqbqzJkzOnjwoP744w/LXJwODg4ym81ycnJSbGysFStHYUCYQ4H65ptv9PHHH+vkyZOqUKGCnnjiCT388MOqVKmS7OzsVKJECc2cOVOfffaZhg0bpunTp1u7ZADId2azWceOHZOzs7OqVKmS7byaCQkJOn78uEJCQjRv3jxt2rRJL7/8sj7//HMrVY3CgjCHAmU2m3XixAnNnj1bixcv1tmzZyVJZcuWlYODgyIjI2UymdS3b19NmTJFFStWtHLFAGBd2QW7V199VbNmzdLevXvl7+9vpcpQWBDmYDUJCQnas2ePVq5cqfPnz+vixYtyd3dX79691aNHDzk7O1u7RAAoNDLmkjt9+rQee+wxXbp0SeHh4dYuC4UAAyBgNa6urmrfvr3at2+v1NRUOTg4WLskACi0Mkasnjt3TqmpqRo2bJiVK0JhwZU5AABsiNls1tmzZ1WyZEnWYoUkwhwAAIBNY5ZBAAAAG0aYAwAAsGGEOQAAABtGmAMAALBhhDkAAAAbRpgDAACwYYQ5AAAAG0aYAwAAsGGEOQAAABv2fwYQZJkoNozxAAAAAElFTkSuQmCC" 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" }, - "execution_count": 28, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from qiskit.visualization import plot_histogram\n", - "\n", - "evidence = {str(i): 0 for i in range(n - 1)}\n", - "# Initialize quantum bayesian\n", - "qbayesian = QBayesian(circuit=qc)\n", - "# Inference\n", - "samples = qbayesian.rejection_sampling(evidence=evidence)\n", - "print(samples)\n", + "# Sampling\n", + "qb_2n.threshold = 0.97\n", + "samples = qb_2n.rejection_sampling(evidence=evidence)\n", "plot_histogram(samples)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:06.927046Z", - "start_time": "2023-11-13T17:24:06.032255Z" + "end_time": "2023-11-24T10:51:29.976190Z", + "start_time": "2023-11-24T10:51:29.861726Z" } }, - "id": "cbb3c2d9a11b43ac" + "id": "a6fc4d5d394d301a" }, { "cell_type": "markdown", "source": [ - "# Step 5: Burglary Alarm Example: \n", - "\n", - "Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." + "#### 3.1.2. Burglary Alarm Example\n", + "For the advanced example, we can do this in the same way. However, we look at the trivial case of how to obtain the joint probability of the network. This can be calculated by providing no evidence for the rejection sampling method." ], "metadata": { "collapsed": false }, - "id": "72989e15f2fdd872" + "id": "9f6ab51740b00957" }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 57, "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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" 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" }, + "execution_count": 57, "metadata": {}, - "output_type": "display_data" + "output_type": "execute_result" } ], "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# Create a directed graph\n", - "G = nx.DiGraph()\n", - "# Add nodes\n", - "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", - "# Add edges\n", - "G.add_edges_from(\n", - " [(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"), (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")]\n", - ")\n", - "# Manually set positions\n", - "pos = {\n", - " \"Burglary\": (0, 1),\n", - " \"Earthquake\": (1, 1),\n", - " \"Alarm\": (0.5, 0.5),\n", - " \"JohnCalls\": (0, 0),\n", - " \"MaryCalls\": (1, 0),\n", - "}\n", - "# Draw the network\n", - "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", - "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", - "plt.show()" + "# Initialize quantum bayesian inference framework\n", + "qb_ba = QBayesian(circuit=qc_ba)\n", + "# Inference\n", + "counts = qb_ba.rejection_sampling(evidence={})\n", + "plot_histogram({c_key: c_val for c_key, c_val in counts.items()})" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:07.016037Z", - "start_time": "2023-11-13T17:24:06.935911Z" + "end_time": "2023-11-24T10:51:30.056180Z", + "start_time": "2023-11-24T10:51:29.975890Z" } }, - "id": "16f5ec62b6f90570" + "id": "8d4904619b35503a" }, { "cell_type": "markdown", "source": [ - "The Bayesian Network for this scenario involves the following variables:\n", - "\n", - "Burglary (B): Whether a burglary has occurred.\n", - "Earthquake (E): Whether an earthquake has occurred.\n", - "Alarm (A): Whether the alarm goes off.\n", - "John Calls (J): Whether John calls you.\n", - "Mary Calls (M): Whether Mary calls you." + "\n", + "## 4. How to Run an Inference" ], "metadata": { "collapsed": false }, - "id": "85ffd7ab1e8316e4" + "id": "5d22c72ca6352a56" }, { - "cell_type": "code", - "execution_count": 30, - "outputs": [], + "cell_type": "markdown", "source": [ - "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", - "theta_E = 2 * np.arcsin(np.sqrt(0.002))\n", - "theta_A_nBnE = 2 * np.arcsin(np.sqrt(0.001))\n", - "theta_A_nBE = 2 * np.arcsin(np.sqrt(0.29))\n", - "theta_A_BnE = 2 * np.arcsin(np.sqrt(0.94))\n", - "theta_A_BE = 2 * np.arcsin(np.sqrt(0.95))\n", - "theta_J_nA = 2 * np.arcsin(np.sqrt(0.05))\n", - "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_M_nA = 2 * np.arcsin(np.sqrt(0.9))\n", - "theta_M_A = 2 * np.arcsin(np.sqrt(0.3))" + "### 4.1 Set Up\n", + "Quantum Bayesian inference is here based on quantum rejection sampling. Quantum rejection sampling plays a pivotal role in the inference process that follows. After the quantum state is manipulated to include evidence, measurement is performed. However, in quantum rejection sampling, only those measurement outcomes that align with the evidence are considered, effectively 'rejecting' irrelevant outcomes, similar to the traditional rejection sampling method.\n", + "\n", + "The synergy of quantum state manipulation with quantum rejection sampling leads to a more efficient inference process compared to classical approaches, harnessing the inherent parallelism of quantum computing to simultaneously process multiple probabilities. This advanced method has significant implications in areas like quantum machine learning and data analysis, where it could outperform classical algorithms in tasks such as pattern recognition and decision-making.\n", + "\n", + "You can use the `inference` method from `QBayesian` to estimate probabilities given evidence." ], "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-13T17:24:07.019984Z", - "start_time": "2023-11-13T17:24:07.014632Z" - } + "collapsed": false }, - "id": "f79d7c9a5cca338" + "id": "d66d7e40d62819b6" }, { "cell_type": "markdown", "source": [ - "The Bayesian network can be represented by the following quantum circuit:" + "#### 4.1. Two Node Bayesian Network Example\n", + "Using `QBayesian`, you can draw various probabilistic conclusions. For the Bayesian network with two nodes, this is limited due to the number of variables. However, if we want to know what the probability of P(Y=0|X=1) is, we can do the following:" ], "metadata": { "collapsed": false }, - "id": "d2693a276552450f" + "id": "b3916bfec5e40bfc" }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 58, "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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+ "text/plain": "0.0985" }, - "execution_count": 31, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# Initialize register\n", - "var = [\"B\", \"E\", \"A\", \"J\", \"M\"]\n", - "qr = [QuantumRegister(1, name=v) for v in var]\n", - "qc = QuantumCircuit(*qr, name=\"State preparation\")\n", - "# Specify control qubits\n", - "# P(B)\n", - "qc.ry(theta_B, qr[0])\n", - "# P(E)\n", - "qc.ry(theta_E, qr[1])\n", - "# P(A|B,E)\n", - "qc.mcry(theta_E, [qr[0][0], qr[1][0]], qr[2])\n", - "# P(A|-B,E)\n", - "qc.x(qr[0])\n", - "qc.mcry(theta_A_BnE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[0])\n", - "# P(A|B,-E)\n", - "qc.x(qr[1])\n", - "qc.mcry(theta_A_nBE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[1])\n", - "# P(A|-B,-E)\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", - "qc.mcry(theta_A_nBnE, [qr[0][0], qr[1][0]], qr[2])\n", - "qc.x(qr[0])\n", - "qc.x(qr[1])\n", - "# P(J|A)\n", - "qc.cry(theta_J_A, qr[2], qr[3])\n", - "# P(M|A)\n", - "qc.cry(theta_M_A, qr[2], qr[4])\n", - "# P(J|-A) + P(M|-A)\n", - "qc.x(qr[2])\n", - "qc.cry(theta_J_nA, qr[2], qr[3])\n", - "qc.cry(theta_M_nA, qr[2], qr[4])\n", - "qc.x(qr[2])\n", - "# Draw circuit\n", - "qc.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" + "query = {\"Y\": 0}\n", + "evidence = {\"X\": 1}\n", + "# Inference\n", + "qb_2n.inference(query=query, evidence=evidence)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:07.365475Z", - "start_time": "2023-11-13T17:24:07.025977Z" + "end_time": "2023-11-24T10:51:30.114701Z", + "start_time": "2023-11-24T10:51:30.065751Z" } }, - "id": "85bb861283b06275" + "id": "841bce19ea097bf1" + }, + { + "cell_type": "markdown", + "source": [ + "#### 4.2. Burglary Alarm Example" + ], + "metadata": { + "collapsed": false + }, + "id": "fe7797d512bc1470" }, { "cell_type": "markdown", "source": [ - "Using this network, you can perform various probabilistic inferences. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." + "Here we have more options to choose from. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." ], "metadata": { "collapsed": false @@ -493,13 +681,13 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 59, "outputs": [ { "data": { - "text/plain": "0.00527" + "text/plain": "0.0058" }, - "execution_count": 32, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -507,16 +695,14 @@ "source": [ "query = {\"B\": 1}\n", "evidence = {\"J\": 1}\n", - "# Initialize quantum bayesian inference framework\n", - "qbayesian = QBayesian(circuit=qc)\n", "# Inference\n", - "qbayesian.inference(query=query, evidence=evidence)" + "qb_ba.inference(query=query, evidence=evidence)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:08.724581Z", - "start_time": "2023-11-13T17:24:07.365152Z" + "end_time": "2023-11-24T10:51:30.498306Z", + "start_time": "2023-11-24T10:51:30.246954Z" } }, "id": "5468619791203a79" @@ -524,39 +710,47 @@ { "cell_type": "markdown", "source": [ - "The joint probability can be also plot with no evidence for the rejection sampling method." + "We can also set the threshold to accept the evidence higher for the inference, and sometimes we can also improve our result by setting the evidence acceptance threshold higher:" ], "metadata": { "collapsed": false }, - "id": "e0f6e7b50aa14131" + "id": "5316dde91cf95cc8" }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 60, "outputs": [ { "data": { - "text/plain": "
", - "image/png": 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" + "text/plain": "0.0057" }, - "execution_count": 33, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "counts = qbayesian.rejection_sampling(evidence={})\n", - "plot_histogram({c_key: c_val for c_key, c_val in counts.items()})" + "# Inference\n", + "qb_ba.threshold = 0.97\n", + "qb_ba.inference(query=query, evidence=evidence)" ], "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-13T17:24:08.888941Z", - "start_time": "2023-11-13T17:24:08.724739Z" + "end_time": "2023-11-24T10:51:31.208567Z", + "start_time": "2023-11-24T10:51:30.517525Z" } }, - "id": "2d4094095ef21b20" + "id": "a5434c7c7c45040a" + }, + { + "cell_type": "markdown", + "source": [], + "metadata": { + "collapsed": false + }, + "id": "28b3cdd72e905dec" } ], "metadata": { diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index c192e0bf3..a7cd4c9df 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -12,87 +12,133 @@ """Quantum Bayesian Inference""" from typing import Tuple, Dict, Set -from qiskit import QuantumCircuit, transpile, ClassicalRegister +from qiskit import QuantumCircuit, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator -from qiskit_aer import AerSimulator +from qiskit.primitives import BaseSampler, Sampler +from qiskit.circuit import Qubit class QBayesian: r""" - Implements Quantum Bayesian Inference algorithm. The algorithm has been developed in [1]. + Implements a convenient Quantum Bayesian Inference algorithm that has been developed in [1]. + + The quantum Bayesian inference (QBI) does quantum rejection sampling and inference for a + Bayesian network with binary random variables represented by a given quantum circuit. + + A quantum circuit can be passed in various forms as long as it represents the joint probability + distribution of the Bayesian network. Note that 'QBayesian' defines an order for the qubits in + the circuit. The last qubit in the circuit will correspond to the most significant bit in the + joint probability distribution. For example, if the random variables A, B, and C are entered + into the circuit in this order with (A=1, B=0 and C=0), the probability is represented by the + probability amplitude of quantum state 001. + + Only binary random variables are supported. For a random variable with more than two states, see + for example [2]. **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. - + [2]: Borujeni, Sima E., et al. "Quantum circuit representation of Bayesian networks." + Expert Systems with Applications 176 (2021): 114768. Usage: ------ - To use the `QBayesian` class, instantiate it with a quantum circuit that represents the - Bayesian network. You can then use the `inference` method to estimate probabilities given - evidence, optionally using rejection sampling and Grover's algorithm for amplification. + To use the `QBayesian` class, instantiate it with a quantum circuit that represents the + Bayesian network. You can then use the `inference` method to estimate probabilities given + evidence, optionally using rejection sampling and Grover's algorithm for amplification. Example: -------- - # Define a quantum circuit - qc = QuantumCircuit(...) + # Define a quantum circuit + qc = QuantumCircuit(...) - # Initialize the framework - qb = QBayesian(qc) + # Initialize the framework + qb = QBayesian(qc) - # Perform inference - result = qb.inference(query={...}, evidence={...}) + # Perform inference + result = qb.inference(query={...}, evidence={...}) - print("Probability of query given evidence:", result) + print("Probability of query given evidence:", result) + + The following attributes can be set via the constructor but can also be read and + updated once the QBayesian object has been constructed. + + Attributes: + converged (bool): True if a solution for the evidence with the given threshold was found + without reaching the maximum number of times the Grover operator was integrated (limit). + limit: The maximum number of times the Grover operator is integrated (2^limit). + sampler (BaseSampler): The sampler primitive used to compute the samples and inferences. + samples (Dict[str, float]): Samples generated from the rejection sampling. + shots (int): The number of samples that are obtained. + threshold (float): The threshold to accept the evidence """ - # Discrete quantum Bayesian network - def __init__(self, circuit: QuantumCircuit): + def __init__( + self, + circuit: QuantumCircuit, + shots: int = 10_000, + limit: int = 10, + threshold: float = 0.9, + sampler: BaseSampler = Sampler(), + ): """ - Run the provided quantum circuit on the Aer simulator backend. For other simulator - overwrite the method run_circuit(). - Args: - circuit (QuantumCircuit): The quantum circuit representing the Bayesian network. - Each random variable should be assigned to exactly one register of one qubit. The - first qubit in the circuit will be the one of highest order. - + circuit: The quantum circuit that represents the Bayesian network. Each random variable + should be assigned to exactly one register of one qubit. A state vector is used as + an oracle for the Grover operator. The last qubit in the circuit corresponds to the + most significant bit passed in the state vector. Example: In a circuit with 2 qubits + and the first qubit as evidence with value 0, the good states are 00 and 10. + shots: The number of samples drawn from the circuit. + limit: The maximum number of times the Grover operator is integrated (2^limit). + threshold (float): The threshold to accept the evidence. The threshold value for the + acceptance of the evidence. For example, if set to 0.9, this means that each + evidence qubit must be equal to the value of the evidence variable at least 90% of + the time in order to be accepted. + sampler: The sampler primitive used to compute the Bayesian inference. + If ``None`` is given, a default instance of the reference sampler defined + by :class:`~qiskit.primitives.Sampler` will be used. Raises: ValueError: If any register in the circuit is not mapped to exactly one qubit. - """ # Test valid input for qrg in circuit.qregs: if qrg.size > 1: raise ValueError("Every register needs to be mapped to exactly one unique qubit") # Initialize parameter - self.circ = circuit + self._circ = circuit + self.shots = shots + self.limit = limit + self.threshold = threshold + if sampler is None: + sampler = Sampler() + self.sampler = sampler + # Label of register mapped to its qubit - self.label2qubit = {qrg.name: qrg[0] for qrg in self.circ.qregs} + self._label2qubit = {qrg.name: qrg[0] for qrg in self._circ.qregs} # Label of register mapped to its qubit index bottom up in significance - self.label2qidx = { - qrg.name: self.circ.num_qubits - idx - 1 for idx, qrg in enumerate(self.circ.qregs) + self._label2qidx = { + qrg.name: self._circ.num_qubits - idx - 1 for idx, qrg in enumerate(self._circ.qregs) } - # Samples from rejection sampling - self.samples: Dict[str, int] = {} + # Distribution of samples from rejection sampling + self.samples: Dict[str, float] = {} # True if rejection sampling converged after limit self.converged = bool() - def get_grover_op(self, evidence: dict) -> GroverOperator: + def _get_grover_op(self, evidence: Dict[str, int]) -> GroverOperator: """ Constructs a Grover operator based on the provided evidence. The evidence is used to determine the "good states" that the Grover operator will amplify. Args: - evidence (dict): A dictionary representing the evidence with keys as variable labels - and values as states. + evidence: A dictionary representing the evidence with keys as variable labels + and values as states. Returns: GroverOperator: The constructed Grover operator. """ # Evidence to reversed qubit index sorted by index - num_qubits = self.circ.num_qubits + num_qubits = self._circ.num_qubits e2idx = sorted( - [(self.label2qidx[e_key], e_val) for e_key, e_val in evidence.items()], + [(self._label2qidx[e_key], e_val) for e_key, e_val in evidence.items()], key=lambda x: x[0], ) # Binary format of good states @@ -110,114 +156,98 @@ def get_grover_op(self, evidence: dict) -> GroverOperator: oracle = Statevector( [int(format(i, f"0{num_qubits}b") in good_states) for i in range(2**num_qubits)] ) - return GroverOperator(oracle, state_preparation=self.circ) + return GroverOperator(oracle, state_preparation=self._circ) - def run_circuit(self, circuit: QuantumCircuit, shots=100_000) -> dict: + def _run_circuit(self, circuit: QuantumCircuit) -> Dict[str, float]: """Run the quantum circuit for the number of shots on the Aer simulator backend.""" - # Get the Aer simulator backend - simulator_backend = AerSimulator() - # Transpile the circuit for the given backend - transpiled_circuit = transpile(circuit, simulator_backend) - # Run the transpiled circuit on the simulator - job = simulator_backend.run(transpiled_circuit, shots=shots) + # Sample from circuit + job = self.sampler.run(circuit, shots=self.shots) result = job.result() # Get the counts of quantum state results - counts = result.get_counts(transpiled_circuit) - # Convert counts to relative counts (probabilities) - relative_counts = {state: count / shots for state, count in counts.items()} - return relative_counts + counts = result.quasi_dists[0].binary_probabilities() + return counts - def power_grover( - self, grover_op: GroverOperator, evidence: dict, k: int, threshold: float - ) -> Tuple[GroverOperator, set]: + def __power_grover( + self, grover_op: GroverOperator, evidence: Dict[str, int], k: int + ) -> Tuple[QuantumCircuit, Set[Tuple[Qubit, int]]]: """ Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns a tuple containing the updated quantum circuit and a set of the measured evidence qubits. Args: - grover_op (GroverOperator): The Grover operator to be applied. - evidence (dict): A dictionary representing the evidence. - k (int): The power to which the Grover operator is raised. - threshold (float): The threshold for accepted evidence + grover_op: The Grover operator to be applied. + evidence: A dictionary representing the evidence. + k: The power to which the Grover operator is raised. Returns: tuple: A tuple containing the updated quantum circuit and a set of the - measured evidence qubits. + measured evidence qubits. """ # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) + qc = QuantumCircuit(*self._circ.qregs) + qc.append(self._circ, self._circ.qregs) # Apply Grover operator 2^k times - qc_grover = QuantumCircuit(*self.circ.qregs) - qc_grover.append(grover_op, self.circ.qregs) + qc_grover = QuantumCircuit(*self._circ.qregs) + qc_grover.append(grover_op, self._circ.qregs) qc_grover = qc_grover.power(2**k) - qc.append(qc_grover, self.circ.qregs) + qc.append(qc_grover, self._circ.qregs) # Add quantum circuit for measuring - qc_measure = QuantumCircuit(*self.circ.qregs) - qc_measure.append(qc, self.circ.qregs) + qc_measure = QuantumCircuit(*self._circ.qregs) + qc_measure.append(qc, self._circ.qregs) # Create a classical register with the size of the evidence measurement_ecr = ClassicalRegister(len(evidence)) qc_measure.add_register(measurement_ecr) # Map the evidence qubits to the classical bits and measure them - evidence_qubits = [self.label2qubit[e_key] for e_key in evidence] + evidence_qubits = [self._label2qubit[e_key] for e_key in evidence] qc_measure.measure(evidence_qubits, measurement_ecr) # Run the circuit with the Grover operator and measurements - e_samples = self.run_circuit(qc_measure, shots=1024 * self.circ.num_qubits) - e_count = {self.label2qubit[e]: 0 for e in evidence} + e_samples = self._run_circuit(qc_measure) + e_count = {self._label2qubit[e]: 0.0 for e in evidence} for e_sample_key, e_sample_val in e_samples.items(): # Go through reverse binary that matches order of qubits for i, char in enumerate(e_sample_key[::-1]): if int(char) == 1: e_count[evidence_qubits[i]] += e_sample_val - else: - e_count[evidence_qubits[i]] += -e_sample_val # Assign to every evidence qubit if it is measured with high probability (th) 1 o/w 0 e_meas = { - (e_count_key, int(e_count_val >= threshold)) + (e_count_key, int(e_count_val >= self.threshold)) for e_count_key, e_count_val in e_count.items() } return qc, e_meas - def rejection_sampling( - self, evidence: dict, shots: int = 100000, limit: int = 10, threshold: float = 0.8 - ) -> dict: + def rejection_sampling(self, evidence: Dict[str, int]) -> Dict[str, float]: """ Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude amplification and iterates until the evidence matches or a limit is reached. Args: - evidence (dict): A dictionary representing the evidence. - shots (int): The number of times the circuit will be executed. - limit (int): The maximum number of iterations for the Grover operator. - threshold (float): The threshold for accepted evidence + evidence: A dictionary representing the evidence. Returns: - dict: A dictionary containing the samples as a dictionary + dict: A dictionary containing the distribution of the samples """ # If evidence is empty if len(evidence) == 0: # Create circuit - qc = QuantumCircuit(*self.circ.qregs) - qc.append(self.circ, self.circ.qregs) + qc = QuantumCircuit(*self._circ.qregs) + qc.append(self._circ, self._circ.qregs) # Measure qc.measure_all() # Run circuit - self.samples = self.run_circuit(qc, shots=shots) + self.samples = self._run_circuit(qc) return self.samples # Get Grover operator if evidence not empty - grover_op = self.get_grover_op(evidence) + grover_op = self._get_grover_op(evidence) # Amplitude amplification - true_e = {(self.label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} + true_e = {(self._label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} meas_e: Set[Tuple[str, int]] = set() best_qc, best_inter = QuantumCircuit(), 0 self.converged = False k = -1 # If the measurement of the evidence qubits matches the evidence stop - while (true_e != meas_e) and (k < limit): + while (true_e != meas_e) and (k < self.limit): # Increment power k += 1 # Create circuit with 2^k times Grover operator - qc, meas_e = self.power_grover( - grover_op=grover_op, evidence=evidence, k=k, threshold=threshold - ) + qc, meas_e = self.__power_grover(grover_op=grover_op, evidence=evidence, k=k) # Test number of if len(true_e.intersection(meas_e)) > best_inter: best_qc = qc @@ -225,24 +255,26 @@ def rejection_sampling( self.converged = True # Create a classical register with the size of the evidence - best_qc_meas = QuantumCircuit(*self.circ.qregs) - best_qc_meas.append(best_qc, self.circ.qregs) - measurement_qcr = ClassicalRegister(self.circ.num_qubits - len(evidence)) + best_qc_meas = QuantumCircuit(*self._circ.qregs) + best_qc_meas.append(best_qc, self._circ.qregs) + measurement_qcr = ClassicalRegister(self._circ.num_qubits - len(evidence)) best_qc_meas.add_register(measurement_qcr) # Map the query qubits to the classical bits and measure them query_qubits = [ - (label, self.label2qidx[label], qubit) - for label, qubit in self.label2qubit.items() + (label, self._label2qidx[label], qubit) + for label, qubit in self._label2qubit.items() if label not in evidence ] query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1], reverse=True) # Measure query variables and return their count best_qc_meas.measure([q[2] for q in query_qubits_sorted], measurement_qcr) # Run circuit - counts = self.run_circuit(best_qc_meas, shots=shots) + counts = self._run_circuit(best_qc_meas) # Build default string with evidence query_string = "" - var_idx_sorted = [label for label, _ in sorted(self.label2qidx.items(), key=lambda x: x[1])] + var_idx_sorted = [ + label for label, _ in sorted(self._label2qidx.items(), key=lambda x: x[1]) + ] for var in var_idx_sorted: if var in evidence: query_string += str(evidence[var]) @@ -260,37 +292,32 @@ def rejection_sampling( def inference( self, - query: dict, - evidence: dict = None, - shots: int = 100000, - limit: int = 10, - threshold: float = 0.8, + query: Dict[str, int], + evidence: Dict[str, int] = None, ) -> float: """ Performs inference on the query variables given the evidence. It uses rejection sampling if evidence is provided and calculates the probability of the query. Args: - query (dict): The query variables with keys as variable labels and values as states. - If Q is a real subset of X without E, it will be marginalized. - evidence (dict, optional): The evidence variables. If provided, rejection sampling is - executed. If you want to indicate no evidence insert an empty list. - shots (int): The number of times the circuit will be executed. - limit (int): The maximum number of 2^k times the Grover operator is integrated - threshold (float): The threshold for accepted evidence + query: The query variables with keys as variable labels and values as states. + If Q is a real subset of X without E, it will be marginalized. + evidence: The evidence variables. If specified, rejection sampling is executed. If you + want to indicate the case of no evidence, insert an empty list. If you do not + provide any evidence, the samples from previous rejection sampling are used. Returns: float: The probability of the query given the evidence. Raises: ValueError: If evidence is required for rejection sampling and none is provided. """ if evidence is not None: - self.rejection_sampling(evidence, shots, limit, threshold) + self.rejection_sampling(evidence) else: if not self.samples: raise ValueError("Provide evidence or indicate no evidence with empty list") # Get sorted indices of query qubits - query_indices_rev = [(self.label2qidx[q_key], q_val) for q_key, q_val in query.items()] + query_indices_rev = [(self._label2qidx[q_key], q_val) for q_key, q_val in query.items()] # Get probability of query - res = 0 + res = 0.0 for sample_key, sample_val in self.samples.items(): add = True for q_idx, q_val in query_indices_rev: diff --git a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 60c5a7185..2daa36701 100644 --- a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -1,22 +1,13 @@ --- -prelude: > - The Qiskit Machine Learning library introduces the `QBayesian` class, - implementing the Quantum Bayesian Inference algorithm. This new feature - enhances the library's capabilities in quantum machine learning, - particularly in the area of probabilistic reasoning and inference - on quantum computers. - features: - | Introduction of the `QBayesian` class in the Qiskit Machine Learning library. - This class implements Quantum Bayesian Inference, allowing users to perform + This class implements quantum Bayesian inference, allowing users to perform probabilistic reasoning with quantum circuits. The implementation is based on the algorithm described in the paper "Quantum inference on Bayesian networks" by Low, Yoder, and Chuang. - - | The `QBayesian` class supports various functionalities including: - - Initialization with a quantum circuit representing a Bayesian network. - Rejection sampling for estimating probabilities given evidence, with Grover's algorithm-based amplification. - Approximate Bayesian inference using rejection sampling, @@ -24,21 +15,3 @@ features: - | The `13_quantum_bayesian_inference` notebook describes a tutorial for the usage of the `QBayesian` class - -issues: - - | - Users should ensure that each register in the quantum circuit passed to - `QBayesian` is mapped to exactly one qubit. The class raises a `ValueError` - if this condition is not met. - -upgrade: - - | - Users looking to leverage advanced probabilistic inference techniques in - quantum computing can now use the `QBayesian` class. To use this feature, - ensure that the latest version of the Qiskit Machine Learning library is installed. - -other: - - | - The `QBayesian` class is a significant addition for researchers and practitioners - working in quantum machine learning, particularly in the domain of Bayesian inference. - It opens up new possibilities for complex probabilistic modeling on quantum computers. diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index e32aa2a21..71fc479c1 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -125,11 +125,14 @@ def test_inference(self): def test_parameter(self): """Tests parameter of methods""" # Test set threshold - self.qbayesian.rejection_sampling(evidence={"B": 1}, threshold=0.9) + self.qbayesian.threshold = 0.9 + self.qbayesian.rejection_sampling(evidence={"B": 1}) # Test set limit - self.qbayesian.rejection_sampling(evidence={"B": 1}, limit=1) + self.qbayesian.limit = 1 + self.qbayesian.rejection_sampling(evidence={"B": 1}) # Test set shots - self.qbayesian.inference(query={"B": 1}, evidence={"A": 0, "C": 0}, shots=10) + self.qbayesian.shots = 10 + self.qbayesian.inference(query={"B": 1}, evidence={"A": 0, "C": 0}) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="No ValueError in constructor with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(2, "qr"))) From e3b3f3c280248c717f9c664b85549e8d11460858 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 24 Nov 2023 16:21:36 +0100 Subject: [PATCH 27/48] Fixed format --- .../13_quantum_bayesian_inference.ipynb | 495 +++++++++--------- .../algorithms/inference/qbayesian.py | 24 +- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 2 +- 3 files changed, 261 insertions(+), 260 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index e9ed1f6dc..7d8183645 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -2,6 +2,10 @@ "cells": [ { "cell_type": "markdown", + "id": "4f1ee7dfd66dd6ac", + "metadata": { + "collapsed": false + }, "source": [ "# Quantum Bayesian Inference with Qiskit\n", "\n", @@ -10,22 +14,29 @@ "\n", "The tutorial is structured as follows:\n", "\n", - "1. [Introduction](#1.-Introduction)\n", - "2. [How to Instantiate QBI](#2.-How-to-Instantiate-QBIs)\n", - "3. [How to Run Rejection Sampling](#3.-How-to-Run-an-Rejection-Sampling)\n", - "4. [How to Run an Inference](#4.-How-to-Run-an-Inference)" + "1. [Introduction](#1.-introduction)\n", + "2. [How to Instantiate QBI](#2.-how-to-instantiate-qbi)\n", + "3. [How to Run Rejection Sampling](#3.-how-to-run-rejection-sampling)\n", + "4. [How to Run an Inference](#4.-how-to-run-an-inference)" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 1. Introduction" ], "metadata": { "collapsed": false }, - "id": "4f1ee7dfd66dd6ac" + "id": "494f210f33019c5b" }, { "cell_type": "markdown", + "id": "3237c8b584b541bd", + "metadata": { + "collapsed": false + }, "source": [ - "\n", - "## 1. Introduction\n", - "\n", "### 1.1. Quantum vs. Classical Bayesian Inference\n", "\n", "Bayesian networks, or belief networks, are graphical models that illustrate probabilistic relationships between variables using nodes (representing variables) and edges (indicating conditional dependencies) in a directed acyclic graph. Each node is associated with conditional probability tables (CPTs) that detail the influence of parent nodes on their children. \n", @@ -38,43 +49,30 @@ "\n", "### 1.2. Implementation in `qiskit-machine-learning`\n", "\n", - "The QBI in `qiskit-machine-learning` can be used for different quantum circuits representing Bayesian networks with. The implementation is based on the Sampler primitive from [qiskit primitives](https://qiskit.org/documentation/apidoc/primitives.html). The primitive is the entry point to run QBI on either a simulator or real quantum hardware. QBI takes in an optional instance of its corresponding primitive, which can be any subclass of `BaseSampler`.\n", + "The QBI in `qiskit-machine-learning` can be used for different quantum circuits representing Bayesian networks with. The implementation is based on the `Sampler` primitive from [qiskit primitives](https://qiskit.org/documentation/apidoc/primitives.html). The primitive is the entry point to run QBI on either a simulator or real quantum hardware. QBI takes in an optional instance of its corresponding primitive, which can be any subclass of `BaseSampler`.\n", "\n", "The `qiskit.primitives` module provides a reference implementation for the `Sampler` class to run statevector simulations. By default, if no instance is passed to a QBI class, an instance of the corresponding reference primitive of `Sampler` is created automatically by QBI.\n", "For more information about primitives please refer to the [primitives documentation](https://qiskit.org/documentation/apidoc/primitives.html).\n", "\n", "The `QBayesian` class is used for QBI in `qiskit-machine-learning`. It is initialized with a quantum circuit that represents a Bayesian network. This enables the execution of quantum rejection sampling and inference.\n" - ], - "metadata": { - "collapsed": false - }, - "id": "3237c8b584b541bd" + ] }, { "cell_type": "markdown", - "source": [ - "***\n", - "\n", - "Let's now look into specific examples for the `QBayesian` implementations. But first, let's set the algorithmic seed to ensure that the results don't change between runs." - ], + "id": "36c0c73ab1fe5686", "metadata": { "collapsed": false }, - "id": "bafaeda078302d7f" + "source": [ + "## 2. How to Instantiate QBI" + ] }, { "cell_type": "markdown", - "source": [ - "\n", - "## 2. How to Instantiate QBI" - ], + "id": "6adf88f1d249b336", "metadata": { "collapsed": false }, - "id": "36c0c73ab1fe5686" - }, - { - "cell_type": "markdown", "source": [ "### 2.1. Create Rotations for the Bayesian Networks\n", "In quantum computing, the rotation matrix around the y-axis, denoted as $R_y(\\theta)$, is used to rotate the state of a qubit around the y-axis of the Bloch sphere by an angle $\\theta$. This approach allows for precise control over the quantum state of a qubit, enabling the encoding of specific probabilities in quantum algorithms. When this rotation is applied to a qubit initially in the $|0\\rangle$ state, the resulting state $|\\psi\\rangle$ is:\n", @@ -93,33 +91,32 @@ "\n", "This approach can be extended for conditional probabilities. For example, with the Bayesian network shown above, you can use the following formula to calculate the joint probability distribution:\n", "$$(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(R_y\\otimes{I})|00\\rangle$$" - ], - "metadata": { - "collapsed": false - }, - "id": "6adf88f1d249b336" + ] }, { "cell_type": "markdown", + "id": "f0be387a44da5bac", + "metadata": { + "collapsed": false + }, "source": [ "#### 2.1.1. Two Node Bayesian Network Example\n", "\n", "In the first example we consider a simple Bayesian network that is only based on two nodes." - ], - "metadata": { - "collapsed": false - }, - "id": "f0be387a44da5bac" + ] }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 112, "id": "initial_id", "metadata": { "collapsed": true, + "jupyter": { + "outputs_hidden": true + }, "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.146074Z", - "start_time": "2023-11-24T10:51:29.080310Z" + "end_time": "2023-11-24T15:15:30.327929Z", + "start_time": "2023-11-24T15:15:30.244802Z" } }, "outputs": [ @@ -155,6 +152,10 @@ }, { "cell_type": "markdown", + "id": "19b5a6da03a35a85", + "metadata": { + "collapsed": false + }, "source": [ "\n", "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", @@ -162,15 +163,19 @@ "$$P(Y|X)=0.9$$\n", "$$P(Y|-X)=0.3$$\n", "The corresponding rotation angles are:" - ], - "metadata": { - "collapsed": false - }, - "id": "19b5a6da03a35a85" + ] }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 113, + "id": "326c1d2e72f41202", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.328087Z", + "start_time": "2023-11-24T15:15:30.310156Z" + } + }, "outputs": [], "source": [ "# Include libraries\n", @@ -180,31 +185,31 @@ "theta_X = 2 * np.arcsin(np.sqrt(0.2))\n", "theta_Y_X = 2 * np.arcsin(np.sqrt(0.9))\n", "theta_Y_nX = 2 * np.arcsin(np.sqrt(0.3))" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.149471Z", - "start_time": "2023-11-24T10:51:29.121013Z" - } - }, - "id": "326c1d2e72f41202" + ] }, { "cell_type": "markdown", + "id": "e1dd146c9d2bdad3", + "metadata": { + "collapsed": false + }, "source": [ "#### 2.1.2. Burglary Alarm Example\n", "\n", "Now consider a more complex network. Imagine you have an alarm system in your house that is triggered by either a burglary or an earthquake. You also have two neighbors, John and Mary, who will call you if they hear the alarm. The network has directed edges from the Burglary and Earthquake nodes to the Alarm node, indicating that both burglary and earthquake can cause the alarm to ring. There are also edges from the Alarm node to the John Calls and Mary Calls nodes, indicating that the alarm influences whether John and Mary call you." - ], - "metadata": { - "collapsed": false - }, - "id": "e1dd146c9d2bdad3" + ] }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 114, + "id": "e4e5d93f2afa6aee", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.394662Z", + "start_time": "2023-11-24T15:15:30.323415Z" + } + }, "outputs": [ { "data": { @@ -238,18 +243,14 @@ "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", "plt.show()" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.262231Z", - "start_time": "2023-11-24T10:51:29.125917Z" - } - }, - "id": "e4e5d93f2afa6aee" + ] }, { "cell_type": "markdown", + "id": "587dc2c38a0a3ca9", + "metadata": { + "collapsed": false + }, "source": [ "The Bayesian Network for this scenario involves the following variables:\n", "\n", @@ -271,15 +272,19 @@ "$$P(M|-A) = 0.9$$\n", "$$P(M|A) = 0.3$$\n", "Then we get:\n" - ], - "metadata": { - "collapsed": false - }, - "id": "587dc2c38a0a3ca9" + ] }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 115, + "id": "a815411b4f10c78c", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.399139Z", + "start_time": "2023-11-24T15:15:30.397184Z" + } + }, "outputs": [], "source": [ "theta_B = 2 * np.arcsin(np.sqrt(0.001))\n", @@ -292,47 +297,47 @@ "theta_J_A = 2 * np.arcsin(np.sqrt(0.9))\n", "theta_M_nA = 2 * np.arcsin(np.sqrt(0.9))\n", "theta_M_A = 2 * np.arcsin(np.sqrt(0.3))" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.264208Z", - "start_time": "2023-11-24T10:51:29.256015Z" - } - }, - "id": "a815411b4f10c78c" + ] }, { "cell_type": "markdown", - "source": [ - "### 2.2. Create a Quantum Circuit for the Bayesian Networks\n", - "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." - ], + "id": "473ea24e63019832", "metadata": { "collapsed": false }, - "id": "473ea24e63019832" + "source": [ + "### 2.2. Create a Quantum Circuit for the Bayesian Networks\n", + "A Bayesian network can be represented as a quantum circuit where each node is a qubit, and the edges are quantum gates that represent the conditional dependencies." + ] }, { "cell_type": "markdown", - "source": [ - "#### 2.2.1 Two Node Bayesian Network Example" - ], + "id": "33797564f68ae67", "metadata": { "collapsed": false }, - "id": "33797564f68ae67" + "source": [ + "#### 2.2.1 Two Node Bayesian Network Example" + ] }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 116, + "id": "4f99dbe56bc6910a", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.459369Z", + "start_time": "2023-11-24T15:15:30.401179Z" + } + }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, - "execution_count": 53, + "execution_count": 116, "metadata": {}, "output_type": "execute_result" } @@ -357,36 +362,36 @@ "# Apply another X gate on the first qubit\n", "qc_2n.x(0)\n", "qc_2n.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.380180Z", - "start_time": "2023-11-24T10:51:29.268991Z" - } - }, - "id": "4f99dbe56bc6910a" + ] }, { "cell_type": "markdown", - "source": [ - "#### 2.2.2. Burglary Alarm Example" - ], + "id": "7596c28a61daad7d", "metadata": { "collapsed": false }, - "id": "7596c28a61daad7d" + "source": [ + "#### 2.2.2. Burglary Alarm Example" + ] }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 117, + "id": "79045cc1a7706f87", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.862217Z", + "start_time": "2023-11-24T15:15:30.477851Z" + } + }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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}, - "execution_count": 54, + "execution_count": 117, "metadata": {}, "output_type": "execute_result" } @@ -428,29 +433,24 @@ "qc_ba.x(qr[2])\n", "# Draw circuit\n", "qc_ba.draw(\"mpl\", style=\"bw\", plot_barriers=False, justify=\"none\", fold=-1)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.788086Z", - "start_time": "2023-11-24T10:51:29.391611Z" - } - }, - "id": "79045cc1a7706f87" + ] }, { "cell_type": "markdown", - "source": [ - "\n", - "## 3. How to Run Rejection Sampling" - ], + "id": "b8cc65c8d0c64c91", "metadata": { "collapsed": false }, - "id": "b8cc65c8d0c64c91" + "source": [ + "## 3. How to Run Rejection Sampling" + ] }, { "cell_type": "markdown", + "id": "eff9038bd1a6a91e", + "metadata": { + "collapsed": false + }, "source": [ "### 3.1. Set up\n", "\n", @@ -463,33 +463,37 @@ "Quantum rejection sampling is particularly beneficial in complex or high-dimensional probability distribution scenarios, where classical computers face challenges. Its applications extend to quantum machine learning, probabilistic modeling, and other areas of quantum computing. \n", "\n", "To use the `QBayesian` class, instantiate it with a quantum circuit that represents the Bayesian network. You can then use the rejection sampling method to estimate probabilities given evidence." - ], - "metadata": { - "collapsed": false - }, - "id": "eff9038bd1a6a91e" + ] }, { "cell_type": "markdown", - "source": [ - "#### 3.1.1 Two Node Bayesian Network Example\n", - "If we want to carry out a rejection sampling with X=1 as evidence, we can do this in the following way:" - ], + "id": "c3fd5b7532b845c4", "metadata": { "collapsed": false }, - "id": "c3fd5b7532b845c4" + "source": [ + "#### 3.1.1 Two Node Bayesian Network Example\n", + "If we want to carry out a rejection sampling with X=1 as evidence, we can do this in the following way:" + ] }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 118, + "id": "1e602fda98a6356d", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:30.962348Z", + "start_time": "2023-11-24T15:15:30.866907Z" + } + }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 55, + "execution_count": 118, "metadata": {}, "output_type": "execute_result" } @@ -504,36 +508,36 @@ "# Sampling\n", "samples = qb_2n.rejection_sampling(evidence=evidence)\n", "plot_histogram(samples)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.892049Z", - "start_time": "2023-11-24T10:51:29.787284Z" - } - }, - "id": "1e602fda98a6356d" + ] }, { "cell_type": "markdown", - "source": [ - "We can also set the threshold to accept the evidence. For example, if set to 0.9, this means that each evidence qubit must be equal to the value of the evidence variable at least 90% of the time in order to be accepted. Sometimes we can also improve our result by setting the threshold for acceptance of the evidence higher:" - ], + "id": "166108a390743bd4", "metadata": { "collapsed": false }, - "id": "166108a390743bd4" + "source": [ + "We can also set the threshold to accept the evidence. For example, if set to 0.9, this means that each evidence qubit must be equal to the value of the evidence variable at least 90% of the time in order to be accepted. Sometimes we can also improve our result by setting the threshold for acceptance of the evidence higher:" + ] }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 119, + "id": "a6fc4d5d394d301a", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:31.028658Z", + "start_time": "2023-11-24T15:15:30.934751Z" + } + }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 56, + "execution_count": 119, "metadata": {}, "output_type": "execute_result" } @@ -543,37 +547,37 @@ "qb_2n.threshold = 0.97\n", "samples = qb_2n.rejection_sampling(evidence=evidence)\n", "plot_histogram(samples)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:29.976190Z", - "start_time": "2023-11-24T10:51:29.861726Z" - } - }, - "id": "a6fc4d5d394d301a" + ] }, { "cell_type": "markdown", - "source": [ - "#### 3.1.2. Burglary Alarm Example\n", - "For the advanced example, we can do this in the same way. However, we look at the trivial case of how to obtain the joint probability of the network. This can be calculated by providing no evidence for the rejection sampling method." - ], + "id": "9f6ab51740b00957", "metadata": { "collapsed": false }, - "id": "9f6ab51740b00957" + "source": [ + "#### 3.1.2. Burglary Alarm Example\n", + "For the advanced example, we can do this in the same way. However, we look at the trivial case of how to obtain the joint probability of the network. This can be calculated by providing no evidence for the rejection sampling method." + ] }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 120, + "id": "8d4904619b35503a", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:31.122882Z", + "start_time": "2023-11-24T15:15:31.032051Z" + } + }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 57, + "execution_count": 120, "metadata": {}, "output_type": "execute_result" } @@ -584,29 +588,24 @@ "# Inference\n", "counts = qb_ba.rejection_sampling(evidence={})\n", "plot_histogram({c_key: c_val for c_key, c_val in counts.items()})" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:30.056180Z", - "start_time": "2023-11-24T10:51:29.975890Z" - } - }, - "id": "8d4904619b35503a" + ] }, { "cell_type": "markdown", - "source": [ - "\n", - "## 4. How to Run an Inference" - ], + "id": "5d22c72ca6352a56", "metadata": { "collapsed": false }, - "id": "5d22c72ca6352a56" + "source": [ + "## 4. How to Run an Inference" + ] }, { "cell_type": "markdown", + "id": "d66d7e40d62819b6", + "metadata": { + "collapsed": false + }, "source": [ "### 4.1 Set Up\n", "Quantum Bayesian inference is here based on quantum rejection sampling. Quantum rejection sampling plays a pivotal role in the inference process that follows. After the quantum state is manipulated to include evidence, measurement is performed. However, in quantum rejection sampling, only those measurement outcomes that align with the evidence are considered, effectively 'rejecting' irrelevant outcomes, similar to the traditional rejection sampling method.\n", @@ -614,32 +613,36 @@ "The synergy of quantum state manipulation with quantum rejection sampling leads to a more efficient inference process compared to classical approaches, harnessing the inherent parallelism of quantum computing to simultaneously process multiple probabilities. This advanced method has significant implications in areas like quantum machine learning and data analysis, where it could outperform classical algorithms in tasks such as pattern recognition and decision-making.\n", "\n", "You can use the `inference` method from `QBayesian` to estimate probabilities given evidence." - ], - "metadata": { - "collapsed": false - }, - "id": "d66d7e40d62819b6" + ] }, { "cell_type": "markdown", - "source": [ - "#### 4.1. Two Node Bayesian Network Example\n", - "Using `QBayesian`, you can draw various probabilistic conclusions. For the Bayesian network with two nodes, this is limited due to the number of variables. However, if we want to know what the probability of P(Y=0|X=1) is, we can do the following:" - ], + "id": "b3916bfec5e40bfc", "metadata": { "collapsed": false }, - "id": "b3916bfec5e40bfc" + "source": [ + "#### 4.1. Two Node Bayesian Network Example\n", + "Using `QBayesian`, you can draw various probabilistic conclusions. For the Bayesian network with two nodes, this is limited due to the number of variables. However, if we want to know what the probability of P(Y=0|X=1) is, we can do the following:" + ] }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 121, + "id": "841bce19ea097bf1", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:31.180074Z", + "start_time": "2023-11-24T15:15:31.131794Z" + } + }, "outputs": [ { "data": { - "text/plain": "0.0985" + "text/plain": "0.1003" }, - "execution_count": 58, + "execution_count": 121, "metadata": {}, "output_type": "execute_result" } @@ -649,45 +652,45 @@ "evidence = {\"X\": 1}\n", "# Inference\n", "qb_2n.inference(query=query, evidence=evidence)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:30.114701Z", - "start_time": "2023-11-24T10:51:30.065751Z" - } - }, - "id": "841bce19ea097bf1" + ] }, { "cell_type": "markdown", - "source": [ - "#### 4.2. Burglary Alarm Example" - ], + "id": "fe7797d512bc1470", "metadata": { "collapsed": false }, - "id": "fe7797d512bc1470" + "source": [ + "#### 4.2. Burglary Alarm Example" + ] }, { "cell_type": "markdown", - "source": [ - "Here we have more options to choose from. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian Networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." - ], + "id": "bb0e805d2f7fb30c", "metadata": { "collapsed": false }, - "id": "bb0e805d2f7fb30c" + "source": [ + "Here we have more options to choose from. For example, if John calls, you can calculate the probability of a burglary having occurred. Bayesian networks are particularly useful in such scenarios where you have uncertain information (like John calling) and you want to infer the state of a more fundamental variable (like a burglary)." + ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 122, + "id": "5468619791203a79", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:31.410222Z", + "start_time": "2023-11-24T15:15:31.195373Z" + } + }, "outputs": [ { "data": { - "text/plain": "0.0058" + "text/plain": "0.0048000000000000004" }, - "execution_count": 59, + "execution_count": 122, "metadata": {}, "output_type": "execute_result" } @@ -697,35 +700,35 @@ "evidence = {\"J\": 1}\n", "# Inference\n", "qb_ba.inference(query=query, evidence=evidence)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:30.498306Z", - "start_time": "2023-11-24T10:51:30.246954Z" - } - }, - "id": "5468619791203a79" + ] }, { "cell_type": "markdown", - "source": [ - "We can also set the threshold to accept the evidence higher for the inference, and sometimes we can also improve our result by setting the evidence acceptance threshold higher:" - ], + "id": "5316dde91cf95cc8", "metadata": { "collapsed": false }, - "id": "5316dde91cf95cc8" + "source": [ + "We can also set the threshold to accept the evidence higher for the inference, and sometimes we can also improve our result by setting the evidence acceptance threshold higher:" + ] }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 123, + "id": "a5434c7c7c45040a", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-24T15:15:32.089164Z", + "start_time": "2023-11-24T15:15:31.424204Z" + } + }, "outputs": [ { "data": { - "text/plain": "0.0057" + "text/plain": "0.0052" }, - "execution_count": 60, + "execution_count": 123, "metadata": {}, "output_type": "execute_result" } @@ -734,42 +737,34 @@ "# Inference\n", "qb_ba.threshold = 0.97\n", "qb_ba.inference(query=query, evidence=evidence)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T10:51:31.208567Z", - "start_time": "2023-11-24T10:51:30.517525Z" - } - }, - "id": "a5434c7c7c45040a" + ] }, { "cell_type": "markdown", - "source": [], + "id": "28b3cdd72e905dec", "metadata": { "collapsed": false }, - "id": "28b3cdd72e905dec" + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.6" + "pygments_lexer": "ipython3", + "version": "3.9.6" } }, "nbformat": 4, diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index a7cd4c9df..191c144b8 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -21,7 +21,7 @@ class QBayesian: r""" - Implements a convenient Quantum Bayesian Inference algorithm that has been developed in [1]. + Implements a convenient quantum Bayesian inference algorithm that has been developed in [1]. The quantum Bayesian inference (QBI) does quantum rejection sampling and inference for a Bayesian network with binary random variables represented by a given quantum circuit. @@ -33,14 +33,15 @@ class QBayesian: into the circuit in this order with (A=1, B=0 and C=0), the probability is represented by the probability amplitude of quantum state 001. - Only binary random variables are supported. For a random variable with more than two states, see - for example [2]. + For Bayesian networks with random variables that have more than two states, see for example [2]. **References** + [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. [2]: Borujeni, Sima E., et al. "Quantum circuit representation of Bayesian networks." Expert Systems with Applications 176 (2021): 114768. + Usage: ------ To use the `QBayesian` class, instantiate it with a quantum circuit that represents the @@ -49,7 +50,6 @@ class QBayesian: Example: -------- - # Define a quantum circuit qc = QuantumCircuit(...) @@ -61,8 +61,8 @@ class QBayesian: print("Probability of query given evidence:", result) - The following attributes can be set via the constructor but can also be read and - updated once the QBayesian object has been constructed. + The following attributes can be set via the constructor but can also be read and updated once + the QBayesian object has been constructed. Attributes: converged (bool): True if a solution for the evidence with the given threshold was found @@ -71,9 +71,11 @@ class QBayesian: sampler (BaseSampler): The sampler primitive used to compute the samples and inferences. samples (Dict[str, float]): Samples generated from the rejection sampling. shots (int): The number of samples that are obtained. - threshold (float): The threshold to accept the evidence + threshold (float): The threshold to accept the evidence. + """ + # Discrete quantum Bayesian network def __init__( self, circuit: QuantumCircuit, @@ -129,6 +131,7 @@ def _get_grover_op(self, evidence: Dict[str, int]) -> GroverOperator: """ Constructs a Grover operator based on the provided evidence. The evidence is used to determine the "good states" that the Grover operator will amplify. + Args: evidence: A dictionary representing the evidence with keys as variable labels and values as states. @@ -174,13 +177,14 @@ def __power_grover( Applies the Grover operator to the quantum circuit 2^k times, measures the evidence qubits, and returns a tuple containing the updated quantum circuit and a set of the measured evidence qubits. + Args: grover_op: The Grover operator to be applied. evidence: A dictionary representing the evidence. k: The power to which the Grover operator is raised. Returns: - tuple: A tuple containing the updated quantum circuit and a set of the - measured evidence qubits. + tuple: A tuple containing the updated quantum circuit and a set of the measured evidence + qubits. """ # Create circuit qc = QuantumCircuit(*self._circ.qregs) @@ -219,6 +223,7 @@ def rejection_sampling(self, evidence: Dict[str, int]) -> Dict[str, float]: Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude amplification and iterates until the evidence matches or a limit is reached. + Args: evidence: A dictionary representing the evidence. Returns: @@ -298,6 +303,7 @@ def inference( """ Performs inference on the query variables given the evidence. It uses rejection sampling if evidence is provided and calculates the probability of the query. + Args: query: The query variables with keys as variable labels and values as states. If Q is a real subset of X without E, it will be marginalized. diff --git a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 2daa36701..5f6156db4 100644 --- a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -14,4 +14,4 @@ features: with Grover's algorithm-based amplification. - | The `13_quantum_bayesian_inference` notebook describes a tutorial for the - usage of the `QBayesian` class + usage of the `QBayesian` class. From c30ef64998c720539d80bd92caf046f323b29fa2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 24 Nov 2023 18:20:14 +0100 Subject: [PATCH 28/48] Removed shots --- .../13_quantum_bayesian_inference.ipynb | 100 +++++++++--------- .../algorithms/inference/qbayesian.py | 10 +- test/algorithms/inference/test_qbayesian.py | 8 +- 3 files changed, 57 insertions(+), 61 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 7d8183645..6bb345e1c 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -107,7 +107,7 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 13, "id": "initial_id", "metadata": { "collapsed": true, @@ -115,8 +115,8 @@ "outputs_hidden": true }, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.327929Z", - "start_time": "2023-11-24T15:15:30.244802Z" + "end_time": "2023-11-24T17:18:40.882177Z", + "start_time": "2023-11-24T17:18:40.795755Z" } }, "outputs": [ @@ -167,13 +167,13 @@ }, { "cell_type": "code", - "execution_count": 113, + "execution_count": 14, "id": "326c1d2e72f41202", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.328087Z", - "start_time": "2023-11-24T15:15:30.310156Z" + "end_time": "2023-11-24T17:18:40.883941Z", + "start_time": "2023-11-24T17:18:40.859940Z" } }, "outputs": [], @@ -201,13 +201,13 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 15, "id": "e4e5d93f2afa6aee", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.394662Z", - "start_time": "2023-11-24T15:15:30.323415Z" + "end_time": "2023-11-24T17:18:40.974767Z", + "start_time": "2023-11-24T17:18:40.879794Z" } }, "outputs": [ @@ -276,13 +276,13 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 16, "id": "a815411b4f10c78c", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.399139Z", - "start_time": "2023-11-24T15:15:30.397184Z" + "end_time": "2023-11-24T17:18:40.980883Z", + "start_time": "2023-11-24T17:18:40.977441Z" } }, "outputs": [], @@ -322,13 +322,13 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 17, "id": "4f99dbe56bc6910a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.459369Z", - "start_time": "2023-11-24T15:15:30.401179Z" + "end_time": "2023-11-24T17:18:41.049766Z", + "start_time": "2023-11-24T17:18:40.984841Z" } }, "outputs": [ @@ -337,7 +337,7 @@ "text/plain": "
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UiIhIGSwlIiJSBkuJiIiUwVIiIiJlsJSIiEgZLCUiIlIGS4mIiJTBUiIiImXwm2fJcCICh8Oh+/O6XC73/9rtdl2fOzg4GJqm6fqcAxnnAPWUJiJidgjybXa7HaGhoWbH6JXm5mZ+fbWOOAeop3j4joiIlMHDd+RRtbW1yr77tNvtiIyMNDuGz+McoNthKZFHhYSEKPuCRJ7BOUC3w8N3RESkDJYSEREpg6VERETKYCkREZEyWEpERKQMlhIpq7CwEJqmdbmFhobCZrNh69atcDqdZkckA3H8ByaeEk7KW7hwIVJTUyEiqKmpQV5eHl588UWUlpZi165dZscjg3H8BxaWEinPZrNh8eLF7n+vXLkSEyZMwO7du5GTk4OIiAgT05HROP4Di08cvvvtb38LTdMQFBSE+vr626774x//GJqmYcqUKWhqavJQQtJTSEgIEhMTISK4ePGi2XHIwzj+vs0nSmn+/PkYM2YMWlpasGPHjluul5OTg/z8fAwfPhyHDh3CkCFDPJiS9NT5YhQeHm5yEjIDx993+UQpWSwWvPzyywCA7du3o62trds6Bw8exJo1axAQEICPP/4Yd999t6djUh85HA7U19ejrq4OJSUleO6551BcXIwZM2YgNjbW7HhkMI7/ACM+wuFwSEREhACQDz74oMt9RUVFEhQUJAAkPz/fpIQDV3NzswAQANLc3Nzjxx0/ftz9uP+9Pfnkk1JdXa1ETrqzvmxbT49/X3OSvnxiTwkAgoKC8PzzzwMAtm7d6l5eVVWF9PR0fPvtt3j99dexaNEisyJSHy1fvhxHjx7F4cOHkZubi/DwcFy+fBmBgYHudbKysrBgwYIuj7t69SqioqLw4Ycfejoy6YjjP8CY3Yp6unr1qoSGhgoAOX78uNjtdrHZbAJA5s2bJy6Xy+yIA1J/95TeeeedLstPnjwpmqZJZmame1lDQ4OMGDFC9u3b516WlZUl8+bNMzwn3Vl/9pQ8Nf59zUn68qlSEhH52c9+JgAkLS1NMjIyBIBMmzZNHA6H2dEGLL1LSURkyZIlAkBOnjzpXnbkyBEJDw+XqqoqOXDggFitVqmvrzc8J92ZnqUkYsz49zUn6cvnSunSpUsyePBg98SKjo6Wqqoqs2MNaEaUUllZmVgsFnnooYe6LH/mmWdkzpw5EhERIZ9++qlHctKd6V1KRox/X3OSvnzmb0qdRo4ciYULFwIAgoODcejQIYwYMcLkVKS3cePGISsrC3/5y19w4sQJ9/JNmzahvLwcKSkp+OEPf2hiQjISx993+eQVHTo/4f3ggw9i6tSpuj73tGnTUFNTo+tz+jqXy2XI865evRr79+/H2rVrcfz4cQA3Plg5duxYTJ48uV/PPX78ePj5+dx7NtMYMQeMHH+Ac6A/rFYrTp8+3afH+mQpffXVVwCgeyEBQE1NDaqqqnR/XuouOTkZInLL++Pi4tDR0WHIz66urjbkeannzBx/gHPALD5ZSmfPngUAJCQk6P7cVqtV9+f0dS6Xy+v+A4+KiuK7ZB1xDgws/Xmd9LlSqqqqcl//zog9pb7ukg5kdrsdoaGhZsfolbKyMoSEhJgdw2dwDlBP+Vwpde4lhYWFYcyYMSanITMUFhaaHYFMxPH3bj63b9r59yQjDt0REZGxfK6UjPx7EhERGYulREREyvC5vylduHDB7AhERNRHPrenRL6lpaUFP/rRjxAbG4v4+Hj84Ac/QHl5ebf1KioqYLFYkJCQ4L7xW0m91/PPP4/Ro0dD0zT334n/V0VFBZKTkxEWFnbTIyMlJSVITk5GXFwc4uLiUFBQYGxo0oXP7SmR71m+fDlSUlKgaRref/99LFu27KZnWA0ZMuSWL2DkXebNm4dVq1Zh1qxZt1xn6NChWL9+Pa5fv47Vq1d3uc/hcCA9PR15eXmYNWsWOjo6cPXqVaNjkw64p0RKCwwMRGpqKjRNAwAkJiaioqLC3FBkuKSkJMTExNx2nfDwcMyaNeumnyXat28fEhMT3aVmsVjclx8jtbGUyKts27YN6enpN73Pbrdj+vTpsNlsePPNNw29BA2p7fz58wgICMDjjz+OhIQELFmyBHV1dWbHoh5gKZHX2LBhA8rLy7Fx48Zu90VFRaGqqgpFRUX47LPPcOLECWzevNmElKQCp9OJzz77DDt37kRxcTGio6Px7LPPmh2LeoClRF5h06ZNKCgowJEjRxAcHNzt/oCAAAwfPhzAjcM62dnZXb7SgAaWUaNGYc6cOYiOjoamaVi8eDFOnTpldizqAZYSKW/Lli3Yv38/jh49imHDht10nW+++Qbt7e0AgNbWVhQUFBhy7UPyDgsWLEBRUREaGxsBAIcPH0Z8fLzJqagnWEqktMuXL+Oll17Cf//7X8yZMwcJCQm4//77AQBr167Fjh07AAB///vfMXXqVMTHx8Nms8FqtXY7I4u8x4oVKxATE4PLly/j0Ucfxbhx4wAAy5YtwyeffALgxhl2MTExmD9/Ps6fP4+YmBi8+uqrAG7sKb322muYOXMmpkyZgmPHjrnnCqlNk9t9YQmRDr57hejm5mZlr7zsLTm9kbdsW2/J6cu4p0RERMpgKRERkTJ4RQfyKLvdbnaEW1I5my9ReTurnG2gYCmRR0VGRpodgUzGOUC3w8N3RESkDJ59R4YTETgcDrNj9EpwcLD7envUf5wD1FMsJSIiUgYP3xERkTJYSkREpAyWEhERKYOlREREymApERGRMlhKRESkDJYSEREpg6VERETKYCkREZEyWEpERKQMlhIRESmDpURERMpgKRERkTJYSkREpAyWEhERKYOlREREymApERGRMlhKRESkDJYSEREpg6VERETKYCkREZEyWEpERKQMlhIRESmDpURERMpgKRERkTL+D+kL6o/0beeWAAAAAElFTkSuQmCC" }, - "execution_count": 116, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -376,13 +376,13 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 18, "id": "79045cc1a7706f87", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.862217Z", - "start_time": "2023-11-24T15:15:30.477851Z" + "end_time": "2023-11-24T17:18:41.514314Z", + "start_time": "2023-11-24T17:18:41.054658Z" } }, "outputs": [ @@ -391,7 +391,7 @@ "text/plain": "
", "image/png": 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}, - "execution_count": 117, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -478,22 +478,22 @@ }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 19, "id": "1e602fda98a6356d", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:30.962348Z", - "start_time": "2023-11-24T15:15:30.866907Z" + "end_time": "2023-11-24T17:18:41.634489Z", + "start_time": "2023-11-24T17:18:41.506369Z" } }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 118, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -522,22 +522,22 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 20, "id": "a6fc4d5d394d301a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:31.028658Z", - "start_time": "2023-11-24T15:15:30.934751Z" + "end_time": "2023-11-24T17:18:41.712575Z", + "start_time": "2023-11-24T17:18:41.591765Z" } }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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OnNVqrcg6AAAA4IRKvZoVAAAAlcvhlbknnnhCJpNJM2fOVEBAgMM3AzaZTPp//+//OV0gAAAAimey2Ww2RzqazWaZTCYdOnRIt956q8xmxxb1TCaT8vLyylWkO8jIyJCvr6/S09Pl4+Pj6nIA4E9p5FxXVwD8Zv7zlTu+o9nD4ZW5//73v5KkBg0aFHgNAAAA13E4zAUHB5f4GgAAADceF0AAAAAYmMMrcwkJCU7vJCgoyOn3AgAAoHgOh7nGjRsX+yzWkphMJuXm5pb5fQAAACidw2Fu+PDhToU5AAAAVB6Hw9zHH39ciWUAAADAGVwAAQAAYGCEOQAAAAPjcV4AAAAG5raP89q9e7emT5+unTt3KicnR61atdL48eM1ePDgMo1z5swZzZo1S998840SExNVvXp13XrrrRo+fLieeeYZh8fhcV4A4Ho8zgvuhMd5lWDz5s0KDw+Xt7e3hgwZopo1a2rFihWKjIxUYmKiJkyY4NA4Bw4cUFhYmM6fP68BAwbowQcfVGZmpg4dOqTVq1eXKcwBAAC4I4dX5m6U3NxcNW/eXCdPntT333+v0NBQSVJ6ero6duyo48ePKzY2ttTHiWVkZKhVq1a6fPmyNmzYoNatWxfaj4eHw1mWlTkAcAOszMGduMvKnNtdALFp0ybFx8dr2LBh9iAnSb6+vpo8ebKuXr2qRYsWlTrO+++/r4SEBM2ePbtQkJNUpiAHAADgrsqdaL766it9/PHH2r9/v9LT0+Xr66t27dppxIgRuu+++8o83pYtWyRJYWFhhbaFh4dLkrZu3VrqOEuXLpXJZNKgQYN05MgRRUdH6/Lly2revLnuuusuValSpcy1AQAAuBunw1xubq6GDRumFStWyGazycPDQ3Xq1FFycrJWrVql1atXa9CgQVq8eHGZVsHi4uIkSU2bNi20LTAwUDVq1LD3Kc7Vq1f1008/yd/fX++8846mT58uq9Vq3x4SEqKVK1eqVatWxY6RnZ2t7Oxs++uMjAxJUk5OjnJyciRduyjEYrEoLy+vwPj57bm5ubr+KLbFYpHZbC62PX/cfPn/br9/HFpx7Z6enrJarQUuODGZTPLw8Ci2vbjamRNzYk7MyR3nJPEkIriPG/F5coTTYW7WrFn64osv1L17d/373/9Wly5dZDabZbVatXPnTk2ZMkUrVqzQ7NmzNXXqVIfHTU9Pl3TtsGpRfHx87H2Kk5aWpry8PJ07d07//Oc/9dprr+nRRx9VTk6O5s2bp1deeUUDBw7U4cOH5e3tXez8ZsyYUag9Ojpa1apVkyQFBQWpbdu2OnjwoBISEux9mjVrpubNm2vXrl06e/asvT00NFTBwcHatm2bLl68aG/v0qWL6tatq+jo6AJ/uF69eqlq1apas2ZNgRoiIiJ0+fJlbd682d7m4eGhAQMGKDU1VTExMfb2mjVrqnfv3kpMTNSBAwfs7f7+/uratavi4uJ05MgReztzYk7MiTm585wkzlmG+6jsz9PevXsdqsPpCyBCQkLk7e2tgwcPFrnylpOTo9atWys7O1vHjh1zeNywsDCtX79ecXFxatKkSaHtDRo0UGZmZomB7vTp0/arbseOHau5c+cW2B4ZGally5bpk08+0SOPPFLkGEWtzDVq1Eipqan2kxBd/Qv1j/irmzkxJ+bEnEqa06i3WZmD+5j3XOV+ntLS0lSnTp2KuzXJ7yUlJem5554r9hCqp6enBg4cqHfeeadM4+avyBUX1jIyMlSrVi2HxpCke+65p9D2e+65R8uWLdOePXuKDXNeXl7y8vIq1O7p6SlPT88CbRaLRRaLpVDf4v5tSvo3K2+72Wwu8h6AxbUXVztzYk5lbWdOzEmq/DkB7sRVn6dC+3OoVxEaNWqkzMzMEvtkZWUpKCioTOPmnytX1HlxycnJyszMLPJ8uutVr17dvjLn5+dXaHt+27UlewAAAONyOsw9+eSTWrZsmZKSkorcfurUKS1dulRPPvlkmcbt0aOHpGvnpv1eVFRUgT4l6d27tyTp119/LbQtv61x48Zlqg0AAMDdOHzO3PUn5knXruAYO3asfvjhBz3//PPq1q2bAgIClJKSou3bt+vtt99W586dNXfu3DKFptzcXDVr1kynTp0q9qbBR44csY+ZlJSk9PR01atXr8Dh1Z07d+rOO+/U7bffrh07dthX45KTk9W+fXslJSXZH03mCG4aDACux02D4U7c5abBZX426+/ZbLZi2/Pf5+iltfmKe5zXiRMnNGfOnAKP8xoxYoQWLVqkhQsXasSIEQXGmTBhgt588001atRIAwcOVE5Ojr7++mudOXNGM2fO1KRJkxyuiTAHAK5HmIM7cZcw5/AFEMOHDy8ytFWGXr16aceOHZo+fbqWLl2qnJwctWrVSq+++qoiIyMdHueNN95Qq1at9N577+njjz+WyWRS27Zt9cEHH+j++++vxBkAAADcGG73bFZ3xcocALgeK3NwJ+6yMud2z2YFAACA4whzAAAABub0TYMl6eLFi3r33Xe1YcMGnT59usATE/KZTCbFx8eXZzcAAAAohtNh7uzZs+ratavi4+Pl4+NjP6579epV+81469evz128AQAAKpHTh1lffvllxcfH63//9391/vx5SdK4ceOUlZWlH374QR07dlTjxo31yy+/VFixAAAAKMjpMLdmzRr16dNHjzzySKFblnTo0EFr167V8ePHNWPGjHIXCQAAgKI5HeaSkpLUtm1b+2uLxVLgWae1atVS//79tWzZsvJVCAAAgGI5HeZ8fX2Vk5Njf12rVi2dPHmyQB8fHx+lpKQ4Xx0AAABK5HSYCwkJ0fHjx+2v27Ztq/Xr1+vcuXOSpMuXL2v16tUKCgoqd5EAAAAomtNhLiwsTBs3btSlS5ckSU899ZTOnDmjNm3a6KGHHlLLli0VHx9f6HmpAAAAqDhOh7mnn35a8+fPt4e5Bx54QK+//rqysrK0YsUKJScna/z48Zo4cWKFFQsAAICCKvzZrHl5eUpNTVXdunULXeVqZDybFQBcj2ezwp24y7NZy/UEiKJYLBYFBARU9LAAAAAoQrnDXFJSkpYsWaL9+/crPT1dvr6+atu2rYYMGaJ69epVRI0AAAAoRrnC3HvvvaeJEycqOztb1x+t/fTTTzVlyhTNmTNHzz77bLmLBAAAQNGcDnNLlizR3/72N910002aMmWK/vKXvyggIEApKSnatm2b3n77bfv2wYMHV2TNAAAA+D9OXwDRrl07nTx5UgcOHFD9+vULbT958qTatm2roKAg7d27t9yFuhoXQACA63EBBNyJu1wA4fStSQ4dOqTBgwcXGeQkqWHDhnrooYd06NAhZ3cBAACAUjgd5vz8/FS9evUS+9SoUUN+fn7O7gIAAAClcDrM3XPPPVq9erVyc3OL3J6Tk6PVq1fr3nvvdbo4AAAAlMzpMPfaa6+pevXqCgsL0/fff19gW0xMjMLCwlSzZk3Nnj273EUCAACgaA5fzRoSElKo7erVq9q3b5/uvPNOeXh46KabblJqaqp9ta5evXpq166d4uPjK65iAAAA2Dkc5qxWa6HHc3l6eiooKKhA2+8viLBareUoDwAAACVxOMwdP368EssAAACAM5w+Zw4AAACuV+5ns0pSbm6ujhw5ooyMDPn4+KhZs2by8KiQoQEAAFCCcq3MpaWlaeTIkfL19VXr1q3VrVs3tW7dWn5+fho1apTOnTtXUXUCAACgCE4vn6Wlpalz5846evSoateurb/85S+qV6+ekpOTtWfPHi1YsEBbt25VTEyMateuXZE1AwAA4P84vTL3r3/9S0ePHtXEiRN14sQJrVu3TgsXLtTatWt14sQJvfTSS4qLi9O///3viqwXAAAA1zHZbDabM28MCQlR48aNtWnTpmL79O7dW8ePH9exY8ecLtBdOPqwWwBA5Rk519UVAL+Z/3zlju9o9nB6Ze706dPq0qVLiX26dOmi06dPO7sLAAAAlMLpMOfr66sTJ06U2OfEiRPy9fV1dhcAAAAohdNhrkePHlq+fLk2bNhQ5PaNGzdq+fLl6tmzp7O7AAAAQCmcvpp1+vTp+vbbbxUeHq6IiAj16NFDAQEBSklJ0ZYtW7R27VpVq1ZN06ZNq8h6AQAAcB2nw9ztt9+uqKgojRgxQt9++62+/fZbmUwm5V9Pccstt+jjjz/W7bffXmHFAgAAoKByPaahW7duiouL03fffaf9+/fbnwDRtm1b3XnnnTKZTBVVJwAAAIrgdJh74okn1KpVK40bN07dunVTt27dKrIuAAAAOMDpCyAWL16sM2fOVGQtAAAAKCOnw9wtt9yipKSkiqwFAAAAZeR0mHviiSf07bff6tSpUxVZDwAAAMrA6XPmBg0apM2bN6tr16568cUX1aFDBwUEBBR50UNQUFC5igQAAEDRnA5zISEh9luRPPfcc8X2M5lMys3NdXY3AAAAKIHTYW748OHcegQAAMDFnA5zH3/8cQWWAQAAAGc4fQEEAAAAXK9cT4CQpOzsbK1Zs0b79+9Xenq6fH191bZtW0VERMjLy6siagQAAEAxyhXmVq1apVGjRuns2bP2Z7JK1y56qFu3rj788EMNHDiw3EUCAACgaE6HuY0bN2rQoEGyWCx64okn9Je//EUBAQFKSUnRtm3b9Omnn+qBBx5QVFSUevfuXZE1AwAA4P+YbNcvqZVBt27ddPDgQe3cuVMtW7YstP3gwYO68847FRoaqu3bt5e7UFfLyMiQr6+v0tPT5ePj4+pyAOBPaeRcV1cA/Gb+85U7vqPZw+kLIPbv36/IyMgig5wktW7dWoMHD9a+ffuc3QUAAABK4XSYq1atmvz9/UvsU7duXVWrVs3ZXQAAAKAUToe5vn37asOGDSX22bBhg/r16+fsLgAAAFAKp8PcnDlzdObMGQ0fPlyJiYkFtiUmJurRRx9Vamqq5syZU+4iAQAAUDSnr2Z99NFHVatWLX322WdasmSJgoKC7FezJiQkKC8vT61bt9YjjzxS4H0mk0kbN24sd+EAAAAoR5jbsmWL/X/n5ubq2LFjOnbsWIE+P/74Y6H38TxXAACAiuN0mLNarRVZBwAAAJzAs1kBAAAMrMLCXEJCgrZt21ZRwwEAAMABFRbmFi5cqF69elXUcAAAAHAAh1kBAAAMjDAHAABgYIQ5AAAAA6uwMOfr66ugoKCKGg4AAAAOqLAw9/zzz+u///1vRQ2n3bt3KyIiQn5+fqpevbo6d+6sZcuWOT3e+fPn1aBBA5lMJt11110VVicAAIArOX3T4Mq0efNmhYeHy9vbW0OGDFHNmjW1YsUKRUZGKjExURMmTCjzmGPGjFF6enolVAsAAOA6Doe5/HvIdezYUd7e3mW6p1z37t0d7pubm6uRI0fKbDZr27ZtCg0NlSRNmzZNHTt21OTJk/Xggw8qODjY4TFXrFihxYsX691339WYMWMcfh8AAIC7czjM9ezZUyaTSYcOHdKtt95qf+2IvLw8hwvatGmT4uPj9fjjj9uDnHTtnLzJkydrxIgRWrRokaZNm+bQeGfPntUzzzyjRx99VAMGDCDMAQCAPxSHw9y0adNkMpl00003FXhd0bZs2SJJCgsLK7QtPDxckrR161aHx3v66adlsVj09ttvc5gVAAD84Tgc5l5++eUSX1eUuLg4SVLTpk0LbQsMDFSNGjXsfUrz6aef6ssvv9TKlStVq1atMoW57OxsZWdn219nZGRIknJycpSTkyNJMpvNslgsysvLk9VqtffNb8/NzZXNZrO3WywWmc3mYtvzx83n4XHtz5Obm+tQu6enp6xWa4GVUJPJJA8Pj2Lbi6udOTEn5sSc3HFOUsUvIgDOuhGfJ0e43QUQ+YHL19e3yO0+Pj4OhbLTp0/rueee09ChQ3XvvfeWuY5Zs2ZpxowZhdqjo6NVrVo1SVJQUJDatm2rgwcPKiEhwd6nWbNmat68uXbt2qWzZ8/a20NDQxUcHKxt27bp4sWL9vYuXbqobt26io6OLvCH69Wrl6pWrao1a9YUqCEiIkKXL1/W5s2b7W0eHh4aMGCAUlNTFRMTY2+vWbOmevfurcTERB04cMDe7u/vr65duyouLk5HjhyxtzMn5sScmJM7z0nyEeAuKvvztHfvXofqMNmu/6lUBhcvXtTZs2fVqFEjeXp62tuXLl2qVatWydvbW6NHj1a7du3KNG5YWJjWr1+vuLg4NWnSpND2Bg0aKDMzs9RAFxERob179+qXX36xHxo+fvy4br75ZoWHh2vdunUlvr+olblGjRopNTVVPj7Xvkxc/Qv1j/irmzkxJ+bEnEqa06i3WZmD+5j3XOV+ntLS0lSnTh2lp6fbs0dRnF6Ze/HFF/Xpp58qJSXFHub+85//aMyYMfYP7JIlS7R37141b97c4XHzV+SKC2sZGRmqVatWiWMsWrRIa9eu1fLly+1Brqy8vLzk5eVVqN3T07NAeJWufSlZLJZCfX87LOBY++/HdabdbDbLbC58+8Di2ournTkxp7K2MyfmJFX+nAB34qrPU6H9OdSrCFu3blXfvn3thxwlafbs2WrQoIG2bdumZcuWyWaz6fXXXy/TuPnnyhV1XlxycrIyMzOLPJ/uevv375ckPfTQQzKZTPb/br75ZklSVFSUTCZTgatlAQAAjMjplbmkpKQCT1I4dOiQEhMT9dprr6lbt26SpC+++KJM96OTpB49emjWrFmKjo7WkCFDCmyLioqy9ylJly5dlJmZWag9MzNTS5cuVcOGDRUeHs7jxwAAgOE5Heays7NVpUoV++utW7fKZDIVuKVISEiIVq1aVaZx+/Tpo5CQEC1evFjPPfecffUsPT1dM2fOVJUqVTR8+HB7/6SkJKWnp6tevXr2Q7SRkZGKjIwsNPbx48e1dOlS3X777VqwYEGZ6gIAAHBHTh9mbdiwoQ4ePGh//c0336h27dpq3bq1ve3cuXOqUaNGmcb18PDQggULZLVa1b17d40aNUoTJkxQmzZtFBsbq5kzZ6px48b2/pMmTVKLFi301VdfOTsVAAAAw3J6Za5///5677339MILL8jb21vr1q0rsGImSbGxsU4dyuzVq5d27Nih6dOna+nSpcrJyVGrVq306quvFrniBgAA8Gfl9K1JkpOT1bVrVx0/flySVK9ePf3www9q2LChJOnMmTNq2LChxowZozfffLPCCnaVjIwM+fr6lnp5MACg8oyc6+oKgN/Mf75yx3c0ezi9MhcYGKhffvlFGzdulCR17969wI5SU1P1+uuv2x/BBQAAgIpXridAVK1aVXfffXeR22677Tbddttt5RkeAAAApXD6AggAAAC4XrlW5vLy8rRs2TJt2LBBp0+fLvD4q3wmk8l+KBYAAAAVy+kwl5WVpbCwMH3//fey2WwymUwFnruX/9pk4jl6AAAAlcXpw6yvvPKKYmJiNGPGDKWmpspms+nll19WUlKSli5dqpCQED300ENFrtYBAACgYjgd5r788kt17txZU6dOVe3ate3tAQEBeuihh7R582Zt2LChzM9mBQAAgOOcDnMJCQnq3LnzbwOZzQVW4Ro2bKgBAwZo0aJF5asQAAAAxXI6zFWvXl1m829v9/X1VVJSUoE+gYGBSkhIcL46AAAAlMjpMBccHFwgqLVs2VKbNm2yr87ZbDZt3LhR9erVK3+VAAAAKJLTYa5Pnz7avHmzcnNzJUmPPfaYEhIS1KVLF02cOFHdunXTgQMHNGjQoAorFgAAAAU5fWuSkSNHqk6dOjp79qzq1aunJ554Qvv379f777+vAwcOSJIGDRqkl19+uYJKBQAAwO+ZbNffHK4CnD17VseOHVNwcLACAwMrcmiXcvRhtwCAyjNyrqsrAH4z//nKHd/R7FGuJ0AUxd/fX/7+/hU9LAAAAIrAs1kBAAAMzOmVuZCQEIf6mUwmxcfHO7sbAAAAlMDpMGe1Wot87mp6erouXLggSapXr56qVKnidHEAAAAomdNh7vjx4yVuGz9+vFJSUrR+/XpndwEAAIBSVMo5c40bN9bSpUt1/vx5TZkypTJ2AQAAAFXiBRCenp7q16+fli1bVlm7AAAA+NOr1KtZL126pLS0tMrcBQAAwJ9apYW57du36/PPP1ezZs0qaxcAAAB/ek5fANG7d+8i23Nzc3Xq1Cn7BRLTpk1zdhcAAAAohdNhbsuWLUW2m0wm1apVS2FhYRo/frz69evn7C4AAABQinLdZw4AAACuVe5ns545c0anTp2S1WpVgwYNFBgYWBF1AQAAwAFOXQCRnZ2t1157TU2bNlW9evXUvn17dezYUQ0aNNBNN92kcePGlXhTYQAAAFSMMoe5xMREdejQQZMmTVJ8fLzq1aunjh07qmPHjqpXr57S0tL09ttvq3379tqwYYP9fUlJSdxzDgAAoIKVKczl5OQoIiJCP//8s4YOHapDhw7p5MmTiomJUUxMjE6ePKlDhw7p4YcfVlpamu677z4dP35c8fHx6tatmw4fPlxZ8wAAAPhTKtM5c/PmzdMvv/yi6dOna/r06UX2adasmT755BPdeuutmj59uh5++GEdP35cqampuuOOOyqkaAAAAFxTppW5ZcuWqUmTJg7dO27q1Klq2rSpYmJidOXKFUVFRWnAgAFOFwoAAIDCyhTmfv31V4WFhclkMpXa12Qy2fv+8MMP6tmzp7M1AgAAoBhlCnOZmZny9fV1uL+Pj488PDzUpEmTMhcGAACA0pUpzNWtW1dHjx51uH98fLzq1q1b5qIAAADgmDKFuS5dumjt2rVKTk4utW9ycrK+/fZbdevWzeniAAAAULIyhbmnn35amZmZuv/++5Wamlpsv3Pnzun+++/XpUuX9NRTT5W7SAAAABStTLcm6dWrl0aOHKn58+erRYsWeuqpp9S7d281atRI0rUbCm/cuFHz589XamqqRo0axYUPAAAAlajMz2Z9//335ePjo7feekuzZs3SrFmzCmy32Wwym8164YUXCm0DAABAxSpzmLNYLHr99dc1atQoffzxx4qJibGfQxcYGKiuXbvqscceU9OmTSu8WAAAABRU5jCXr2nTpvr3v/9dkbUAAACgjMp0AQQAAADcC2EOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBgbhvmdu/erYiICPn5+al69erq3Lmzli1b5tB7bTab1q5dq2eeeUatW7eWr6+vqlWrpjZt2mjmzJm6cuVKJVcPAABwY3i4uoCibN68WeHh4fL29taQIUNUs2ZNrVixQpGRkUpMTNSECRNKfH92drYiIiLk5eWlnj17Kjw8XFeuXFFUVJSmTJmilStXasuWLapWrdoNmhEAAEDlMNlsNpuri7hebm6umjdvrpMnT+r7779XaGioJCk9PV0dO3bU8ePHFRsbq+Dg4GLHyMnJ0WuvvaZnn31WtWrVKtA+aNAgrV69Wq+99pomTpzocF0ZGRny9fVVenq6fHx8nJ4fAMB5I+e6ugLgN/Ofr9zxHc0ebneYddOmTYqPj9ewYcPsQU6SfH19NXnyZF29elWLFi0qcQxPT09NmTKlQJDLb580aZIkaevWrRVeOwAAwI3mdmFuy5YtkqSwsLBC28LDwyWVL4h5enpKkjw83PIIMwAAQJm4XaKJi4uTJDVt2rTQtsDAQNWoUcPexxkfffSRpKLD4vWys7OVnZ1tf52RkSHp2qHanJwcSZLZbJbFYlFeXp6sVqu9b357bm6urj+KbbFYZDabi23PHzdffuDMzc11qN3T01NWq1V5eXn2NpPJJA8Pj2Lbi6udOTEn5sSc3HFOkkmAu7gRnydHuF2YS09Pl3TtsGpRfHx87H3Kau3atZo3b55atGihv/71ryX2nTVrlmbMmFGoPTo62n7hRFBQkNq2bauDBw8qISHB3qdZs2Zq3ry5du3apbNnz9rbQ0NDFRwcrG3btunixYv29i5duqhu3bqKjo4u8Ifr1auXqlatqjVr1hSoISIiQpcvX9bmzZvtbR4eHhowYIBSU1MVExNjb69Zs6Z69+6txMREHThwwN7u7++vrl27Ki4uTkeOHLG3MyfmxJyYkzvPSeKcZbiPyv487d2716E63O4CiLCwMK1fv15xcXFq0qRJoe0NGjRQZmZmmQPd7t271adPH3l4eGj79u26/fbbS+xf1Mpco0aNlJqaaj8J0dW/UP+Iv7qZE3NiTsyppDmNepuVObiPec9V7ucpLS1NderUKfUCCLdbmctfkSsurGVkZBS6sKE0e/bsUVhYmMxms6KiokoNcpLk5eUlLy+vQu2enp728+7yWSwWWSyWQn2LOy+vuPbfj+tMu9lsltlc+FTI4tqLq505MaeytjMn5iRV/pwAd+Kqz1Oh/TnU6wbKP1euqPPikpOTlZmZWeT5dMXZs2eP+vXrJ6vVqqioKHXo0KHCagUAAHA1twtzPXr0kHTt3LTfi4qKKtCnNPlBLi8vT+vWrVOnTp0qrlAAAAA34HZhrk+fPgoJCdHixYsLnDyYnp6umTNnqkqVKho+fLi9PSkpSYcPHy50WHbv3r3q16+fcnNztXbtWnXp0uVGTQEAAOCGcbtz5jw8PLRgwQKFh4ere/fuBR7ndeLECc2ZM0eNGze29580aZIWLVqkhQsXasSIEZKktLQ09evXTxcuXNBdd92l9evXa/369QX24+fnp+eff/7GTQwAAKASuF2Yk65dmr5jxw5Nnz5dS5cuVU5Ojlq1aqVXX31VkZGRpb4/IyND58+flyStW7dO69atK9QnODiYMAcAAAzP7W5N4q54NisAuB7PZoU74dmsAAAAKDfCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYg9t577331LhxY3l7e6tTp07atWtXif2XL1+u5s2by9vbW61atdKaNWsKbE9JSdGIESNUv359VatWTXfddZfi4uIK9ImPj9f9998vf39/+fj4aPDgwUpJSanwuQEAUNEIc3ArS5cu1fjx4zV9+nTt27dPbdq0UXh4uM6cOVNk/507d2ro0KH661//qv379+u+++7Tfffdp59//lmSZLPZdN999+nYsWP6+uuvtX//fgUHB6tv377KysqSJGVlZSksLEwmk0mbNm3Sd999p6tXr2rgwIGyWq03bO4AADjDZLPZbK4uwggyMjLk6+ur9PR0+fj4uLqcP6xOnTqpQ4cOevfddyVJVqtVjRo10t/+9jf9/e9/L9Q/MjJSWVlZ+uabb+xtnTt3VmhoqD744APFxsaqWbNm+vnnn3X77bfbxwwMDNTMmTP15JNPKjo6Wv3799f58+ftf9v09HTVqlVL0dHR6tu37w2YOQBHjJzr6gqA38x/vnLHdzR7sDIHt3H16lXt3bu3QHgym83q27evYmJiinxPTExMobAVHh5u75+dnS1J8vb2LjCml5eXduzYYe9jMpnk5eVl7+Pt7S2z2WzvAwCAuyLMwW2kpqYqLy9PAQEBBdoDAgKUnJxc5HuSk5NL7N+8eXMFBQVp0qRJOn/+vK5evapXX31VJ0+eVFJSkqRrK3nVq1fXSy+9pEuXLikrK0svvPCC8vLy7H0AAHBXhDn8oXl6eurLL79UbGysateurWrVqmnz5s3q37+/zOZr//f39/fX8uXLtXr1atWoUUO+vr66cOGC2rVrZ+8DAIC78nB1AUC+m266SRaLpdBVpCkpKQoMDCzyPYGBgaX2v+OOO3TgwAGlp6fr6tWr8vf3V6dOndS+fXt7n7CwMMXHxys1NVUeHh7y8/NTYGCgQkJCKnCGAABUPJYd4DaqVKmiO+64Qxs3brS3Wa1Wbdy4UV26dCnyPV26dCnQX5LWr19fZH9fX1/5+/srLi5Oe/bs0b333luoz0033SQ/Pz9t2rRJZ86c0T333FPOWQEAULlYmYNbGT9+vB577DG1b99eHTt21Ny5c5WVlaXHH39ckjR8+HA1aNBAs2bNkiSNHTtWPXr00BtvvKEBAwZoyZIl2rNnjz788EP7mMuXL5e/v7+CgoL0008/aezYsbrvvvsUFhZm77Nw4UK1aNFC/v7+iomJ0dixYzVu3Dg1a9bsxv4DAABQRoQ5uJXIyEidPXtW06ZNU3JyskJDQ7Vu3Tr7RQ4JCQkFzmPr2rWrFi9erKlTp2ry5Mlq2rSpVq5cqZYtW9r7JCUlafz48UpJSVG9evU0fPhw/eMf/yiw3yNHjmjSpElKS0tT48aNNWXKFI0bN+7GTBoAgHLgPnMO4j5zAOB63GcO7oT7zAEAAKDcCHMAAAAGRpgDAAAwMC6AcDOcDwJ3UtnngwAAyo+VOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADMxtw9zu3bsVEREhPz8/Va9eXZ07d9ayZcvKNEZ2drb++c9/qmnTpvL29lb9+vU1atQonTlzppKqBgAAuLE8XF1AUTZv3qzw8HB5e3tryJAhqlmzplasWKHIyEglJiZqwoQJpY5htVp17733KioqSp07d9agQYMUFxenBQsWaOPGjfr+++/l7+9/A2YDAABQedxuZS43N1cjR46U2WzWtm3b9OGHH+qNN97Qjz/+qFtvvVWTJ0/WiRMnSh1n0aJFioqK0tChQ7Vz507Nnj1bK1as0Pvvv69jx45p6tSpN2A2AAAAlcvtwtymTZsUHx+vYcOGKTQ01N7u6+uryZMn6+rVq1q0aFGp48yfP1+SNGvWLJlMJnv7U089pZCQEH322We6fPlyhdcPAABwI7ldmNuyZYskKSwsrNC28PBwSdLWrVtLHOPKlSv64Ycf1KxZMwUHBxfYZjKZ1K9fP2VlZWnPnj0VUzQAAICLuF2Yi4uLkyQ1bdq00LbAwEDVqFHD3qc48fHxslqtRY5x/diljQMAAODu3O4CiPT0dEnXDqsWxcfHx96nPGNc368o2dnZys7OLjRmWlqacnJyJElms1kWi0V5eXmyWq32vvntubm5stls9naLxSKz2Vxse05Ojq5e8SxxbsCNdO5cToHXHh7XvjJyc3MLtHt6espqtSovL8/eZjKZ5OHhUWx7cZ+bivw8OVI7czLWnK5eMQlwFxcuVO7nKS0tTZIKfHaK4nZhzl3MmjVLM2bMKNR+8803u6AawDX+d5KrKwAA93WjviMvXrxY7AKV5IZhLr/Y4lbNMjIyVKtWrXKPcX2/okyaNEnjx4+3v7ZarUpLS1OdOnUKXFAB95ORkaFGjRopMTHRvgoLALiG70jjsNlsunjxourXr19iP7cLc9efz3bHHXcU2JacnKzMzEx17NixxDFCQkJkNpuLPSeupPPy8nl5ecnLy6tAm5+fX2nlw434+PjwRQUAxeA70hhKWnjK53YXQPTo0UOSFB0dXWhbVFRUgT7FqVq1qjp27KgjR44UuiedzWbT+vXrVb16dbVv376CqgYAAHANtwtzffr0UUhIiBYvXqwDBw7Y29PT0zVz5kxVqVJFw4cPt7cnJSXp8OHDhQ6pjho1StK1w6XXnzg4b948HTt2TA8//LCqVq1auZMBAACoZG4X5jw8PLRgwQJZrVZ1795do0aN0oQJE9SmTRvFxsZq5syZaty4sb3/pEmT1KJFC3311VcFxnnssccUHh6uzz//XF27dtXf//53Pfjgg3r22Wd1880365VXXrnBM8ON4uXlpenTpxc6TA4A4Dvyj8hkK+16VxfZtWuXpk+frp07dyonJ0etWrXS+PHjFRkZWaDfiBEjtGjRIi1cuFAjRowosC07O1uzZ8/WJ598osTERNWuXVt33323XnnlFQUEBNzA2QAAAFQOtw1zAAAAKJ3bHWYFAACA4whzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8zB8KxWq6tLAADAZQhzMDyz+bf/GxPsAKCwvLw8V5eASkSYg2GlpKRowoQJioqK0oULFyT9FuxsNhvBDsCfXv73oMVikeT4dyMPhzIWHucFw5o+fbr+9a9/qXHjxrrtttvUs2dP9ejRQ61bty7wAGmr1SqbzSaLxaItW7boypUruuuuu1xYOQDcGP/5z3+0ZcsWDR8+XD169FCNGjXs2/JD3fVHN2BMhDkYVtu2bfXrr7+qXbt22rdvn3JychQcHKw777xTvXr10p133qnmzZvb+1+6dElDhw7VN998o6ysLHl7e7uwegCofDfffLNOnDghLy8vtWnTRmFhYYqIiFCnTp1kMpns/XJzc+Xh4aFLly7pww8/VJs2bdSrVy8XVo6yIMzBkBITE9W9e3fVqVNHMTEx2rt3r9asWaNVq1bp4MGDMpvNuv3229W9e3d1795d4eHhOnLkiO655x516NBBq1atcvUUAKBS/fLLL2rVqpXuuOMO1apVSxs2bJAkVa9eXXfeeaciIiIUFhZW4Efvjh071L17d3Xt2lU7duxwVekoIw9XFwA4IykpSRkZGerRo4c8PT3VoUMHdezYUWPGjNG+ffv09ddfa+3atXrvvff00UcfqX379vL09FRKSopGjRrl6vIBoNL99NNPkqRhw4Zp3Lhxio2N1cqVK/X5558rOjpa0dHRCgwMVM+ePdW/f3/dfffd2rVrlyRp0qRJriwdZcTKHAzp6NGjeumllzRo0CANGzas0PacnBydPn1a27dv1+rVq7VhwwadP39efn5+SktLc0HFAHBjffjhh3r66af17bffqn///gW27d69W59//rm++OILnTx5UpLUtGlTZWRk6PLly/aLymAMhDkYVnp6unJzc1WnTp1i+1itVpnNZs2bN0/PPPOMnnnmGb333ns3sEoAuPFsNpt++OEHLVu2TKNHj9Ytt9xib7/+XLkrV65o48aNWr58uVauXKmMjAyNHj1a77zzjqtKhxMIczCc338ZSdfuoWQymYq9KuvFF1/UnDlztGfPHrVr1+5GlAkALpeZmakqVaqoSpUqhbb9/rt0zJgxev/997Vv3z6FhobewCpRXoQ5GFL+l1BycrLq1q1bIMTl5eXJbDbbv6ROnjypAQMG6PTp0zp79qyrSgYAt5P/XRofH6/IyEilp6crLi7O1WWhjLgAAoaSm5ur7777Th999JFiY2NlNptVtWpVtWnTRoMGDVLXrl3tN8fM5+3trREjRqh+/fouqhoA3FP+j95Dhw5p3759mjhxoosrgjNYmYOhzJkzR//617908eJFNWnSRBaLRUeOHLFvb968uUaOHKmhQ4cqMDDQ3n716lV5eHhwc0wAfypFnZZSlJSUFK1bt04DBw5U7dq1b0BlqEiEORjGf//7X7Vq1Urt2rXTokWLVKVKFQUEBCg5OVmrV6/W8uXLtWXLFklS79699dprr3F+HIA/lcuXLyshIUFBQUGqWrVqmd6bl5dX6MgGjIEwB8OYNm2a5s2bp8WLF6tPnz6SCv/q/OmnnzRnzhwtW7ZMwcHB+uyzz3THHXc4/OsUAIxs9uzZWrFihR544AF17txZzZo1U0BAQIkh7ezZs6pVq5Y8PDjzyqgIczCMQYMG6cCBA9q8ebOCgoLsj5/Jf3D09V9Wb7/9tsaNG6fHHntMCxcudGHVAHDjNGzYUKdPn5bFYpGvr6+6du2qsLAwderUSSEhIYVu5ZSVlaWXX35Z586d0/z581mZMyhiOAyjbdu2+uqrr5SZmSlJ9l+RJpPJ/gWUvwI3duxYbd++XZs2bdKxY8cUEhLisroB4EaIjY1Venq6unTpomHDhmn9+vWKiYnRN998o6CgIPXs2VN9+/ZV27Zt1aBBA/n5+ennn3/W/Pnz1bNnT4KcgRHmYBj5D31++OGH9cYbb6hbt25F3jsp/7yPZs2aae3atfbwBwB/ZLGxsbpy5YrCwsI0evRo3X333Tpy5IhiYmK0adMmrVixQp999pluu+029e7dW3fddZc2btyojIwMjRw50tXloxw4zArDyMvL00svvaQ333xTzZs31+jRo/Xggw8qICCgUN/z58/r+eef19q1a3XmzBkXVAsAN9YXX3yhwYMHa8mSJRo8eLC9PScnRydOnNCPP/6o7du3a8uWLTp06JA8PT1ls9nk5eXFYw4NjjAHw5k3b55ef/11HTt2TPXr19f999+v/v37q1GjRrJYLPLz89M777yjuXPn6tlnn9Ubb7zh6pIBoNLZbDYdPnxY3t7euvnmm4u88CsrK0uxsbE6cuSIFi5cqPXr12vMmDH6n//5HxdVjYpAmIPh2Gw2HT16VPPnz9eSJUvsD4muW7euPD09lZSUJKvVqqFDh+rVV19Vw4YNXVwxALhWUcHuueee07vvvqu9e/eqbdu2LqoMFYEwB0PLysrSrl27tGrVKp0+fVpnzpyRj4+PBg8erEGDBsnb29vVJQKA27BarTKbzTp+/LjuvfdenT9/XgkJCa4uC+XEBRAwtOrVq6tXr17q1auXcnJy5Onp6eqSAMBt5T8F59SpU8rJydGzzz7r4opQEViZAwDgT8Zms+nkyZOqXbu2qlev7upyUE6EOQAAAAPjqeMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAG9v8BYQhuSNKSSyoAAAAASUVORK5CYII=" 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" }, - "execution_count": 119, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -562,22 +562,22 @@ }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 21, "id": "8d4904619b35503a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:31.122882Z", - "start_time": "2023-11-24T15:15:31.032051Z" + "end_time": "2023-11-24T17:18:41.846121Z", + "start_time": "2023-11-24T17:18:41.706557Z" } }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 120, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -628,21 +628,21 @@ }, { "cell_type": "code", - "execution_count": 121, + "execution_count": 22, "id": "841bce19ea097bf1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:31.180074Z", - "start_time": "2023-11-24T15:15:31.131794Z" + "end_time": "2023-11-24T17:18:41.904413Z", + "start_time": "2023-11-24T17:18:41.855290Z" } }, "outputs": [ { "data": { - "text/plain": "0.1003" + "text/plain": "0.1004712084149367" }, - "execution_count": 121, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -676,21 +676,21 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 23, "id": "5468619791203a79", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:31.410222Z", - "start_time": "2023-11-24T15:15:31.195373Z" + "end_time": "2023-11-24T17:18:42.146331Z", + "start_time": "2023-11-24T17:18:41.920458Z" } }, "outputs": [ { "data": { - "text/plain": "0.0048000000000000004" + "text/plain": "0.0054042995153299" }, - "execution_count": 122, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -714,21 +714,21 @@ }, { "cell_type": "code", - "execution_count": 123, + "execution_count": 24, "id": "a5434c7c7c45040a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T15:15:32.089164Z", - "start_time": "2023-11-24T15:15:31.424204Z" + "end_time": "2023-11-24T17:18:42.955787Z", + "start_time": "2023-11-24T17:18:42.163155Z" } }, "outputs": [ { "data": { - "text/plain": "0.0052" + "text/plain": "0.0056128979765628" }, - "execution_count": 123, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 191c144b8..7fa86e7e8 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2021, 2023. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -70,7 +70,6 @@ class QBayesian: limit: The maximum number of times the Grover operator is integrated (2^limit). sampler (BaseSampler): The sampler primitive used to compute the samples and inferences. samples (Dict[str, float]): Samples generated from the rejection sampling. - shots (int): The number of samples that are obtained. threshold (float): The threshold to accept the evidence. """ @@ -79,7 +78,6 @@ class QBayesian: def __init__( self, circuit: QuantumCircuit, - shots: int = 10_000, limit: int = 10, threshold: float = 0.9, sampler: BaseSampler = Sampler(), @@ -91,7 +89,6 @@ def __init__( an oracle for the Grover operator. The last qubit in the circuit corresponds to the most significant bit passed in the state vector. Example: In a circuit with 2 qubits and the first qubit as evidence with value 0, the good states are 00 and 10. - shots: The number of samples drawn from the circuit. limit: The maximum number of times the Grover operator is integrated (2^limit). threshold (float): The threshold to accept the evidence. The threshold value for the acceptance of the evidence. For example, if set to 0.9, this means that each @@ -109,7 +106,6 @@ def __init__( raise ValueError("Every register needs to be mapped to exactly one unique qubit") # Initialize parameter self._circ = circuit - self.shots = shots self.limit = limit self.threshold = threshold if sampler is None: @@ -162,9 +158,9 @@ def _get_grover_op(self, evidence: Dict[str, int]) -> GroverOperator: return GroverOperator(oracle, state_preparation=self._circ) def _run_circuit(self, circuit: QuantumCircuit) -> Dict[str, float]: - """Run the quantum circuit for the number of shots on the Aer simulator backend.""" + """Run the quantum circuit with the sampler.""" # Sample from circuit - job = self.sampler.run(circuit, shots=self.shots) + job = self.sampler.run(circuit) result = job.result() # Get the counts of quantum state results counts = result.quasi_dists[0].binary_probabilities() diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 71fc479c1..e64cc19d4 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2021, 2023. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -20,7 +20,7 @@ from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister from qiskit_machine_learning.algorithms import QBayesian - +from qiskit.primitives import Sampler class TestQBayesianInference(QiskitMachineLearningTestCase): """Test QBayesianInference Algorithm""" @@ -130,8 +130,8 @@ def test_parameter(self): # Test set limit self.qbayesian.limit = 1 self.qbayesian.rejection_sampling(evidence={"B": 1}) - # Test set shots - self.qbayesian.shots = 10 + # Test sampler + self.qbayesian.sampler = Sampler() self.qbayesian.inference(query={"B": 1}, evidence={"A": 0, "C": 0}) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="No ValueError in constructor with invalid input."): From 52cdeb075a6bd7b30579d1a22f2e1b1b09c530a9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 24 Nov 2023 18:28:40 +0100 Subject: [PATCH 29/48] Fixed format --- test/algorithms/inference/test_qbayesian.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index e64cc19d4..5a5824a41 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -19,8 +19,9 @@ from qiskit_algorithms.utils import algorithm_globals from qiskit import QuantumCircuit from qiskit.circuit import QuantumRegister -from qiskit_machine_learning.algorithms import QBayesian from qiskit.primitives import Sampler +from qiskit_machine_learning.algorithms import QBayesian + class TestQBayesianInference(QiskitMachineLearningTestCase): """Test QBayesianInference Algorithm""" From a85253ee6493c2b093c38f33b282751f0b66faf3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 26 Nov 2023 21:37:04 +0100 Subject: [PATCH 30/48] Adjusted format for documentation + added format result --- .../13_quantum_bayesian_inference.ipynb | 235 ++++++-------- .../algorithms/inference/qbayesian.py | 302 ++++++++++-------- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 39 +++ ...m-bayesian-inference-92c6025432d9b7e0.yaml | 17 - test/algorithms/inference/test_qbayesian.py | 24 +- 5 files changed, 328 insertions(+), 289 deletions(-) create mode 100644 releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml delete mode 100644 releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 6bb345e1c..ee2d38199 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -7,7 +7,7 @@ "collapsed": false }, "source": [ - "# Quantum Bayesian Inference with Qiskit\n", + "# Quantum Bayesian Inference\n", "\n", "## Overview\n", "This notebook demonstrates a quantum Bayesian inference (QBI) implementations provided in `qiskit-machine-learning`, and how it can be integrated into basic quantum machine learning (QML) workflows.\n", @@ -106,49 +106,14 @@ ] }, { - "cell_type": "code", - "execution_count": 13, - "id": "initial_id", + "cell_type": "markdown", + "source": [ + "![Two Node Bayesian Network Example](Two_Node_Bayesian_Network.png)" + ], "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - }, - "ExecuteTime": { - "end_time": "2023-11-24T17:18:40.882177Z", - "start_time": "2023-11-24T17:18:40.795755Z" - } + "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": "
", - "image/png": 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" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "import networkx as nx\n", - "\n", - "# Create a directed graph\n", - "G = nx.DiGraph()\n", - "# Add nodes. The nodes will be positioned at (0, 0) and (1, 0) respectively.\n", - "G.add_node(\"X\", pos=(0, 0))\n", - "G.add_node(\"Y\", pos=(1, 0))\n", - "# Add a directed edge from A to B\n", - "G.add_edge(\"X\", \"Y\")\n", - "# Get the positions of each node\n", - "pos = nx.get_node_attributes(G, \"pos\")\n", - "# Draw the graph\n", - "nx.draw(\n", - " G, pos, with_labels=True, node_size=2000, node_color=\"skyblue\", arrowstyle=\"->\", arrowsize=20\n", - ")\n", - "# Show the plot\n", - "plt.show()" - ] + "id": "5a1d3cd4b14d9c1e" }, { "cell_type": "markdown", @@ -157,23 +122,18 @@ "collapsed": false }, "source": [ - "\n", - "For the quantum circuit we need rotation angles that represent the conditional probability tables. For example:\n", - "$$P(X)=0.2$$\n", - "$$P(Y|X)=0.9$$\n", - "$$P(Y|-X)=0.3$$\n", - "The corresponding rotation angles are:" + "For the quantum circuit we need rotation angles that represent the conditional probability tables. The corresponding rotation angles are:" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 109, "id": "326c1d2e72f41202", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:40.883941Z", - "start_time": "2023-11-24T17:18:40.859940Z" + "end_time": "2023-11-26T20:32:35.652594Z", + "start_time": "2023-11-26T20:32:35.602217Z" } }, "outputs": [], @@ -200,50 +160,14 @@ ] }, { - "cell_type": "code", - "execution_count": 15, - "id": "e4e5d93f2afa6aee", + "cell_type": "markdown", + "source": [ + "![Burglary Alarm](Burglary_Alarm.png)" + ], "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-24T17:18:40.974767Z", - "start_time": "2023-11-24T17:18:40.879794Z" - } + "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": "
", - "image/png": 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" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "# Create a directed graph\n", - "G = nx.DiGraph()\n", - "# Add nodes\n", - "G.add_nodes_from([\"Burglary\", \"Earthquake\", \"Alarm\", \"JohnCalls\", \"MaryCalls\"])\n", - "# Add edges\n", - "G.add_edges_from(\n", - " [(\"Burglary\", \"Alarm\"), (\"Earthquake\", \"Alarm\"), (\"Alarm\", \"JohnCalls\"), (\"Alarm\", \"MaryCalls\")]\n", - ")\n", - "# Manually set positions\n", - "pos = {\n", - " \"Burglary\": (0, 1),\n", - " \"Earthquake\": (1, 1),\n", - " \"Alarm\": (0.5, 0.5),\n", - " \"JohnCalls\": (0, 0),\n", - " \"MaryCalls\": (1, 0),\n", - "}\n", - "# Draw the network\n", - "nx.draw(G, pos, with_labels=True, node_size=3500, node_color=\"lightblue\", font_size=10)\n", - "plt.title(\"Bayesian Network - Burglary Alarm Example\")\n", - "plt.show()" - ] + "id": "69003c40f9bcbafd" }, { "cell_type": "markdown", @@ -260,29 +184,18 @@ "John Calls (J): Whether John calls you.\n", "Mary Calls (M): Whether Mary calls you.\n", "\n", - "Use this as conditional probability tables:\n", - "$$P(B)=0.001$$\n", - "$$P(E)=0.002$$\n", - "$$P(A|-B,-E) = 0.001$$\n", - "$$P(A|-B,E) = 0.29$$\n", - "$$P(A|B,-E) = 0.94$$\n", - "$$P(A|B,E) = 0.95$$\n", - "$$P(J|-A) = 0.05$$\n", - "$$P(J|A) = 0.9$$\n", - "$$P(M|-A) = 0.9$$\n", - "$$P(M|A) = 0.3$$\n", - "Then we get:\n" + "Use the conditional probability tables:\n" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 110, "id": "a815411b4f10c78c", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:40.980883Z", - "start_time": "2023-11-24T17:18:40.977441Z" + "end_time": "2023-11-26T20:32:35.661940Z", + "start_time": "2023-11-26T20:32:35.610856Z" } }, "outputs": [], @@ -322,13 +235,13 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 111, "id": "4f99dbe56bc6910a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.049766Z", - "start_time": "2023-11-24T17:18:40.984841Z" + "end_time": "2023-11-26T20:32:35.714886Z", + "start_time": "2023-11-26T20:32:35.615920Z" } }, "outputs": [ @@ -337,7 +250,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 17, + "execution_count": 111, "metadata": {}, "output_type": "execute_result" } @@ -376,13 +289,13 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 112, "id": "79045cc1a7706f87", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.514314Z", - "start_time": "2023-11-24T17:18:41.054658Z" + "end_time": "2023-11-26T20:32:36.198008Z", + "start_time": "2023-11-26T20:32:35.689896Z" } }, "outputs": [ @@ -391,7 +304,7 @@ "text/plain": "
", "image/png": 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}, - "execution_count": 18, + "execution_count": 112, "metadata": {}, "output_type": "execute_result" } @@ -478,13 +391,13 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 113, "id": "1e602fda98a6356d", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.634489Z", - "start_time": "2023-11-24T17:18:41.506369Z" + "end_time": "2023-11-26T20:32:36.298746Z", + "start_time": "2023-11-26T20:32:36.206404Z" } }, "outputs": [ @@ -493,7 +406,7 @@ "text/plain": "
", "image/png": 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Oc/Hx8WrdunWFPnPjjTfqxhtvdPaUAAAA+BOnN0DMmDFDK1asKLPPt99+q0ceecTZUwAAAKAcToe5RYsWae/evWX2+fnnn7V48WJnTwEAAIByVOlz5v7s4sWLDt1LBwAAAOdUKmmZTKYS2202m5KTkxUTE8OGBwAAgGpUoZU5s9ksi8Vif37ctGnT7D9f+T8PDw+1atVKu3fv1rBhw6qlcAAAAFRwZa5nz5721bgtW7YoICCgxOfKWSwWNWjQQH379tXo0aOrpFAAAAAUV6Ewt2nTJvt/m81m/eMf/9DUqVOruiYAAAA4yOl75qxWa1XWAQAAACdU625WAAAAVC+HV+YeeeQRmUwmzZgxQ35+fg4/DNhkMunf//630wUCAACgdCabzWZzpKPZbJbJZNL+/fvVtm1bmc2OLeqZTCYVFBRUqkh3kJ2dLV9fX2VlZcnHx8fV5QDA39Loea6uAPjDgvHVO76j2cPhlbnff/9dktSsWbMiPwMAAMB1HA5zLVu2LPNnAAAAXH1sgAAAADAwh1fmkpKSnD5JQECA058FAABA6RwOc4GBgaW+i7UsJpNJ+fn5Ff4cAAAAyudwmBsxYoRTYc5ZO3bsUFRUlH744Qfl5eWpQ4cOmjBhgoYMGVKhcU6cOKGZM2fq22+/VXJysmrXrq22bdtqxIgRevzxx6upegAAgKvD4TC3aNGiaiyjqI0bNyo8PFze3t4aNmyY6tatq2XLlmno0KFKTk7WxIkTHRpn7969CgsL0+nTpzVo0CDdd999ysnJ0f79+7Vy5UrCHAAAMDyHnzN3teTn56t9+/Y6duyYfvzxR3Xu3FmSlJWVpZCQEB05ckTx8fHl7qbNzs5Whw4ddOHCBa1bt04dO3Ysdh4PD8ffZsZz5gDA9XjOHNyJuzxnzu12s27YsEGJiYkaPny4PchJkq+vr6ZMmaJLly5p8eLF5Y7z3nvvKSkpSbNmzSoW5CRVKMgBAAC4K7d7ndemTZskSWFhYcWOhYeHS5I2b95c7jhLly6VyWRSZGSkDh48qDVr1ujChQtq3769br/9dtWoUcPhmgAAANxVhe6ZM5lMeu655+Tn5+fwPXQVDXMJCQmSpDZt2hQ75u/vrzp16tj7lObSpUv65Zdf1KhRI7399tuKioqS1Wq1Hw8KCtLy5cvVoUOHUsfIzc1Vbm6u/efs7GxJUl5envLy8iRdfsWZxWJRQUFBkfEL2/Pz83XlVWyLxSKz2Vxqe+G4hQpXD/+8G7i0dk9PT1mt1iKvTzOZTPLw8Ci1vbTamRNzYk7MyR3nJF29jXhAea7G98kRbvc6r6ysLEmXL6uWxMfHx96nNJmZmSooKNCpU6f0r3/9S3PmzNHDDz+svLw8zZ8/X6+88ooGDx6sAwcOyNvbu8QxZs6cqenTpxdrX7NmjWrVqiXp8vPzgoODtW/fviLP4WvXrp3at2+v7du36+TJk/b2zp07q2XLltqyZYvOnj1rb+/evbsaN26sNWvWFPmH69Onj2rWrKlVq1YVqSEiIkIXLlzQxo0b7W0eHh4aNGiQMjIyFBcXZ2+vW7eu+vbtq+TkZO3du9fe3qhRI/Xo0UMJCQk6ePCgvZ05MSfmxJzceU4S9yzDfVT392nXrl0O1eF2GyDCwsK0du1aJSQkqHXr1sWON2vWTDk5OWUGupSUFHvofOaZZzRv3rwix4cOHaro6Gh9/PHHeuihh0oco6SVuRYtWigjI8N+E6Kr/0L9K/7VzZyYE3NiTmXNacxbrMzBfcx/unq/T5mZmWrYsGG5GyDcbhdA4YpcaWEtOztb9evXd2gMSbrzzjuLHb/zzjsVHR2tnTt3lhrmvLy85OXlVazd09NTnp6eRdosFossFkuxvqVtsiit/c/jOtNuNptlNhff11Jae2m1MyfmVNF25sScpOqfE+BOXPV9KnY+h3qV4euvv9Zdd92lgIAA+fr6KiAgQHfffbeWL1/u1HiF98qVdF9cWlqacnJySryf7kq1a9e2r8zVq1ev2PHCtstL9gAAAMbldJjLz8/XkCFDdN9992nlypVKS0tTrVq1lJaWphUrVigyMlJDhgyp8Ku8evXqJenyvWl/FhsbW6RPWfr27StJ+u2334odK2wLDAysUG0AAADuxukwN3PmTH355Ze67bbbtHXrVl28eFGpqam6ePGitmzZotDQUC1btkyzZs2q0Lj9+vVTUFCQlixZUuTmwaysLM2YMUM1atTQiBEj7O2pqak6cOBAscuyjz32mCRp1qxZOnPmjL09LS1Nb731lsxmsyIjIys+cQAAADfi9AaIoKAgeXt7a9++fSVe083Ly1PHjh2Vm5urw4cPV2js0l7ndfToUc2dO7fI67xGjRqlxYsXa+HChRo1alSRcSZOnKg33nhDLVq00ODBg5WXl6dvvvlGJ06c0IwZMzR58mSHa+INEADgerwBAu7E8G+ASE1N1eDBg8u8qXXw4MFKTU2t8Nh9+vTRtm3bdOutt2rp0qV6//335efnp88//9zh97JK0uuvv66FCxfan4u3ZMkStW3bVl999VWFghwAAIC7cno3a4sWLZSTk1Nmn3PnzikgIMCp8UNCQhQTE1Nuv0WLFpX5AONRo0YVW7EDAAD4q3B6Ze7RRx9VdHR0qStvx48f19KlS/Xoo486XRwAAADK5vDK3JVPJpakIUOG6Pvvv1dwcLDGjx+v0NBQ+fn5KT09XVu3btVbb72l0NBQ3X///VVeNAAAAC5zeAOE2WyWyVT8yds2m63U9sLPVfTxJO6IDRAA4HpsgIA7cZcNEA6vzI0YMaLE0AYAAADXcTjMlbXJAAAAAK5R6dd5AQAAwHUIcwAAAAbm9HPmJOns2bN65513tG7dOqWkpCg3N7dYH5PJpMTExMqcBgAAAKVwOsydPHlSPXr0UGJionx8fOw7Li5duqQLFy5Ikpo2bSpPT88qKxYAAABFOX2Zddq0aUpMTNT//u//6vTp05KkZ599VufOndNPP/2kkJAQBQYG6tdff62yYgEAAFCU02Fu1apV6tevnx566KFijyzp0qWLYmJidOTIEU2fPr3SRQIAAKBkToe51NRUBQcH23+2WCz2y6uSVL9+fQ0cOFDR0dGVqxAAAAClcjrM+fr6Ki8vz/5z/fr1dezYsSJ9fHx8lJ6e7nx1AAAAKJPTYS4oKEhHjhyx/xwcHKy1a9fq1KlTkqQLFy5o5cqVCggIqHSRAAAAKJnTYS4sLEzr16/X+fPnJUljx47ViRMn1KlTJ91///268cYblZiYqFGjRlVVrQAAAPgTp8PcY489pgULFtjD3L333qvXXntN586d07Jly5SWlqYJEyZo0qRJVVYsAAAAijLZbDZbVQ5YUFCgjIwMNW7cuNguVyMrfI5eVlaWfHx8XF0OAPwtjZ7n6gqAPywYX73jO5o9KvUGiJJYLBb5+flV9bAAAAAoQaXDXGpqqj7//HPt2bNHWVlZ8vX1VXBwsIYNG6YmTZpURY0AAAAoRaXC3LvvvqtJkyYpNzdXV16t/eSTT/TCCy9o7ty5GjduXKWLBAAAQMmcDnOff/65nnrqKV1zzTV64YUXdNttt8nPz0/p6enasmWL3nrrLfvxIUOGVGXNAAAA+D9Ob4C46aabdOzYMe3du1dNmzYtdvzYsWMKDg5WQECAdu3aVelCXY0NEADgemyAgDtxlw0QTj+aZP/+/RoyZEiJQU6Smjdvrvvvv1/79+939hQAAAAoh9Nhrl69eqpdu3aZferUqaN69eo5ewoAAACUw+kwd+edd2rlypXKz88v8XheXp5Wrlypu+66y+niAAAAUDanw9ycOXNUu3ZthYWF6ccffyxyLC4uTmFhYapbt65mzZpV6SIBAABQMod3swYFBRVru3Tpknbv3q1bb71VHh4euuaaa5SRkWFfrWvSpIluuukmJSYmVl3FAAAAsHM4zFmt1mKv5/L09FRAQECRtj9viLBarZUoDwAAAGVxOMwdOXKkGssAAACAM5y+Zw4AAACuV+l3s0pSfn6+Dh48qOzsbPn4+Khdu3by8KiSoQEAAFCGSq3MZWZmavTo0fL19VXHjh0VGhqqjh07ql69ehozZoxOnTpVVXUCAACgBE4vn2VmZqpbt246dOiQGjRooNtuu01NmjRRWlqadu7cqQ8//FCbN29WXFycGjRoUJU1AwAA4P84vTL38ssv69ChQ5o0aZKOHj2q1atXa+HChYqJidHRo0f13HPPKSEhQa+++mpV1gsAAIArmGw2m82ZDwYFBSkwMFAbNmwotU/fvn115MgRHT582OkC3YWjL7sFAFSf0fNcXQHwhwXjq3d8R7OH0ytzKSkp6t69e5l9unfvrpSUFGdPAQAAgHI4HeZ8fX119OjRMvscPXpUvr6+zp4CAAAA5XA6zPXq1UtffPGF1q1bV+Lx9evX64svvlDv3r2dPQUAAADK4fRu1qioKH333XcKDw9XRESEevXqJT8/P6Wnp2vTpk2KiYlRrVq1NHXq1KqsFwAAAFdwOszdcMMNio2N1ahRo/Tdd9/pu+++k8lkUuF+imuvvVaLFi3SDTfcUGXFAgAAoKhKvaYhNDRUCQkJ+v7777Vnzx77GyCCg4N16623ymQyVVWdAAAAKIHTYe6RRx5Rhw4d9Oyzzyo0NFShoaFVWRcAAAAc4PQGiCVLlujEiRNVWQsAAAAqyOkwd+211yo1NbUqawEAAEAFOR3mHnnkEX333Xc6fvx4VdYDAACACnD6nrnIyEht3LhRPXr00H/913+pS5cu8vPzK3HTQ0BAQKWKBAAAQMmcDnNBQUH2R5E8/fTTpfYzmUzKz8939jQAAAAog9NhbsSIETx6BAAAwMWcDnOLFi2qwjIAAADgDKc3QAAAAMD1KvUGCEnKzc3VqlWrtGfPHmVlZcnX11fBwcGKiIiQl5dXVdQIAACAUlQqzK1YsUJjxozRyZMn7e9klS5vemjcuLE++OADDR48uNJFAgAAoGROh7n169crMjJSFotFjzzyiG677Tb5+fkpPT1dW7Zs0SeffKJ7771XsbGx6tu3b1XWDAAAgP9jsl25pFYBoaGh2rdvn3744QfdeOONxY7v27dPt956qzp37qytW7dWulBXy87Olq+vr7KysuTj4+PqcgDgb2n0PFdXAPxhwfjqHd/R7OH0Bog9e/Zo6NChJQY5SerYsaOGDBmi3bt3O3sKAAAAlMPpMFerVi01atSozD6NGzdWrVq1nD0FAAAAyuF0mOvfv7/WrVtXZp9169ZpwIABzp4CAAAA5XA6zM2dO1cnTpzQiBEjlJycXORYcnKyHn74YWVkZGju3LmVLhIAAAAlc3o368MPP6z69evr008/1eeff66AgAD7btakpCQVFBSoY8eOeuihh4p8zmQyaf369ZUuHAAAAJUIc5s2bbL/d35+vg4fPqzDhw8X6fPzzz8X+xzvcwUAAKg6Toc5q9ValXUAAADACbybFQAAwMCqLMwlJSVpy5YtVTUcAAAAHFBlYW7hwoXq06dPVQ0HAAAAB3CZFQAAwMDcNszt2LFDERERqlevnmrXrq1u3bopOjra6fFOnz6tZs2ayWQy6fbbb6/CSgEAAFzH6d2s1Wnjxo0KDw+Xt7e3hg0bprp162rZsmUaOnSokpOTNXHixAqP+eSTTyorK6saqgUAAHCdKluZ8/X1VUBAQKXHyc/P1+jRo2U2m7VlyxZ98MEHev311/Xzzz+rbdu2mjJlio4ePVqhMZctW6YlS5Zo9uzZla4PAADAnVRZmBs/frx+//33So+zYcMGJSYmavjw4ercubO93dfXV1OmTNGlS5e0ePFih8c7efKkHn/8cT388MMaNGhQpesDAABwJ253z1zhmyXCwsKKHQsPD5ckbd682eHxHnvsMVksFr311ltVUh8AAIA7cfieucJnyIWEhMjb27tCz5Tr2bOnw30TEhIkSW3atCl2zN/fX3Xq1LH3Kc8nn3yir776SsuXL1f9+vUrdM9cbm6ucnNz7T9nZ2dLkvLy8pSXlydJMpvNslgsKigoKPJGjML2/Px82Ww2e7vFYpHZbC61vXDcQh4el/958vPzHWr39PSU1WpVQUGBvc1kMsnDw6PU9tJqZ07MiTkxJ3eck8QrIeE+rsb3yREOh7nevXvLZDJp//79atu2rf1nR1w5ofIUBi5fX98Sj/v4+DgUylJSUvT000/rgQce0F133eXw+QvNnDlT06dPL9a+Zs0a1apVS5IUEBCg4OBg7du3T0lJSfY+7dq1U/v27bV9+3adPHnS3t65c2e1bNlSW7Zs0dmzZ+3t3bt3V+PGjbVmzZoi/3B9+vRRzZo1tWrVqiI1RERE6MKFC9q4caO9zcPDQ4MGDVJGRobi4uLs7XXr1lXfvn2VnJysvXv32tsbNWqkHj16KCEhQQcPHrS3MyfmxJyYkzvPSfIR4C6q+/u0a9cuh+ow2a78U6kM06ZNk8lk0lNPPaUGDRrYf3ZEVFSUQ/2ky5dX165dq4SEBLVu3brY8WbNmiknJ6fcQBcREaFdu3bp119/1TXXXCNJOnLkiFq1aqXw8HCtXr26zM+XtDLXokULZWRkyMfn8i8TV/+F+lf8q5s5MSfmxJzKmtOYt1iZg/uY/3T1fp8yMzPVsGFDZWVl2bNHSRxemZs2bVqZP1eVwhW50sJadna26tevX+YYixcvVkxMjL744gt7kKsoLy8veXl5FWv39PSUp6dnkTaLxSKLxVKs7x+XBRxr//O4zrSbzWaZzcVvhSytvbTamRNzqmg7c2JOUvXPCXAnrvo+FTufQ72uosJ75Uq6Ly4tLU05OTkl3k93pT179kiS7r//fplMJvv/WrVqJUmKjY2VyWQqslsWAADAiJx+aPDZs2d18uRJtWjRoshfUEuXLtWKFSvk7e2tJ554QjfddFOFxu3Vq5dmzpypNWvWaNiwYUWOxcbG2vuUpXv37srJySnWnpOTo6VLl6p58+YKDw+vkufiAQAAuJLD98z92eOPP65PPvlE6enp9g0B77//vp588kn7fRE1a9bUrl271L59e4fHzc/PV7t27XT8+HH9+OOP9tWzrKwshYSE6MiRIzp48KACAwMlSampqcrKylKTJk1K3TRRqCL3zP1Zdna2fH19y71uDQCoPqPnuboC4A8Lxlfv+I5mD6cvs27evFn9+/e3BzlJmjVrlpo1a6YtW7YoOjpaNptNr732WoXG9fDw0Icffiir1aqePXtqzJgxmjhxojp16qT4+HjNmDHDHuQkafLkybruuuv09ddfOzsVAAAAw3L6MmtqamqRF9bv379fycnJmjNnjkJDQyVJX375ZYWeR1eoT58+2rZtm6KiorR06VLl5eWpQ4cOmj17toYOHepsyQAAAH85Toe53Nxc1ahRw/7z5s2bZTKZiry5ISgoSCtWrHBq/JCQEMXExJTbb9GiRVq0aJFDYwYGBsrJq8oAAABuyenLrM2bN9e+ffvsP3/77bdq0KCBOnbsaG87deqU6tSpU7kKAQAAUCqnV+YGDhyod999V//85z/l7e2t1atXa8SIEUX6xMfHs2MUAACgGjkd5iZPnqyVK1fqjTfekCQ1adJE//rXv+zHT5w4oe+//15PPvlk5asEAABAiZwOc/7+/vr111+1fv16SVLPnj2LbJvNyMjQa6+9pvDw8MpXCQAAgBI5Heaky8+Ru+OOO0o8dv311+v666+vzPAAAAAoh9u9zgsAAACOq9TKXEFBgaKjo7Vu3TqlpKQoNze3WB+TyWS/FAsAAICq5XSYO3funMLCwvTjjz/KZrPJZDIVeYZb4c8mk6lKCgUAAEBxTl9mfeWVVxQXF6fp06crIyNDNptN06ZNU2pqqpYuXaqgoCDdf//9Ja7WAQAAoGo4Hea++uordevWTS+++KIaNGhgb/fz89P999+vjRs3at26dRV+NysAAAAc53SYS0pKUrdu3f4YyGwusgrXvHlzDRo0SIsXL65chQAAACiV02Gudu3aMpv/+Livr69SU1OL9PH391dSUpLz1QEAAKBMToe5li1bFglqN954ozZs2GBfnbPZbFq/fr2aNGlS+SoBAABQIqfDXL9+/bRx40bl5+dLkkaOHKmkpCR1795dkyZNUmhoqPbu3avIyMgqKxYAAABFOf1oktGjR6thw4Y6efKkmjRpokceeUR79uzRe++9p71790qSIiMjNW3atCoqFQAAAH9msl35cLgqcPLkSR0+fFgtW7aUv79/VQ7tUtnZ2fL19VVWVlaRd9ACAK6e0fNcXQHwhwXjq3d8R7NHpd4AUZJGjRqpUaNGVT0sAAAASsC7WQEAAAzM6ZW5oKAgh/qZTCYlJiY6exoAAACUwekwZ7VaS3zvalZWls6cOSNJatKkiWrUqOF0cQAAACib02HuyJEjZR6bMGGC0tPTtXbtWmdPAQAAgHJUyz1zgYGBWrp0qU6fPq0XXnihOk4BAAAAVeMGCE9PTw0YMEDR0dHVdQoAAIC/vWrdzXr+/HllZmZW5ykAAAD+1qotzG3dulWfffaZ2rVrV12nAAAA+NtzegNE3759S2zPz8/X8ePH7Rskpk6d6uwpAAAAUA6nw9ymTZtKbDeZTKpfv77CwsI0YcIEDRgwwNlTAAAAoByVes4cAAAAXKvS72Y9ceKEjh8/LqvVqmbNmsnf378q6gIAAIADnNoAkZubqzlz5qhNmzZq0qSJbrnlFoWEhKhZs2a65ppr9Oyzz5b5UGEAAABUjQqHueTkZHXp0kWTJ09WYmKimjRpopCQEIWEhKhJkybKzMzUW2+9pVtuuUXr1q2zfy41NZVnzgEAAFSxCoW5vLw8RURE6D//+Y8eeOAB7d+/X8eOHVNcXJzi4uJ07Ngx7d+/Xw8++KAyMzN1991368iRI0pMTFRoaKgOHDhQXfMAAAD4W6rQPXPz58/Xr7/+qqioKEVFRZXYp127dvr444/Vtm1bRUVF6cEHH9SRI0eUkZGhm2++uUqKBgAAwGUVWpmLjo5W69atHXp23Isvvqg2bdooLi5OFy9eVGxsrAYNGuR0oQAAACiuQmHut99+U1hYmEwmU7l9TSaTve9PP/2k3r17O1sjAAAASlGhMJeTkyNfX1+H+/v4+MjDw0OtW7eucGEAAAAoX4XCXOPGjXXo0CGH+ycmJqpx48YVLgoAAACOqVCY6969u2JiYpSWllZu37S0NH333XcKDQ11ujgAAACUrUJh7rHHHlNOTo7uueceZWRklNrv1KlTuueee3T+/HmNHTu20kUCAACgZBV6NEmfPn00evRoLViwQNddd53Gjh2rvn37qkWLFpIuP1B4/fr1WrBggTIyMjRmzBg2PgAAAFSjCr+b9b333pOPj4/efPNNzZw5UzNnzixy3GazyWw265///GexYwAAAKhaFQ5zFotFr732msaMGaNFixYpLi7Ofg+dv7+/evTooZEjR6pNmzZVXiwAAACKqnCYK9SmTRu9+uqrVVkLAAAAKqhCGyAAAADgXghzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABkaYAwAAMDDCHAAAgIER5gAAAAzMbcPcjh07FBERoXr16ql27drq1q2boqOjHfqszWZTTEyMHn/8cXXs2FG+vr6qVauWOnXqpBkzZujixYvVXD0AAMDV4eHqAkqyceNGhYeHy9vbW8OGDVPdunW1bNkyDR06VMnJyZo4cWKZn8/NzVVERIS8vLzUu3dvhYeH6+LFi4qNjdULL7yg5cuXa9OmTapVq9ZVmhEAAED1MNlsNpuri7hSfn6+2rdvr2PHjunHH39U586dJUlZWVkKCQnRkSNHFB8fr5YtW5Y6Rl5enubMmaNx48apfv36RdojIyO1cuVKzZkzR5MmTXK4ruzsbPn6+iorK0s+Pj5Ozw8A4LzR81xdAfCHBeOrd3xHs4fbXWbdsGGDEhMTNXz4cHuQkyRfX19NmTJFly5d0uLFi8scw9PTUy+88EKRIFfYPnnyZEnS5s2bq7x2AACAq83twtymTZskSWFhYcWOhYeHS6pcEPP09JQkeXi45RVmAACACnG7RJOQkCBJatOmTbFj/v7+qlOnjr2PMz766CNJJYfFK+Xm5io3N9f+c3Z2tqTLl2rz8vIkSWazWRaLRQUFBbJarfa+he35+fm68iq2xWKR2Wwutb1w3EKFgTM/P9+hdk9PT1mtVhUUFNjbTCaTPDw8Sm0vrXbmxJyYE3NyxzlJJgHu4mp8nxzhdmEuKytL0uXLqiXx8fGx96momJgYzZ8/X9ddd53+3//7f2X2nTlzpqZPn16sfc2aNfaNEwEBAQoODta+ffuUlJRk79OuXTu1b99e27dv18mTJ+3tnTt3VsuWLbVlyxadPXvW3t69e3c1btxYa9asKfIP16dPH9WsWVOrVq0qUkNERIQuXLigjRs32ts8PDw0aNAgZWRkKC4uzt5et25d9e3bV8nJydq7d6+9vVGjRurRo4cSEhJ08OBBeztzYk7MiTm585wk7lmG+6ju79OuXbscqsPtNkCEhYVp7dq1SkhIUOvWrYsdb9asmXJycioc6Hbs2KF+/frJw8NDW7du1Q033FBm/5JW5lq0aKGMjAz7TYiu/gv1r/hXN3NiTsyJOZU1pzFvsTIH9zH/6er9PmVmZqphw4blboBwu5W5whW50sJadnZ2sY0N5dm5c6fCwsJkNpsVGxtbbpCTJC8vL3l5eRVr9/T0tN93V8hischisRTrW9p9eaW1/3lcZ9rNZrPM5uK3QpbWXlrtzIk5VbSdOTEnqfrnBLgTV32fip3PoV5XUeG9ciXdF5eWlqacnJwS76crzc6dOzVgwABZrVbFxsaqS5cuVVYrAACAq7ldmOvVq5eky/em/VlsbGyRPuUpDHIFBQVavXq1unbtWnWFAgAAuAG3C3P9+vVTUFCQlixZUuTmwaysLM2YMUM1atTQiBEj7O2pqak6cOBAscuyu3bt0oABA5Sfn6+YmBh17979ak0BAADgqnG7e+Y8PDz04YcfKjw8XD179izyOq+jR49q7ty5CgwMtPefPHmyFi9erIULF2rUqFGSpMzMTA0YMEBnzpzR7bffrrVr12rt2rVFzlOvXj2NHz/+6k0MAACgGrhdmJMub03ftm2boqKitHTpUuXl5alDhw6aPXu2hg4dWu7ns7Ozdfr0aUnS6tWrtXr16mJ9WrZsSZgDAACG53aPJnFXvJsVAFyPd7PCnfBuVgAAAFQaYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzMHtvPvuuwoMDJS3t7e6du2q7du3l9r3119/VWRkpAIDA2UymTRv3rxifbZs2aLBgweradOmMplMWr58ebE+6enpGjVqlJo2bapatWrp9ttvV0JCQhXOCgCA6kGYg1tZunSpJkyYoKioKO3evVudOnVSeHi4Tpw4UWL/8+fPKygoSLNmzZK/v3+Jfc6dO6dOnTrp3XffLfG4zWbT3XffrcOHD+ubb77Rnj171LJlS/Xv31/nzp2rsrkBAFAdeJ2Xg3id19XRtWtXdenSRe+8844kyWq1qkWLFnrqqaf0/PPPl/nZwMBAjR8/vsx37ppMJn399de6++677W3x8fFq166d/vOf/+iGG26wn9ff318zZszQo48+Wul5AagavM4L7oTXeQF/cunSJe3atUv9+/e3t5nNZvXv319xcXHVdt7c3FxJkre3d5Hzenl5adu2bdV2XgAAqgJhDm4jIyNDBQUF8vPzK9Lu5+entLS0ajtv+/btFRAQoMmTJ+v06dO6dOmSZs+erWPHjik1NbXazgsAQFUgzOFvz9PTU1999ZXi4+PVoEED1apVSxs3btTAgQNlNvMVAQC4Nw9XFwAUuuaaa2SxWJSenl6kPT09vdTNDVXl5ptv1t69e5WVlaVLly6pUaNG6tq1q2655ZZqPS8AAJXFsgPcRo0aNXTzzTdr/fr19jar1ar169ere/fuV6UGX19fNWrUSAkJCdq5c6fuuuuuq3JeAACcxcoc3MqECRM0cuRI3XLLLQoJCdG8efN07tw5/eMf/5AkjRgxQs2aNdPMmTMlXd408dtvv9n/+/jx49q7d6/q1Kmj1q1bS5JycnJ06NAh+zl+//137d27Vw0aNFBAQIAk6YsvvlCjRo0UEBCgX375Rc8884zuvvtuhYWFXc3pAwBQYYQ5uJWhQ4fq5MmTmjp1qtLS0tS5c2etXr3avikiKSmpyH1sKSkpCg4Otv88d+5czZ07V7169dKmTZskSTt37lSfPn3sfSZMmCBJGjlypBYtWiRJSk1N1YQJE5Senq4mTZpoxIgReumll6p5tgAAVB7PmXMQz5kDANfjOXNwJzxnDgAAAJVGmAMAADAwwhwAAICBEeYAAAAMjN2sboabe+FOqvvmXgBA5bEyBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEOQAAAAMjzAEAABgYYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADMxtw9yOHTsUERGhevXqqXbt2urWrZuio6MrNEZubq7+9a9/qU2bNvL29lbTpk01ZswYnThxopqqBgAAuLo8XF1ASTZu3Kjw8HB5e3tr2LBhqlu3rpYtW6ahQ4cqOTlZEydOLHcMq9Wqu+66S7GxserWrZsiIyOVkJCgDz/8UOvXr9ePP/6oRo0aXYXZAAAAVB+3W5nLz8/X6NGjZTabtWXLFn3wwQd6/fXX9fPPP6tt27aaMmWKjh49Wu44ixcvVmxsrB544AH98MMPmjVrlpYtW6b33ntPhw8f1osvvngVZgMAAFC93C7MbdiwQYmJiRo+fLg6d+5sb/f19dWUKVN06dIlLV68uNxxFixYIEmaOXOmTCaTvX3s2LEKCgrSp59+qgsXLlR5/QAAAFeT24W5TZs2SZLCwsKKHQsPD5ckbd68ucwxLl68qJ9++knt2rVTy5YtixwzmUwaMGCAzp07p507d1ZN0QAAAC7idmEuISFBktSmTZtix/z9/VWnTh17n9IkJibKarWWOMaVY5c3DgAAgLtzuw0QWVlZki5fVi2Jj4+PvU9lxriyX0lyc3OVm5tbbMzMzEzl5eVJksxmsywWiwoKCmS1Wu19C9vz8/Nls9ns7RaLRWazudT2vLw8XbroWebcgKvp1Km8Ij97eFz+lZGfn1+k3dPTU1arVQUFBfY2k8kkDw+PUttL+95U5ffJkdqZk7HmdOmiSYC7OHOmer9PmZmZklTku1MStwtz7mLmzJmaPn16sfZWrVq5oBrANf53sqsrAAD3dbV+R549e7bUBSrJDcNcYbGlrZplZ2erfv36lR7jyn4lmTx5siZMmGD/2Wq1KjMzUw0bNiyyoQLuJzs7Wy1atFBycrJ9FRYAcBm/I43DZrPp7Nmzatq0aZn93C7MXXk/280331zkWFpamnJychQSElLmGEFBQTKbzaXeE1fWfXmFvLy85OXlVaStXr165ZUPN+Lj48MvKgAoBb8jjaGshadCbrcBolevXpKkNWvWFDsWGxtbpE9patasqZCQEB08eLDYM+lsNpvWrl2r2rVr65ZbbqmiqgEAAFzD7cJcv379FBQUpCVLlmjv3r329qysLM2YMUM1atTQiBEj7O2pqak6cOBAsUuqY8aMkXT5cumVNw7Onz9fhw8f1oMPPqiaNWtW72QAAACqmduFOQ8PD3344YeyWq3q2bOnxowZo4kTJ6pTp06Kj4/XjBkzFBgYaO8/efJkXXfddfr666+LjDNy5EiFh4frs88+U48ePfT888/rvvvu07hx49SqVSu98sorV3lmuFq8vLwUFRVV7DI5AIDfkX9FJlt5+11dZPv27YqKitIPP/ygvLw8dejQQRMmTNDQoUOL9Bs1apQWL16shQsXatSoUUWO5ebmatasWfr444+VnJysBg0a6I477tArr7wiPz+/qzgbAACA6uG2YQ4AAADlc7vLrAAAAHAcYQ4AAMDACHMAAAAGRpgDAAAwMMIcAACAgRHmAAAADIwwBwAAYGCEORie1Wp1dQkAALgMYQ6GZzb/8f/GBDsAKK6goMDVJaAaEeZgWOnp6Zo4caJiY2N15swZSX8EO5vNRrAD8LdX+HvQYrFIcvx3Iy+HMhZe5wXDioqK0ssvv6zAwEBdf/316t27t3r16qWOHTsWeYG01WqVzWaTxWLRpk2bdPHiRd1+++0urBwAro73339fmzZt0ogRI9SrVy/VqVPHfqww1F15dQPGRJiDYQUHB+u3337TTTfdpN27dysvL08tW7bUrbfeqj59+ujWW29V+/bt7f3Pnz+vBx54QN9++63OnTsnb29vF1YPANWvVatWOnr0qLy8vNSpUyeFhYUpIiJCXbt2lclksvfLz8+Xh4eHzp8/rw8++ECdOnVSnz59XFg5KoIwB0NKTk5Wz5491bBhQ8XFxWnXrl1atWqVVqxYoX379slsNuuGG25Qz5491bNnT4WHh+vgwYO688471aVLF61YscLVUwCAavXrr7+qQ4cOuvnmm1W/fn2tW7dOklS7dm3deuutioiIUFhYWJE/erdt26aePXuqR48e2rZtm6tKRwV5uLoAwBmpqanKzs5Wr1695OnpqS5duigkJERPPvmkdu/erW+++UYxMTF699139dFHH+mWW26Rp6en0tPTNWbMGFeXDwDV7pdffpEkDR8+XM8++6zi4+O1fPlyffbZZ1qzZo3WrFkjf39/9e7dWwMHDtQdd9yh7du3S5ImT57sytJRQazMwZAOHTqk5557TpGRkRo+fHix43l5eUpJSdHWrVu1cuVKrVu3TqdPn1a9evWUmZnpgooB4Or64IMP9Nhjj+m7777TwIEDixzbsWOHPvvsM3355Zc6duyYJKlNmzbKzs7WhQsX7JvKYAyEORhWVlaW8vPz1bBhw1L7WK1Wmc1mzZ8/X48//rgef/xxvfvuu1exSgC4+mw2m3766SdFR0friSee0LXXXmtvv/JeuYsXL2r9+vX64osvtHz5cmVnZ+uJJ57Q22+/7arS4QTCHAznz7+MpMvPUDKZTKXuyvqv//ovzZ07Vzt37tRNN910NcoEAJfLyclRjRo1VKNGjWLH/vy79Mknn9R7772n3bt3q3PnzlexSlQWYQ6GVPhLKC0tTY0bNy4S4goKCmQ2m+2/pI4dO6ZBgwYpJSVFJ0+edFXJAOB2Cn+XJiYmaujQocrKylJCQoKry0IFsQEChpKfn6/vv/9eH330keLj42U2m1WzZk116tRJkZGR6tGjh/3hmIW8vb01atQoNW3a1EVVA4B7Kvyjd//+/dq9e7cmTZrk4orgDFbmYChz587Vyy+/rLNnz6p169ayWCw6ePCg/Xj79u01evRoPfDAA/L397e3X7p0SR4eHjwcE8DfSkm3pZQkPT1dq1ev1uDBg9WgQYOrUBmqEmEOhvH777+rQ4cOuummm7R48WLVqFFDfn5+SktL08qVK/XFF19o06ZNkqS+fftqzpw53B8H4G/lwoULSkpKUkBAgGrWrFmhzxYUFBS7sgFjIMzBMKZOnar58+dryZIl6tevn6Tif3X+8ssvmjt3rqKjo9WyZUt9+umnuvnmmx3+6xQAjGzWrFlatmyZ7r33XnXr1k3t2rWTn59fmSHt5MmTql+/vjw8uPPKqAhzMIzIyEjt3btXGzduVEBAgP31M4Uvjr7yl9Vbb72lZ599ViNHjtTChQtdWDUAXD3NmzdXSkqKLBaLfH191aNHD4WFhalr164KCgoq9iinc+fOadq0aTp16pQWLFjAypxBEcNhGMHBwfr666+Vk5MjSfa/Ik0mk/0XUOEK3DPPPKOtW7dqw4YNOnz4sIKCglxWNwBcDfHx8crKylL37t01fPhwrV27VnFxcfr2228VEBCg3r17q3///goODlazZs1Ur149/ec//9GCBQvUu3dvgpyBEeZgGIUvfX7wwQf1+uuvKzQ0tMRnJxXe99GuXTvFxMTYwx8A/JXFx8fr4sWLCgsL0xNPPKE77rhDBw8eVFxcnDZs2KBly5bp008/1fXXX6++ffvq9ttv1/r165Wdna3Ro0e7unxUApdZYRgFBQV67rnn9MYbb6h9+/Z64okndN9998nPz69Y39OnT2v8+PGKiYnRiRMnXFAtAFxdX375pYYMGaLPP/9cQ4YMsbfn5eXp6NGj+vnnn7V161Zt2rRJ+/fvl6enp2w2m7y8vHjNocER5mA48+fP12uvvabDhw+radOmuueeezRw4EC1aNFCFotF9erV09tvv6158+Zp3Lhxev31111dMgBUO5vNpgMHDsjb21utWrUqcePXuXPnFB8fr4MHD2rhwoVau3atnnzySf33f/+3i6pGVSDMwXBsNpsOHTqkBQsW6PPPP7e/JLpx48by9PRUamqqrFarHnjgAc2ePVvNmzd3ccUA4FolBbunn35a77zzjnbt2qXg4GAXVYaqQJiDoZ07d07bt2/XihUrlJKSohMnTsjHx0dDhgxRZGSkvL29XV0iALgNq9Uqs9msI0eO6K677tLp06eVlJTk6rJQSWyAgKHVrl1bffr0UZ8+fZSXlydPT09XlwQAbqvwLTjHjx9XXl6exo0b5+KKUBVYmQMA4G/GZrPp2LFjatCggWrXru3qclBJhDkAAAAD463jAAAABkaYAwAAMDDCHAAAgIER5gAAAAyMMAcAAGBghDkAAAADI8wBAAAYGGEOAADAwAhzAAAABvb/AXPtFa/oODGjAAAAAElFTkSuQmCC" }, - "execution_count": 19, + "execution_count": 113, "metadata": {}, "output_type": "execute_result" } @@ -522,13 +435,13 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 114, "id": "a6fc4d5d394d301a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.712575Z", - "start_time": "2023-11-24T17:18:41.591765Z" + "end_time": "2023-11-26T20:32:36.366001Z", + "start_time": "2023-11-26T20:32:36.273798Z" } }, "outputs": [ @@ -537,7 +450,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 20, + "execution_count": 114, "metadata": {}, "output_type": "execute_result" } @@ -549,6 +462,42 @@ "plot_histogram(samples)" ] }, + { + "cell_type": "markdown", + "source": [ + "We can also print the result in a better format to understand which values belong to which variables:" + ], + "metadata": { + "collapsed": false + }, + "id": "5bf133a4bdd8a976" + }, + { + "cell_type": "code", + "execution_count": 115, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'P(Y=0|X=1)': 0.1004712084149367, 'P(Y=1|X=1)': 0.8995287915850584}\n" + ] + } + ], + "source": [ + "qb_2n.threshold = 0.97\n", + "samples = qb_2n.rejection_sampling(evidence=evidence, format_res=True)\n", + "print(samples)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-26T20:32:36.424810Z", + "start_time": "2023-11-26T20:32:36.372302Z" + } + }, + "id": "4f019762e7f6b861" + }, { "cell_type": "markdown", "id": "9f6ab51740b00957", @@ -557,27 +506,27 @@ }, "source": [ "#### 3.1.2. Burglary Alarm Example\n", - "For the advanced example, we can do this in the same way. However, we look at the trivial case of how to obtain the joint probability of the network. This can be calculated by providing no evidence for the rejection sampling method." + "For the advanced example, we can follow the steps from above in the same way. However, we look at the trivial case of how to obtain the joint probability of the network. This can be calculated by providing no evidence for the rejection sampling method. (For optical reasons, we only plot probabilities that are greater than 0.01%.)" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 116, "id": "8d4904619b35503a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.846121Z", - "start_time": "2023-11-24T17:18:41.706557Z" + "end_time": "2023-11-26T20:32:36.509644Z", + "start_time": "2023-11-26T20:32:36.428970Z" } }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, - "execution_count": 21, + "execution_count": 116, "metadata": {}, "output_type": "execute_result" } @@ -587,7 +536,7 @@ "qb_ba = QBayesian(circuit=qc_ba)\n", "# Inference\n", "counts = qb_ba.rejection_sampling(evidence={})\n", - "plot_histogram({c_key: c_val for c_key, c_val in counts.items()})" + "plot_histogram({c_key: c_val for c_key, c_val in counts.items() if c_val > 0.0001})" ] }, { @@ -628,13 +577,13 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 117, "id": "841bce19ea097bf1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:41.904413Z", - "start_time": "2023-11-24T17:18:41.855290Z" + "end_time": "2023-11-26T20:32:36.567860Z", + "start_time": "2023-11-26T20:32:36.509199Z" } }, "outputs": [ @@ -642,7 +591,7 @@ "data": { "text/plain": "0.1004712084149367" }, - "execution_count": 22, + "execution_count": 117, "metadata": {}, "output_type": "execute_result" } @@ -676,13 +625,13 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 118, "id": "5468619791203a79", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:42.146331Z", - "start_time": "2023-11-24T17:18:41.920458Z" + "end_time": "2023-11-26T20:32:36.802634Z", + "start_time": "2023-11-26T20:32:36.566080Z" } }, "outputs": [ @@ -690,7 +639,7 @@ "data": { "text/plain": "0.0054042995153299" }, - "execution_count": 23, + "execution_count": 118, "metadata": {}, "output_type": "execute_result" } @@ -714,13 +663,13 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 119, "id": "a5434c7c7c45040a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-24T17:18:42.955787Z", - "start_time": "2023-11-24T17:18:42.163155Z" + "end_time": "2023-11-26T20:32:37.624165Z", + "start_time": "2023-11-26T20:32:36.806996Z" } }, "outputs": [ @@ -728,7 +677,7 @@ "data": { "text/plain": "0.0056128979765628" }, - "execution_count": 24, + "execution_count": 119, "metadata": {}, "output_type": "execute_result" } diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 7fa86e7e8..1aa0a1ed1 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -11,7 +11,7 @@ # that they have been altered from the originals. """Quantum Bayesian Inference""" -from typing import Tuple, Dict, Set +from typing import Tuple, Dict, Set, List from qiskit import QuantumCircuit, ClassicalRegister from qiskit.quantum_info import Statevector from qiskit.circuit.library import GroverOperator @@ -21,57 +21,34 @@ class QBayesian: r""" - Implements a convenient quantum Bayesian inference algorithm that has been developed in [1]. - - The quantum Bayesian inference (QBI) does quantum rejection sampling and inference for a - Bayesian network with binary random variables represented by a given quantum circuit. - - A quantum circuit can be passed in various forms as long as it represents the joint probability - distribution of the Bayesian network. Note that 'QBayesian' defines an order for the qubits in - the circuit. The last qubit in the circuit will correspond to the most significant bit in the - joint probability distribution. For example, if the random variables A, B, and C are entered - into the circuit in this order with (A=1, B=0 and C=0), the probability is represented by the - probability amplitude of quantum state 001. + Implements a quantum Bayesian inference (QBI) algorithm that has been developed in [1]. The QBI + includes methods ``rejection_sampling`` and ``inference`` for a Bayesian network with binary + random variables represented by a quantum circuit. A quantum circuit can be passed in various + forms as long as it represents the joint probability distribution of the Bayesian network. For Bayesian networks with random variables that have more than two states, see for example [2]. - **References** + Note that ``QBayesian`` defines an order for the qubits in the circuit. The last qubit in the + circuit will correspond to the most significant bit in the joint probability distribution. For + example, if the random variables A, B, and C are entered into the circuit in this order with + (A=1, B=0 and C=0), the probability is represented by the probability amplitude of quantum + state 001. - [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. - "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. - [2]: Borujeni, Sima E., et al. "Quantum circuit representation of Bayesian networks." - Expert Systems with Applications 176 (2021): 114768. + **Example** - Usage: - ------ - To use the `QBayesian` class, instantiate it with a quantum circuit that represents the - Bayesian network. You can then use the `inference` method to estimate probabilities given - evidence, optionally using rejection sampling and Grover's algorithm for amplification. + .. code-block:: python - Example: - -------- - # Define a quantum circuit qc = QuantumCircuit(...) - # Initialize the framework qb = QBayesian(qc) - - # Perform inference result = qb.inference(query={...}, evidence={...}) + print("Probability of query given evidence: ", result) - print("Probability of query given evidence:", result) - - The following attributes can be set via the constructor but can also be read and updated once - the QBayesian object has been constructed. - - Attributes: - converged (bool): True if a solution for the evidence with the given threshold was found - without reaching the maximum number of times the Grover operator was integrated (limit). - limit: The maximum number of times the Grover operator is integrated (2^limit). - sampler (BaseSampler): The sampler primitive used to compute the samples and inferences. - samples (Dict[str, float]): Samples generated from the rejection sampling. - threshold (float): The threshold to accept the evidence. - + **References** + [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian + networks", Physical Review A 89.6 (2014): 062315. + [2]: Borujeni, Sima E., et al. "Quantum circuit representation of Bayesian networks." + Expert Systems with Applications 176 (2021): 114768. """ # Discrete quantum Bayesian network @@ -85,15 +62,13 @@ def __init__( """ Args: circuit: The quantum circuit that represents the Bayesian network. Each random variable - should be assigned to exactly one register of one qubit. A state vector is used as - an oracle for the Grover operator. The last qubit in the circuit corresponds to the - most significant bit passed in the state vector. Example: In a circuit with 2 qubits - and the first qubit as evidence with value 0, the good states are 00 and 10. + should be assigned to exactly one register of one qubit. The last qubit in the + circuit corresponds to the most significant bit in the binary string, which + represents the measured quantum state. limit: The maximum number of times the Grover operator is integrated (2^limit). - threshold (float): The threshold to accept the evidence. The threshold value for the - acceptance of the evidence. For example, if set to 0.9, this means that each - evidence qubit must be equal to the value of the evidence variable at least 90% of - the time in order to be accepted. + threshold (float): The threshold to accept the evidence. For example, if set to 0.9, + this means that each evidence qubit must be equal to the value of the evidence + variable at least 90% of the time. sampler: The sampler primitive used to compute the Bayesian inference. If ``None`` is given, a default instance of the reference sampler defined by :class:`~qiskit.primitives.Sampler` will be used. @@ -106,11 +81,11 @@ def __init__( raise ValueError("Every register needs to be mapped to exactly one unique qubit") # Initialize parameter self._circ = circuit - self.limit = limit - self.threshold = threshold + self._limit = limit + self._threshold = threshold if sampler is None: sampler = Sampler() - self.sampler = sampler + self._sampler = sampler # Label of register mapped to its qubit self._label2qubit = {qrg.name: qrg[0] for qrg in self._circ.qregs} @@ -119,9 +94,9 @@ def __init__( qrg.name: self._circ.num_qubits - idx - 1 for idx, qrg in enumerate(self._circ.qregs) } # Distribution of samples from rejection sampling - self.samples: Dict[str, float] = {} + self._samples: Dict[str, float] = {} # True if rejection sampling converged after limit - self.converged = bool() + self._converged = bool() def _get_grover_op(self, evidence: Dict[str, int]) -> GroverOperator: """ @@ -160,10 +135,10 @@ def _get_grover_op(self, evidence: Dict[str, int]) -> GroverOperator: def _run_circuit(self, circuit: QuantumCircuit) -> Dict[str, float]: """Run the quantum circuit with the sampler.""" # Sample from circuit - job = self.sampler.run(circuit) + job = self._sampler.run(circuit) result = job.result() # Get the counts of quantum state results - counts = result.quasi_dists[0].binary_probabilities() + counts = result.quasi_dists[0].nearest_probability_distribution().binary_probabilities() return counts def __power_grover( @@ -209,21 +184,47 @@ def __power_grover( e_count[evidence_qubits[i]] += e_sample_val # Assign to every evidence qubit if it is measured with high probability (th) 1 o/w 0 e_meas = { - (e_count_key, int(e_count_val >= self.threshold)) + (e_count_key, int(e_count_val >= self._threshold)) for e_count_key, e_count_val in e_count.items() } return qc, e_meas - def rejection_sampling(self, evidence: Dict[str, int]) -> Dict[str, float]: + def _format_samples(self, samples: Dict[str, float], evidence: List[str]) -> Dict[str, float]: + """Transforms samples keys back to their variables names.""" + f_samples: Dict[str, float] = {} + for smpl_key, smpl_val in samples.items(): + q_str, e_str = "", "" + for var_name, var_idx in sorted(self._label2qidx.items(), key=lambda x: -x[1]): + if var_name in evidence: + e_str += f"{var_name}={smpl_key[var_idx]}," + else: + q_str += f"{var_name}={smpl_key[var_idx]}," + if evidence: + f_samples[f"P({q_str[:-1]}|{e_str[:-1]})"] = smpl_val + else: + f_samples[f"P({q_str[:-1]})"] = smpl_val + return f_samples + + def rejection_sampling( + self, evidence: Dict[str, int], format_res: bool = False + ) -> Dict[str, float]: """ - Performs rejection sampling given the evidence. If evidence is empty, it runs the circuit - and measures all qubits. If evidence is provided, it uses the Grover operator for amplitude - amplification and iterates until the evidence matches or a limit is reached. + Performs rejection sampling given the evidence. Args: - evidence: A dictionary representing the evidence. + evidence: The evidence variables with keys that are linked to the corresponding quantum + register with their names and values, which are binary states of 0 or 1. If evidence + is empty, it measures all qubits. If evidence is provided, it uses the Grover + operator for amplitude amplification and iterates until the evidence matches or a + limit is reached. + format_res: If true, maps the output back to variable names. For example, the output + {'100': 0.23} with evidence A=0, B=0 will be mapped to {'P(C=1|A=0,B=0)': 0.23}. Returns: - dict: A dictionary containing the distribution of the samples + dict: A dictionary that contains the distribution of the samples. The keys are the + values of the variables and the values the probability distribution given the + evidence. The last variable value will appear as first character for the key. If + format_res is true, the output will be mapped back to variables names, for example + {'P(C=1|A=0,B=0)': 0.23}. """ # If evidence is empty if len(evidence) == 0: @@ -233,63 +234,66 @@ def rejection_sampling(self, evidence: Dict[str, int]) -> Dict[str, float]: # Measure qc.measure_all() # Run circuit - self.samples = self._run_circuit(qc) - return self.samples - # Get Grover operator if evidence not empty - grover_op = self._get_grover_op(evidence) - # Amplitude amplification - true_e = {(self._label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} - meas_e: Set[Tuple[str, int]] = set() - best_qc, best_inter = QuantumCircuit(), 0 - self.converged = False - k = -1 - # If the measurement of the evidence qubits matches the evidence stop - while (true_e != meas_e) and (k < self.limit): - # Increment power - k += 1 - # Create circuit with 2^k times Grover operator - qc, meas_e = self.__power_grover(grover_op=grover_op, evidence=evidence, k=k) - # Test number of - if len(true_e.intersection(meas_e)) > best_inter: - best_qc = qc - if true_e == meas_e: - self.converged = True + self._samples = self._run_circuit(qc) + else: + # Get Grover operator if evidence not empty + grover_op = self._get_grover_op(evidence) + # Amplitude amplification + true_e = {(self._label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} + meas_e: Set[Tuple[str, int]] = set() + best_qc, best_inter = QuantumCircuit(), 0 + self._converged = False + k = -1 + # If the measurement of the evidence qubits matches the evidence stop + while (true_e != meas_e) and (k < self._limit): + # Increment power + k += 1 + # Create circuit with 2^k times Grover operator + qc, meas_e = self.__power_grover(grover_op=grover_op, evidence=evidence, k=k) + # Test number of + if len(true_e.intersection(meas_e)) > best_inter: + best_qc = qc + if true_e == meas_e: + self._converged = True - # Create a classical register with the size of the evidence - best_qc_meas = QuantumCircuit(*self._circ.qregs) - best_qc_meas.append(best_qc, self._circ.qregs) - measurement_qcr = ClassicalRegister(self._circ.num_qubits - len(evidence)) - best_qc_meas.add_register(measurement_qcr) - # Map the query qubits to the classical bits and measure them - query_qubits = [ - (label, self._label2qidx[label], qubit) - for label, qubit in self._label2qubit.items() - if label not in evidence - ] - query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1], reverse=True) - # Measure query variables and return their count - best_qc_meas.measure([q[2] for q in query_qubits_sorted], measurement_qcr) - # Run circuit - counts = self._run_circuit(best_qc_meas) - # Build default string with evidence - query_string = "" - var_idx_sorted = [ - label for label, _ in sorted(self._label2qidx.items(), key=lambda x: x[1]) - ] - for var in var_idx_sorted: - if var in evidence: - query_string += str(evidence[var]) - else: - query_string += "q" - # Retrieve valid samples - self.samples = {} - # Replace placeholder q with query variables from samples - for key, val in counts.items(): - query = query_string - for char in key: - query = query.replace("q", char, 1) - self.samples[query] = val - return self.samples + # Create a classical register with the size of the evidence + best_qc_meas = QuantumCircuit(*self._circ.qregs) + best_qc_meas.append(best_qc, self._circ.qregs) + measurement_qcr = ClassicalRegister(self._circ.num_qubits - len(evidence)) + best_qc_meas.add_register(measurement_qcr) + # Map the query qubits to the classical bits and measure them + query_qubits = [ + (label, self._label2qidx[label], qubit) + for label, qubit in self._label2qubit.items() + if label not in evidence + ] + query_qubits_sorted = sorted(query_qubits, key=lambda x: x[1], reverse=True) + # Measure query variables and return their count + best_qc_meas.measure([q[2] for q in query_qubits_sorted], measurement_qcr) + # Run circuit + counts = self._run_circuit(best_qc_meas) + # Build default string with evidence + query_string = "" + var_idx_sorted = [ + label for label, _ in sorted(self._label2qidx.items(), key=lambda x: x[1]) + ] + for var in var_idx_sorted: + if var in evidence: + query_string += str(evidence[var]) + else: + query_string += "q" + # Retrieve valid samples + self._samples = {} + # Replace placeholder q with query variables from samples + for key, val in counts.items(): + query = query_string + for char in key: + query = query.replace("q", char, 1) + self._samples[query] = val + if not format_res: + return self._samples + else: + return self._format_samples(self._samples, list(evidence.keys())) def inference( self, @@ -301,11 +305,13 @@ def inference( evidence is provided and calculates the probability of the query. Args: - query: The query variables with keys as variable labels and values as states. - If Q is a real subset of X without E, it will be marginalized. - evidence: The evidence variables. If specified, rejection sampling is executed. If you - want to indicate the case of no evidence, insert an empty list. If you do not - provide any evidence, the samples from previous rejection sampling are used. + query: The query variables with keys that are linked to the corresponding quantum + register with their names and values, which are binary states of 0 or 1. If Q is a + real subset of X without E, it will be marginalized. + evidence: The evidence variables. If evidence is a dictionary, the rejection sampling is + executed with the keys linked to the corresponding quantum register by their names + and binary values of 0 or 1. If evidence is `None`, the default, then samples from + the previous rejection sampling are used. Returns: float: The probability of the query given the evidence. Raises: @@ -313,14 +319,13 @@ def inference( """ if evidence is not None: self.rejection_sampling(evidence) - else: - if not self.samples: - raise ValueError("Provide evidence or indicate no evidence with empty list") + elif not self._samples: + raise ValueError("Provide evidence or indicate no evidence with an empty dictionary") # Get sorted indices of query qubits query_indices_rev = [(self._label2qidx[q_key], q_val) for q_key, q_val in query.items()] # Get probability of query res = 0.0 - for sample_key, sample_val in self.samples.items(): + for sample_key, sample_val in self._samples.items(): add = True for q_idx, q_val in query_indices_rev: if int(sample_key[q_idx]) != q_val: @@ -329,3 +334,44 @@ def inference( if add: res += sample_val return res + + @property + def converged(self) -> bool: + """Returns ``True`` if a solution for the evidence with the given threshold was found + without reaching the maximum number of times the Grover operator was integrated (limit).""" + return self._converged + + @property + def samples(self) -> Dict[str, float]: + """Returns the samples generated from the rejection sampling.""" + return self._samples + + @property + def limit(self) -> int: + """The maximum number of times the Grover operator is integrated (2^limit).""" + return self._limit + + @limit.setter + def limit(self, limit: int): + """Set the maximum number of times the Grover operator is integrated (2^limit).""" + self._limit = limit + + @property + def sampler(self) -> BaseSampler: + """The sampler primitive used to compute the samples and inferences.""" + return self._sampler + + @sampler.setter + def sampler(self, sampler: BaseSampler): + """Set the sampler primitive used to compute the samples and inferences.""" + self._sampler = sampler + + @property + def threshold(self) -> float: + """The threshold to accept the evidence.""" + return self._threshold + + @threshold.setter + def threshold(self, threshold: float): + """Set the threshold to accept the evidence.""" + self._threshold = threshold diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml new file mode 100644 index 000000000..3649f9b21 --- /dev/null +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -0,0 +1,39 @@ +--- +features: + - | + Added a new class :class:`~qiskit_machine_learning.algorithms.QBayesian` that does quantum Bayesian inference on a + a quantum circuit representing a Bayesian network with binary random variables. + + The computational complexity is reduced from :math:`O(nmP(e)^{-1})` to :math:`O(n2^{m}P(e)^{-\frac{1}{2}})` per + sample, where n is the number of nodes in the Bayesian network with at most m parents per node and e the evidence. + + At least a quantum circuit that represents the Bayesian network has to be provided. A quantum circuit can be passed + in various forms as long as it represents the joint probability distribution of the Bayesian network. Note that + :class:`~qiskit_machine_learning.algorithms.QBayesian` defines an order for the qubits in the circuit. The last + qubit in the circuit will correspond to the most significant bit in the joint probability distribution. For example, + if the random variables A, B, and C are entered into the circuit in this order with (A=1, B=0 and C=0), the + probability is represented by the probability amplitude of quantum state 001. + + An example for using this class is as follows: + + .. code-block:: python + + from qiskit import QuantumCircuit + from qiskit_machine_learning.algorithms import QBayesian + + # Define a quantum circuit + qc = QuantumCircuit(...) + + # Initialize the framework + qb = QBayesian(qc) + + # Perform inference + result = qb.inference(query={...}, evidence={...}) + + print("Probability of query given evidence:", result) + + - | + For the new (:class:~qiskit_machine_learning.algorithms.QBayesian) class a tutorial was added. Please refer to: + - New + `QBI tutorial `__ + introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. diff --git a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml deleted file mode 100644 index 5f6156db4..000000000 --- a/releasenotes/notes/integrated-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ /dev/null @@ -1,17 +0,0 @@ ---- -features: - - | - Introduction of the `QBayesian` class in the Qiskit Machine Learning library. - This class implements quantum Bayesian inference, allowing users to perform - probabilistic reasoning with quantum circuits. The implementation is based on the - algorithm described in the paper "Quantum inference on Bayesian networks" - by Low, Yoder, and Chuang. - - | - The `QBayesian` class supports various functionalities including: - - Rejection sampling for estimating probabilities given evidence, with - Grover's algorithm-based amplification. - - Approximate Bayesian inference using rejection sampling, - with Grover's algorithm-based amplification. - - | - The `13_quantum_bayesian_inference` notebook describes a tutorial for the - usage of the `QBayesian` class. diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 5a5824a41..19f83f4de 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -98,6 +98,28 @@ def test_rejection_sampling(self): ) ) + def test_rejection_sampling_format_res(self): + """Test rejection sampling with different result format""" + test_cases = [{"A": 0, "C": 1}, {"C": 1}, {}] + true_res = [ + {"P(B=0|A=0,C=1)", "P(B=1|A=0,C=1)"}, + {"P(A=0,B=0|C=1)", "P(A=1,B=0|C=1)", "P(A=0,B=1|C=1)", "P(A=1,B=1|C=1)"}, + { + "P(A=0,B=0,C=0)", + "P(A=1,B=0,C=0)", + "P(A=0,B=1,C=0)", + "P(A=1,B=1,C=0)", + "P(A=0,B=0,C=1)", + "P(A=1,B=0,C=1)", + "P(A=0,B=1,C=1)", + "P(A=1,B=1,C=1)", + }, + ] + for evd, res in zip(test_cases, true_res): + self.assertTrue( + res == set(self.qbayesian.rejection_sampling(evidence=evd, format_res=True).keys()) + ) + def test_inference(self): """Test inference with different amount of evidence""" test_q_1, test_e_1 = ({"B": 1}, {"A": 1, "C": 1}) @@ -127,7 +149,7 @@ def test_parameter(self): """Tests parameter of methods""" # Test set threshold self.qbayesian.threshold = 0.9 - self.qbayesian.rejection_sampling(evidence={"B": 1}) + self.qbayesian.rejection_sampling(evidence={"A": 1}) # Test set limit self.qbayesian.limit = 1 self.qbayesian.rejection_sampling(evidence={"B": 1}) From 7f516c1ecdc5e0729eda2733c8f2e79e1ff1507e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 26 Nov 2023 21:45:11 +0100 Subject: [PATCH 31/48] Added test if converged for tutorial --- .../13_quantum_bayesian_inference.ipynb | 30 +++++++++++++++++-- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 3 +- 2 files changed, 29 insertions(+), 4 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index ee2d38199..f0a9af50d 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -690,11 +690,37 @@ }, { "cell_type": "markdown", - "id": "28b3cdd72e905dec", + "source": [ + "And we can also check whether the algorithm converges:" + ], "metadata": { "collapsed": false }, - "source": [] + "id": "cf43ad224f163d80" + }, + { + "cell_type": "code", + "execution_count": 121, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged: True\n" + ] + } + ], + "source": [ + "print(\"Converged: \", qb_ba.converged)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-26T20:42:09.672540Z", + "start_time": "2023-11-26T20:42:09.641774Z" + } + }, + "id": "d01e712eb69a686e" } ], "metadata": { diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 3649f9b21..31b504a41 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -34,6 +34,5 @@ features: - | For the new (:class:~qiskit_machine_learning.algorithms.QBayesian) class a tutorial was added. Please refer to: - - New - `QBI tutorial `__ + - New `QBI tutorial `__ introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. From 93265e432998736e2a6b5315ddcbfc99486e798c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 26 Nov 2023 21:48:44 +0100 Subject: [PATCH 32/48] Revert commit on tutorial 07 --- docs/tutorials/07_pegasos_qsvc.ipynb | 14 ++------------ 1 file changed, 2 insertions(+), 12 deletions(-) diff --git a/docs/tutorials/07_pegasos_qsvc.ipynb b/docs/tutorials/07_pegasos_qsvc.ipynb index c829d43bf..3ca8db2d9 100644 --- a/docs/tutorials/07_pegasos_qsvc.ipynb +++ b/docs/tutorials/07_pegasos_qsvc.ipynb @@ -26,12 +26,7 @@ "cell_type": "code", "execution_count": 1, "id": "impressed-laser", - "metadata": { - "ExecuteTime": { - "end_time": "2023-11-06T20:46:25.509287Z", - "start_time": "2023-11-06T20:46:23.936897Z" - } - }, + "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import make_blobs\n", @@ -52,12 +47,7 @@ "cell_type": "code", "execution_count": 2, "id": "adolescent-composer", - "metadata": { - "ExecuteTime": { - "end_time": "2023-11-06T20:46:25.560893Z", - "start_time": "2023-11-06T20:46:25.511175Z" - } - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", From 1bdf2a61e64c656529634f0b11358b1a7ae0fc0e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 27 Nov 2023 19:25:28 +0100 Subject: [PATCH 33/48] Embedded tutorial images --- .../13_quantum_bayesian_inference.ipynb | 170 +++++++++--------- ...m-bayesian-inference-92c6025432d9b7e0.yaml | 1 + 2 files changed, 86 insertions(+), 85 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index f0a9af50d..f8cba79db 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -22,20 +22,16 @@ }, { "cell_type": "markdown", - "source": [ - "## 1. Introduction" - ], + "id": "494f210f33019c5b", "metadata": { "collapsed": false }, - "id": "494f210f33019c5b" + "source": [ + "## 1. Introduction" + ] }, { "cell_type": "markdown", - "id": "3237c8b584b541bd", - "metadata": { - "collapsed": false - }, "source": [ "### 1.1. Quantum vs. Classical Bayesian Inference\n", "\n", @@ -55,7 +51,11 @@ "For more information about primitives please refer to the [primitives documentation](https://qiskit.org/documentation/apidoc/primitives.html).\n", "\n", "The `QBayesian` class is used for QBI in `qiskit-machine-learning`. It is initialized with a quantum circuit that represents a Bayesian network. This enables the execution of quantum rejection sampling and inference.\n" - ] + ], + "metadata": { + "collapsed": false + }, + "id": "f65b0713535b3fd6" }, { "cell_type": "markdown", @@ -69,10 +69,6 @@ }, { "cell_type": "markdown", - "id": "6adf88f1d249b336", - "metadata": { - "collapsed": false - }, "source": [ "### 2.1. Create Rotations for the Bayesian Networks\n", "In quantum computing, the rotation matrix around the y-axis, denoted as $R_y(\\theta)$, is used to rotate the state of a qubit around the y-axis of the Bloch sphere by an angle $\\theta$. This approach allows for precise control over the quantum state of a qubit, enabling the encoding of specific probabilities in quantum algorithms. When this rotation is applied to a qubit initially in the $|0\\rangle$ state, the resulting state $|\\psi\\rangle$ is:\n", @@ -91,7 +87,11 @@ "\n", "This approach can be extended for conditional probabilities. For example, with the Bayesian network shown above, you can use the following formula to calculate the joint probability distribution:\n", "$$(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(X\\otimes{I})(I\\otimes{I}+P_1\\otimes{(R_y-I)})(R_y\\otimes{I})|00\\rangle$$" - ] + ], + "metadata": { + "collapsed": false + }, + "id": "6adf88f1d249b336" }, { "cell_type": "markdown", @@ -108,7 +108,7 @@ { "cell_type": "markdown", "source": [ - "![Two Node Bayesian Network Example](Two_Node_Bayesian_Network.png)" + "![Two Node Bayesian Network Example](data:image/png;base64,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)" ], "metadata": { "collapsed": false @@ -127,13 +127,13 @@ }, { "cell_type": "code", - "execution_count": 109, + "execution_count": 25, "id": "326c1d2e72f41202", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:35.652594Z", - "start_time": "2023-11-26T20:32:35.602217Z" + "end_time": "2023-11-27T18:21:25.436665Z", + "start_time": "2023-11-27T18:21:25.391836Z" } }, "outputs": [], @@ -161,13 +161,13 @@ }, { "cell_type": "markdown", - "source": [ - "![Burglary Alarm](Burglary_Alarm.png)" - ], + "id": "69003c40f9bcbafd", "metadata": { "collapsed": false }, - "id": "69003c40f9bcbafd" + "source": [ + "![Burglary Alarm](data:image/png;base64,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)" + ] }, { "cell_type": "markdown", @@ -189,13 +189,13 @@ }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 26, "id": "a815411b4f10c78c", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:35.661940Z", - "start_time": "2023-11-26T20:32:35.610856Z" + "end_time": "2023-11-27T18:21:25.483927Z", + "start_time": "2023-11-27T18:21:25.398202Z" } }, "outputs": [], @@ -235,13 +235,13 @@ }, { "cell_type": "code", - "execution_count": 111, + "execution_count": 27, "id": "4f99dbe56bc6910a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:35.714886Z", - "start_time": "2023-11-26T20:32:35.615920Z" + "end_time": "2023-11-27T18:21:25.584278Z", + "start_time": "2023-11-27T18:21:25.413565Z" } }, "outputs": [ @@ -250,7 +250,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 111, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -289,13 +289,13 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 28, "id": "79045cc1a7706f87", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.198008Z", - "start_time": "2023-11-26T20:32:35.689896Z" + "end_time": "2023-11-27T18:21:25.905549Z", + "start_time": "2023-11-27T18:21:25.607813Z" } }, "outputs": [ @@ -304,7 +304,7 @@ "text/plain": "
", "image/png": 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}, - "execution_count": 112, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -391,13 +391,13 @@ }, { "cell_type": "code", - "execution_count": 113, + "execution_count": 29, "id": "1e602fda98a6356d", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.298746Z", - "start_time": "2023-11-26T20:32:36.206404Z" + "end_time": "2023-11-27T18:21:26.010493Z", + "start_time": "2023-11-27T18:21:25.914096Z" } }, "outputs": [ @@ -406,7 +406,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 113, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -435,13 +435,13 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 30, "id": "a6fc4d5d394d301a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.366001Z", - "start_time": "2023-11-26T20:32:36.273798Z" + "end_time": "2023-11-27T18:21:26.110237Z", + "start_time": "2023-11-27T18:21:25.989958Z" } }, "outputs": [ @@ -450,7 +450,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 114, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -464,17 +464,25 @@ }, { "cell_type": "markdown", - "source": [ - "We can also print the result in a better format to understand which values belong to which variables:" - ], + "id": "5bf133a4bdd8a976", "metadata": { "collapsed": false }, - "id": "5bf133a4bdd8a976" + "source": [ + "We can also print the result in a better format to understand which values belong to which variables:" + ] }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 31, + "id": "4f019762e7f6b861", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-27T18:21:26.166872Z", + "start_time": "2023-11-27T18:21:26.120196Z" + } + }, "outputs": [ { "name": "stdout", @@ -488,15 +496,7 @@ "qb_2n.threshold = 0.97\n", "samples = qb_2n.rejection_sampling(evidence=evidence, format_res=True)\n", "print(samples)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.424810Z", - "start_time": "2023-11-26T20:32:36.372302Z" - } - }, - "id": "4f019762e7f6b861" + ] }, { "cell_type": "markdown", @@ -511,13 +511,13 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 32, "id": "8d4904619b35503a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.509644Z", - "start_time": "2023-11-26T20:32:36.428970Z" + "end_time": "2023-11-27T18:21:26.255565Z", + "start_time": "2023-11-27T18:21:26.169458Z" } }, "outputs": [ @@ -526,7 +526,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 116, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -577,13 +577,13 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 33, "id": "841bce19ea097bf1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.567860Z", - "start_time": "2023-11-26T20:32:36.509199Z" + "end_time": "2023-11-27T18:21:26.316893Z", + "start_time": "2023-11-27T18:21:26.266622Z" } }, "outputs": [ @@ -591,7 +591,7 @@ "data": { "text/plain": "0.1004712084149367" }, - "execution_count": 117, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -625,13 +625,13 @@ }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 34, "id": "5468619791203a79", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:36.802634Z", - "start_time": "2023-11-26T20:32:36.566080Z" + "end_time": "2023-11-27T18:21:26.563225Z", + "start_time": "2023-11-27T18:21:26.335834Z" } }, "outputs": [ @@ -639,7 +639,7 @@ "data": { "text/plain": "0.0054042995153299" }, - "execution_count": 118, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -663,13 +663,13 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 35, "id": "a5434c7c7c45040a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-26T20:32:37.624165Z", - "start_time": "2023-11-26T20:32:36.806996Z" + "end_time": "2023-11-27T18:21:27.339180Z", + "start_time": "2023-11-27T18:21:26.574010Z" } }, "outputs": [ @@ -677,7 +677,7 @@ "data": { "text/plain": "0.0056128979765628" }, - "execution_count": 119, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -690,17 +690,25 @@ }, { "cell_type": "markdown", - "source": [ - "And we can also check whether the algorithm converges:" - ], + "id": "cf43ad224f163d80", "metadata": { "collapsed": false }, - "id": "cf43ad224f163d80" + "source": [ + "And we can also check whether the algorithm converges:" + ] }, { "cell_type": "code", - "execution_count": 121, + "execution_count": 36, + "id": "d01e712eb69a686e", + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-11-27T18:21:27.341097Z", + "start_time": "2023-11-27T18:21:27.338846Z" + } + }, "outputs": [ { "name": "stdout", @@ -712,15 +720,7 @@ ], "source": [ "print(\"Converged: \", qb_ba.converged)" - ], - "metadata": { - "collapsed": false, - "ExecuteTime": { - "end_time": "2023-11-26T20:42:09.672540Z", - "start_time": "2023-11-26T20:42:09.641774Z" - } - }, - "id": "d01e712eb69a686e" + ] } ], "metadata": { diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 31b504a41..c8d6eecba 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -34,5 +34,6 @@ features: - | For the new (:class:~qiskit_machine_learning.algorithms.QBayesian) class a tutorial was added. Please refer to: + - New `QBI tutorial `__ introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. From ac91d6886f1ef13773d4fcd936c49bdfc22ea477 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Mon, 27 Nov 2023 20:56:34 +0100 Subject: [PATCH 34/48] Fixed release note format --- .../add-quantum-bayesian-inference-92c6025432d9b7e0.yaml | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index c8d6eecba..37cb1cf2e 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -33,7 +33,8 @@ features: print("Probability of query given evidence:", result) - | - For the new (:class:~qiskit_machine_learning.algorithms.QBayesian) class a tutorial was added. Please refer to: + For the new :class:`~qiskit_machine_learning.algorithms.QBayesian` class, a tutorial was added. Please refer to: - New `QBI tutorial `__ - introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. + introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. + From 6c9cfc61990873e8bf72052980ff4fb75845cc45 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Tue, 28 Nov 2023 18:52:20 +0100 Subject: [PATCH 35/48] Added images and removed base64 for images --- docs/images/Burglary_Alarm.png | Bin 0 -> 42763 bytes docs/images/Two_Node_Bayesian_Network.png | Bin 0 -> 10555 bytes 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 docs/images/Burglary_Alarm.png create mode 100644 docs/images/Two_Node_Bayesian_Network.png diff --git a/docs/images/Burglary_Alarm.png b/docs/images/Burglary_Alarm.png new file mode 100644 index 0000000000000000000000000000000000000000..e683632dad24104827aa58cac3612fa830c7b4be GIT binary patch literal 42763 zcmdqIg%$b>Uu5+Dh!c>%G?%+`1prD}Kk&~5DLqS2;LqS1x#JUAO 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+++++++++---------- 1 file changed, 46 insertions(+), 46 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index f8cba79db..3957f9e1b 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -108,7 +108,7 @@ { "cell_type": "markdown", "source": [ - "![Two Node Bayesian Network Example](data:image/png;base64,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)" + "![Two Node Bayesian Network Example](../images/Two_Node_Bayesian_Network.png)" ], "metadata": { "collapsed": false @@ -127,13 +127,13 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 1, "id": "326c1d2e72f41202", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:25.436665Z", - "start_time": "2023-11-27T18:21:25.391836Z" + "end_time": "2023-11-28T17:51:41.868179Z", + "start_time": "2023-11-28T17:51:41.658159Z" } }, "outputs": [], @@ -166,7 +166,7 @@ "collapsed": false }, "source": [ - "![Burglary Alarm](data:image/png;base64,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)" + "![Burglary Alarm](../images/Burglary_Alarm.png)" ] }, { @@ -189,13 +189,13 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 2, "id": "a815411b4f10c78c", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:25.483927Z", - "start_time": "2023-11-27T18:21:25.398202Z" + "end_time": "2023-11-28T17:51:41.875614Z", + "start_time": "2023-11-28T17:51:41.870414Z" } }, "outputs": [], @@ -235,13 +235,13 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 3, "id": "4f99dbe56bc6910a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:25.584278Z", - "start_time": "2023-11-27T18:21:25.413565Z" + "end_time": "2023-11-28T17:51:42.847437Z", + "start_time": "2023-11-28T17:51:41.880154Z" } }, "outputs": [ @@ -250,7 +250,7 @@ "text/plain": "
", "image/png": "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" }, - "execution_count": 27, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -289,13 +289,13 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 4, "id": "79045cc1a7706f87", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:25.905549Z", - "start_time": "2023-11-27T18:21:25.607813Z" + "end_time": "2023-11-28T17:51:43.181432Z", + "start_time": "2023-11-28T17:51:42.851408Z" } }, "outputs": [ @@ -304,7 +304,7 @@ "text/plain": "
", "image/png": 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}, - "execution_count": 28, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -391,13 +391,13 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 5, "id": "1e602fda98a6356d", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.010493Z", - "start_time": "2023-11-27T18:21:25.914096Z" + "end_time": "2023-11-28T17:51:45.067437Z", + "start_time": "2023-11-28T17:51:43.183331Z" } }, "outputs": [ @@ -406,7 +406,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 29, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -435,13 +435,13 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 6, "id": "a6fc4d5d394d301a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.110237Z", - "start_time": "2023-11-27T18:21:25.989958Z" + "end_time": "2023-11-28T17:51:45.300291Z", + "start_time": "2023-11-28T17:51:45.127277Z" } }, "outputs": [ @@ -450,7 +450,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 30, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -474,13 +474,13 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 7, "id": "4f019762e7f6b861", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.166872Z", - "start_time": "2023-11-27T18:21:26.120196Z" + "end_time": "2023-11-28T17:51:45.377580Z", + "start_time": "2023-11-28T17:51:45.311052Z" } }, "outputs": [ @@ -511,13 +511,13 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 8, "id": "8d4904619b35503a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.255565Z", - "start_time": "2023-11-27T18:21:26.169458Z" + "end_time": "2023-11-28T17:51:45.471861Z", + "start_time": "2023-11-28T17:51:45.382492Z" } }, "outputs": [ @@ -526,7 +526,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 32, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -577,13 +577,13 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 9, "id": "841bce19ea097bf1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.316893Z", - "start_time": "2023-11-27T18:21:26.266622Z" + "end_time": "2023-11-28T17:51:45.539475Z", + "start_time": "2023-11-28T17:51:45.479075Z" } }, "outputs": [ @@ -591,7 +591,7 @@ "data": { "text/plain": "0.1004712084149367" }, - "execution_count": 33, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -625,13 +625,13 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 10, "id": "5468619791203a79", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:26.563225Z", - "start_time": "2023-11-27T18:21:26.335834Z" + "end_time": "2023-11-28T17:51:45.820785Z", + "start_time": "2023-11-28T17:51:45.559257Z" } }, "outputs": [ @@ -639,7 +639,7 @@ "data": { "text/plain": "0.0054042995153299" }, - "execution_count": 34, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -663,13 +663,13 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 11, "id": "a5434c7c7c45040a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:27.339180Z", - "start_time": "2023-11-27T18:21:26.574010Z" + "end_time": "2023-11-28T17:51:46.486813Z", + "start_time": "2023-11-28T17:51:45.831576Z" } }, "outputs": [ @@ -677,7 +677,7 @@ "data": { "text/plain": "0.0056128979765628" }, - "execution_count": 35, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -700,13 +700,13 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 12, "id": "d01e712eb69a686e", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-27T18:21:27.341097Z", - "start_time": "2023-11-27T18:21:27.338846Z" + "end_time": "2023-11-28T17:51:46.490430Z", + "start_time": "2023-11-28T17:51:46.486617Z" } }, "outputs": [ From 47d57a69076d1ba645605874260a4da38ed5a18a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 1 Dec 2023 20:28:36 +0100 Subject: [PATCH 37/48] Fixed documentation QBayesian --- .../algorithms/inference/qbayesian.py | 64 +++++++++---------- 1 file changed, 32 insertions(+), 32 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 1aa0a1ed1..2b03d7c4a 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -21,10 +21,10 @@ class QBayesian: r""" - Implements a quantum Bayesian inference (QBI) algorithm that has been developed in [1]. The QBI - includes methods ``rejection_sampling`` and ``inference`` for a Bayesian network with binary - random variables represented by a quantum circuit. A quantum circuit can be passed in various - forms as long as it represents the joint probability distribution of the Bayesian network. + Implements a quantum Bayesian inference (QBI) algorithm that has been developed in [1]. The + Bayesian network must be based on binary random variables (0/1) and represented by a quantum + circuit. The quantum circuit can be passed in various forms as long as it represents the joint + probability distribution of the network. For Bayesian networks with random variables that have more than two states, see for example [2]. @@ -47,6 +47,7 @@ class QBayesian: **References** [1]: Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. "Quantum inference on Bayesian networks", Physical Review A 89.6 (2014): 062315. + [2]: Borujeni, Sima E., et al. "Quantum circuit representation of Bayesian networks." Expert Systems with Applications 176 (2021): 114768. """ @@ -68,7 +69,7 @@ def __init__( limit: The maximum number of times the Grover operator is integrated (2^limit). threshold (float): The threshold to accept the evidence. For example, if set to 0.9, this means that each evidence qubit must be equal to the value of the evidence - variable at least 90% of the time. + variable at least 90% of the measurements. sampler: The sampler primitive used to compute the Bayesian inference. If ``None`` is given, a default instance of the reference sampler defined by :class:`~qiskit.primitives.Sampler` will be used. @@ -209,22 +210,20 @@ def rejection_sampling( self, evidence: Dict[str, int], format_res: bool = False ) -> Dict[str, float]: """ - Performs rejection sampling given the evidence. + Performs quantum rejection sampling given the evidence. Args: - evidence: The evidence variables with keys that are linked to the corresponding quantum - register with their names and values, which are binary states of 0 or 1. If evidence - is empty, it measures all qubits. If evidence is provided, it uses the Grover - operator for amplitude amplification and iterates until the evidence matches or a - limit is reached. + evidence: The keys of the dictionary are the evidence variables that are linked to the + corresponding quantum register with their names and values (0/1). If evidence is + empty, it measures all qubits. If evidence is given, it uses the Grover operator for + amplitude amplification and repeats until the evidence matches or limit is reached. format_res: If true, maps the output back to variable names. For example, the output {'100': 0.23} with evidence A=0, B=0 will be mapped to {'P(C=1|A=0,B=0)': 0.23}. Returns: - dict: A dictionary that contains the distribution of the samples. The keys are the - values of the variables and the values the probability distribution given the - evidence. The last variable value will appear as first character for the key. If - format_res is true, the output will be mapped back to variables names, for example - {'P(C=1|A=0,B=0)': 0.23}. + A dictionary with the probability distribution of the samples given the evidence, where + the keys are the sequential values of the variables. Note that the last variable value + appears as the first character for the key. If format_res is true, the output will be + mapped back to the variable names, for example {'P(C=1|A=0,B=0)': 0.23}. """ # If evidence is empty if len(evidence) == 0: @@ -301,21 +300,22 @@ def inference( evidence: Dict[str, int] = None, ) -> float: """ - Performs inference on the query variables given the evidence. It uses rejection sampling if - evidence is provided and calculates the probability of the query. + Performs quantum inference for the query variables given the evidence. It uses quantum + rejection sampling if evidence is given and calculates the probability of the query. Args: - query: The query variables with keys that are linked to the corresponding quantum - register with their names and values, which are binary states of 0 or 1. If Q is a - real subset of X without E, it will be marginalized. + query: The keys of the dictionary are the query variables that are linked to the + corresponding quantum registers with their names and values (0/1). If the query + variables are a real subset of all variables without the evidence, the query will be + marginalized. evidence: The evidence variables. If evidence is a dictionary, the rejection sampling is - executed with the keys linked to the corresponding quantum register by their names - and binary values of 0 or 1. If evidence is `None`, the default, then samples from - the previous rejection sampling are used. + executed with the keys representing the variables linked to the corresponding + quantum register by their names and values (0/1). If evidence is ``None``, the + default, then samples from the previous rejection sampling are used. Returns: - float: The probability of the query given the evidence. + The probability of the query given the evidence. Raises: - ValueError: If evidence is required for rejection sampling and none is provided. + ValueError: If evidence is required for rejection sampling and ``None`` is given. """ if evidence is not None: self.rejection_sampling(evidence) @@ -338,7 +338,7 @@ def inference( @property def converged(self) -> bool: """Returns ``True`` if a solution for the evidence with the given threshold was found - without reaching the maximum number of times the Grover operator was integrated (limit).""" + without reaching the maximum number of times the Grover operator was applied (2^limit).""" return self._converged @property @@ -348,27 +348,27 @@ def samples(self) -> Dict[str, float]: @property def limit(self) -> int: - """The maximum number of times the Grover operator is integrated (2^limit).""" + """Returns the maximum number of times the Grover operator can be applied (2^limit).""" return self._limit @limit.setter def limit(self, limit: int): - """Set the maximum number of times the Grover operator is integrated (2^limit).""" + """Set the maximum number of times the Grover operator can be applied (2^limit).""" self._limit = limit @property def sampler(self) -> BaseSampler: - """The sampler primitive used to compute the samples and inferences.""" + """Returns the sampler primitive used to compute the samples.""" return self._sampler @sampler.setter def sampler(self, sampler: BaseSampler): - """Set the sampler primitive used to compute the samples and inferences.""" + """Set the sampler primitive used to compute the samples.""" self._sampler = sampler @property def threshold(self) -> float: - """The threshold to accept the evidence.""" + """Returns the threshold to accept the evidence.""" return self._threshold @threshold.setter From 5efee9f131acf77f19250b4230e63fb45dbdcdf6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 16 Feb 2024 18:37:56 +0100 Subject: [PATCH 38/48] Added Copyright 2024 --- qiskit_machine_learning/algorithms/__init__.py | 4 ++-- qiskit_machine_learning/algorithms/inference/__init__.py | 2 +- qiskit_machine_learning/algorithms/inference/qbayesian.py | 2 +- test/algorithms/inference/__init__.py | 2 +- test/algorithms/inference/test_qbayesian.py | 2 +- 5 files changed, 6 insertions(+), 6 deletions(-) diff --git a/qiskit_machine_learning/algorithms/__init__.py b/qiskit_machine_learning/algorithms/__init__.py index d6566bbef..37a8ef82d 100644 --- a/qiskit_machine_learning/algorithms/__init__.py +++ b/qiskit_machine_learning/algorithms/__init__.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2021, 2023. +# (C) Copyright IBM 2021, 2023, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -56,7 +56,7 @@ NeuralNetworkClassifier VQC -Classifiers +Inference +++++++++++ Algorithms for inference. diff --git a/qiskit_machine_learning/algorithms/inference/__init__.py b/qiskit_machine_learning/algorithms/inference/__init__.py index 5003e7b22..322bb8f1c 100644 --- a/qiskit_machine_learning/algorithms/inference/__init__.py +++ b/qiskit_machine_learning/algorithms/inference/__init__.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2020, 2023. +# (C) Copyright IBM 2023, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 2b03d7c4a..cb19fb1b7 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2023. +# (C) Copyright IBM 2023, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory diff --git a/test/algorithms/inference/__init__.py b/test/algorithms/inference/__init__.py index def83287c..ceef869a8 100644 --- a/test/algorithms/inference/__init__.py +++ b/test/algorithms/inference/__init__.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2021, 2023. +# (C) Copyright IBM 2023, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 19f83f4de..3f9e3ba0f 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2023. +# (C) Copyright IBM 2023, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory From 77ef4ed1c9c3c7a18baf330cca63481d730f0f2d Mon Sep 17 00:00:00 2001 From: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Date: Mon, 19 Feb 2024 12:39:31 -0500 Subject: [PATCH 39/48] Update qiskit_machine_learning/algorithms/__init__.py --- qiskit_machine_learning/algorithms/__init__.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit_machine_learning/algorithms/__init__.py b/qiskit_machine_learning/algorithms/__init__.py index 37a8ef82d..989d6b98f 100644 --- a/qiskit_machine_learning/algorithms/__init__.py +++ b/qiskit_machine_learning/algorithms/__init__.py @@ -1,6 +1,6 @@ # This code is part of a Qiskit project. # -# (C) Copyright IBM 2021, 2023, 2024. +# (C) Copyright IBM 2021, 2024. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory From e7977d70076547913b4e6246eb0017dd353fb30b Mon Sep 17 00:00:00 2001 From: Edoardo Altamura <38359901+edoaltamura@users.noreply.github.com> Date: Thu, 7 Mar 2024 23:20:46 +0100 Subject: [PATCH 40/48] Update releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- .../notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 37cb1cf2e..fd47e35ca 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -36,5 +36,5 @@ features: For the new :class:`~qiskit_machine_learning.algorithms.QBayesian` class, a tutorial was added. Please refer to: - New `QBI tutorial `__ - introduces step-by-step how to do quantum Bayesian inference on a Bayesian network. + that introduces a step-by-step approach for how to do quantum Bayesian inference on a Bayesian network. From eab8e7cadc23dd34868b8056df1c12e7690da217 Mon Sep 17 00:00:00 2001 From: Edoardo Altamura <38359901+edoaltamura@users.noreply.github.com> Date: Thu, 7 Mar 2024 23:21:14 +0100 Subject: [PATCH 41/48] Update releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- .../notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index fd47e35ca..165cc032f 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -35,6 +35,6 @@ features: - | For the new :class:`~qiskit_machine_learning.algorithms.QBayesian` class, a tutorial was added. Please refer to: - - New `QBI tutorial `__ + - New `QBI tutorial <../tutorials/13_quantum_bayesian_inference.html>`__ that introduces a step-by-step approach for how to do quantum Bayesian inference on a Bayesian network. From 551f3db6177dd962c158f4576bc04825a2a03f03 Mon Sep 17 00:00:00 2001 From: Edoardo Altamura <38359901+edoaltamura@users.noreply.github.com> Date: Thu, 7 Mar 2024 23:27:29 +0100 Subject: [PATCH 42/48] Update qiskit_machine_learning/algorithms/inference/qbayesian.py Co-authored-by: Declan Millar --- qiskit_machine_learning/algorithms/inference/qbayesian.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index cb19fb1b7..f3154deb0 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -58,7 +58,7 @@ def __init__( circuit: QuantumCircuit, limit: int = 10, threshold: float = 0.9, - sampler: BaseSampler = Sampler(), + sampler: BaseSampler | None = None, ): """ Args: From 4514da888f3380757fe2521d659a20180e848f55 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sat, 9 Mar 2024 13:45:44 +0100 Subject: [PATCH 43/48] Added tests for getter and setter --- .../algorithms/inference/qbayesian.py | 7 +++--- ...ctor_kernel-pickling-b7fa2b13a15ec9c6.yaml | 3 ++- test/algorithms/inference/test_qbayesian.py | 22 +++++++++++++++---- 3 files changed, 24 insertions(+), 8 deletions(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index f3154deb0..0514bc78f 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -11,6 +11,7 @@ # that they have been altered from the originals. """Quantum Bayesian Inference""" +import copy from typing import Tuple, Dict, Set, List from qiskit import QuantumCircuit, ClassicalRegister from qiskit.quantum_info import Statevector @@ -56,6 +57,7 @@ class QBayesian: def __init__( self, circuit: QuantumCircuit, + *, limit: int = 10, threshold: float = 0.9, sampler: BaseSampler | None = None, @@ -240,7 +242,7 @@ def rejection_sampling( # Amplitude amplification true_e = {(self._label2qubit[e_key], e_val) for e_key, e_val in evidence.items()} meas_e: Set[Tuple[str, int]] = set() - best_qc, best_inter = QuantumCircuit(), 0 + best_qc, best_inter = QuantumCircuit(), -1 self._converged = False k = -1 # If the measurement of the evidence qubits matches the evidence stop @@ -254,7 +256,6 @@ def rejection_sampling( best_qc = qc if true_e == meas_e: self._converged = True - # Create a classical register with the size of the evidence best_qc_meas = QuantumCircuit(*self._circ.qregs) best_qc_meas.append(best_qc, self._circ.qregs) @@ -290,7 +291,7 @@ def rejection_sampling( query = query.replace("q", char, 1) self._samples[query] = val if not format_res: - return self._samples + return copy.deepcopy(self._samples) else: return self._format_samples(self._samples, list(evidence.keys())) diff --git a/releasenotes/notes/fix-fid_statevector_kernel-pickling-b7fa2b13a15ec9c6.yaml b/releasenotes/notes/fix-fid_statevector_kernel-pickling-b7fa2b13a15ec9c6.yaml index 34c512b83..fbdcb8dee 100644 --- a/releasenotes/notes/fix-fid_statevector_kernel-pickling-b7fa2b13a15ec9c6.yaml +++ b/releasenotes/notes/fix-fid_statevector_kernel-pickling-b7fa2b13a15ec9c6.yaml @@ -1,4 +1,5 @@ --- fixes: - | - Fixed a bug where :class:`.FidelityStatevectorKernel` threw an error when pickled. \ No newline at end of file + Fixed a bug where :class:`.FidelityStatevectorKernel` threw an error when pickled. + diff --git a/test/algorithms/inference/test_qbayesian.py b/test/algorithms/inference/test_qbayesian.py index 3f9e3ba0f..a4f5a2693 100644 --- a/test/algorithms/inference/test_qbayesian.py +++ b/test/algorithms/inference/test_qbayesian.py @@ -29,6 +29,11 @@ class TestQBayesianInference(QiskitMachineLearningTestCase): def setUp(self): super().setUp() algorithm_globals.random_seed = 10598 + # Quantum Bayesian inference + qc = self._create_bayes_net() + self.qbayesian = QBayesian(qc) + + def _create_bayes_net(self): # Probabilities theta_a = 2 * np.arcsin(np.sqrt(0.25)) theta_b_na = 2 * np.arcsin(np.sqrt(0.6)) @@ -67,8 +72,7 @@ def setUp(self): qc.x(0) # P(C|B,A) qc.mcry(theta_c_ba, [qr_a[0], qr_b[0]], qr_c[0]) - # Quantum Bayesian inference - self.qbayesian = QBayesian(qc) + return qc def test_rejection_sampling(self): """Test rejection sampling with different amount of evidence""" @@ -150,12 +154,23 @@ def test_parameter(self): # Test set threshold self.qbayesian.threshold = 0.9 self.qbayesian.rejection_sampling(evidence={"A": 1}) + self.assertTrue(self.qbayesian.threshold == 0.9) # Test set limit + # Not converged + self.qbayesian.limit = 0 + self.qbayesian.rejection_sampling(evidence={"B": 1}) + self.assertFalse(self.qbayesian.converged) + self.assertTrue(self.qbayesian.limit == 0) + # Converged self.qbayesian.limit = 1 self.qbayesian.rejection_sampling(evidence={"B": 1}) + self.assertTrue(self.qbayesian.converged) + self.assertTrue(self.qbayesian.limit == 1) # Test sampler - self.qbayesian.sampler = Sampler() + sampler = Sampler() + self.qbayesian.sampler = sampler self.qbayesian.inference(query={"B": 1}, evidence={"A": 0, "C": 0}) + self.assertTrue(self.qbayesian.sampler == sampler) # Create a quantum circuit with a register that has more than one qubit with self.assertRaises(ValueError, msg="No ValueError in constructor with invalid input."): QBayesian(QuantumCircuit(QuantumRegister(2, "qr"))) @@ -179,7 +194,6 @@ def test_trivial_circuit(self): qc.x(0) qc.cry(theta_b_na, control_qubit=qr_a, target_qubit=qr_b) qc.x(0) - qc.draw("mpl", style="bw", plot_barriers=False, justify="none", fold=-1) # Inference self.assertTrue( np.all( From 4db7272365506d859317c062167898e2f675901e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Sun, 10 Mar 2024 00:32:07 +0100 Subject: [PATCH 44/48] Rerun notebook for |: 'ABCMeta' and 'NoneType' --- .../13_quantum_bayesian_inference.ipynb | 48 +++++++++---------- 1 file changed, 24 insertions(+), 24 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index 3957f9e1b..fb9188d32 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -132,8 +132,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:41.868179Z", - "start_time": "2023-11-28T17:51:41.658159Z" + "end_time": "2024-03-09T23:25:43.051947Z", + "start_time": "2024-03-09T23:25:42.797448Z" } }, "outputs": [], @@ -194,8 +194,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:41.875614Z", - "start_time": "2023-11-28T17:51:41.870414Z" + "end_time": "2024-03-09T23:25:43.090872Z", + "start_time": "2024-03-09T23:25:43.065150Z" } }, "outputs": [], @@ -240,8 +240,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:42.847437Z", - "start_time": "2023-11-28T17:51:41.880154Z" + "end_time": "2024-03-09T23:25:43.965635Z", + "start_time": "2024-03-09T23:25:43.104664Z" } }, "outputs": [ @@ -294,8 +294,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:43.181432Z", - "start_time": "2023-11-28T17:51:42.851408Z" + "end_time": "2024-03-09T23:25:44.235362Z", + "start_time": "2024-03-09T23:25:43.968183Z" } }, "outputs": [ @@ -396,8 +396,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.067437Z", - "start_time": "2023-11-28T17:51:43.183331Z" + "end_time": "2024-03-09T23:25:46.137013Z", + "start_time": "2024-03-09T23:25:44.242001Z" } }, "outputs": [ @@ -440,8 +440,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.300291Z", - "start_time": "2023-11-28T17:51:45.127277Z" + "end_time": "2024-03-09T23:25:46.329501Z", + "start_time": "2024-03-09T23:25:46.143383Z" } }, "outputs": [ @@ -479,8 +479,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.377580Z", - "start_time": "2023-11-28T17:51:45.311052Z" + "end_time": "2024-03-09T23:25:46.409633Z", + "start_time": "2024-03-09T23:25:46.338940Z" } }, "outputs": [ @@ -516,8 +516,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.471861Z", - "start_time": "2023-11-28T17:51:45.382492Z" + "end_time": "2024-03-09T23:25:46.491261Z", + "start_time": "2024-03-09T23:25:46.413467Z" } }, "outputs": [ @@ -582,8 +582,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.539475Z", - "start_time": "2023-11-28T17:51:45.479075Z" + "end_time": "2024-03-09T23:25:46.554726Z", + "start_time": "2024-03-09T23:25:46.495158Z" } }, "outputs": [ @@ -630,8 +630,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:45.820785Z", - "start_time": "2023-11-28T17:51:45.559257Z" + "end_time": "2024-03-09T23:25:46.822265Z", + "start_time": "2024-03-09T23:25:46.570581Z" } }, "outputs": [ @@ -668,8 +668,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:46.486813Z", - "start_time": "2023-11-28T17:51:45.831576Z" + "end_time": "2024-03-09T23:25:47.386671Z", + "start_time": "2024-03-09T23:25:46.826683Z" } }, "outputs": [ @@ -705,8 +705,8 @@ "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2023-11-28T17:51:46.490430Z", - "start_time": "2023-11-28T17:51:46.486617Z" + "end_time": "2024-03-09T23:25:47.390809Z", + "start_time": "2024-03-09T23:25:47.388274Z" } }, "outputs": [ From 4f7ac0bc727aa9235c4d8b5058231a8cca499867 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 15 Mar 2024 13:30:34 +0100 Subject: [PATCH 45/48] Added default sampler parameter --- .../13_quantum_bayesian_inference.ipynb | 88 +++++++++---------- .../algorithms/inference/qbayesian.py | 4 +- 2 files changed, 45 insertions(+), 47 deletions(-) diff --git a/docs/tutorials/13_quantum_bayesian_inference.ipynb b/docs/tutorials/13_quantum_bayesian_inference.ipynb index fb9188d32..9aee06e8a 100644 --- a/docs/tutorials/13_quantum_bayesian_inference.ipynb +++ b/docs/tutorials/13_quantum_bayesian_inference.ipynb @@ -127,13 +127,13 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 13, "id": "326c1d2e72f41202", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:43.051947Z", - "start_time": "2024-03-09T23:25:42.797448Z" + "end_time": "2024-03-15T12:25:43.964092Z", + "start_time": "2024-03-15T12:25:43.916109Z" } }, "outputs": [], @@ -189,13 +189,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 14, "id": "a815411b4f10c78c", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:43.090872Z", - "start_time": "2024-03-09T23:25:43.065150Z" + "end_time": "2024-03-15T12:25:43.977309Z", + "start_time": "2024-03-15T12:25:43.922941Z" } }, "outputs": [], @@ -235,13 +235,13 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "id": "4f99dbe56bc6910a", "metadata": { "collapsed": false, + "is_executing": true, "ExecuteTime": { - "end_time": "2024-03-09T23:25:43.965635Z", - "start_time": "2024-03-09T23:25:43.104664Z" + "start_time": "2024-03-15T12:25:43.936275Z" } }, "outputs": [ @@ -250,7 +250,7 @@ "text/plain": "
", "image/png": "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" }, - "execution_count": 3, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -289,13 +289,13 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 16, "id": "79045cc1a7706f87", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:44.235362Z", - "start_time": "2024-03-09T23:25:43.968183Z" + "end_time": "2024-03-15T12:25:44.289098Z", + "start_time": "2024-03-15T12:25:43.993735Z" } }, "outputs": [ @@ -304,7 +304,7 @@ "text/plain": "
", "image/png": 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}, - "execution_count": 4, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -391,13 +391,13 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 17, "id": "1e602fda98a6356d", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.137013Z", - "start_time": "2024-03-09T23:25:44.242001Z" + "end_time": "2024-03-15T12:25:44.414966Z", + "start_time": "2024-03-15T12:25:44.300268Z" } }, "outputs": [ @@ -406,7 +406,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 5, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -435,13 +435,13 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 18, "id": "a6fc4d5d394d301a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.329501Z", - "start_time": "2024-03-09T23:25:46.143383Z" + "end_time": "2024-03-15T12:25:44.544878Z", + "start_time": "2024-03-15T12:25:44.427867Z" } }, "outputs": [ @@ -450,7 +450,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 6, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -474,13 +474,13 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 19, "id": "4f019762e7f6b861", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.409633Z", - "start_time": "2024-03-09T23:25:46.338940Z" + "end_time": "2024-03-15T12:25:44.619555Z", + "start_time": "2024-03-15T12:25:44.540091Z" } }, "outputs": [ @@ -511,13 +511,13 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 20, "id": "8d4904619b35503a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.491261Z", - "start_time": "2024-03-09T23:25:46.413467Z" + "end_time": "2024-03-15T12:25:44.729578Z", + "start_time": "2024-03-15T12:25:44.618613Z" } }, "outputs": [ @@ -526,7 +526,7 @@ "text/plain": "
", "image/png": 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" }, - "execution_count": 8, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -577,13 +577,13 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 21, "id": "841bce19ea097bf1", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.554726Z", - "start_time": "2024-03-09T23:25:46.495158Z" + "end_time": "2024-03-15T12:25:44.795158Z", + "start_time": "2024-03-15T12:25:44.744036Z" } }, "outputs": [ @@ -591,7 +591,7 @@ "data": { "text/plain": "0.1004712084149367" }, - "execution_count": 9, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -625,13 +625,13 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 22, "id": "5468619791203a79", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:46.822265Z", - "start_time": "2024-03-09T23:25:46.570581Z" + "end_time": "2024-03-15T12:25:45.014942Z", + "start_time": "2024-03-15T12:25:44.794874Z" } }, "outputs": [ @@ -639,7 +639,7 @@ "data": { "text/plain": "0.0054042995153299" }, - "execution_count": 10, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -663,13 +663,13 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 23, "id": "a5434c7c7c45040a", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:47.386671Z", - "start_time": "2024-03-09T23:25:46.826683Z" + "end_time": "2024-03-15T12:25:45.806883Z", + "start_time": "2024-03-15T12:25:45.028762Z" } }, "outputs": [ @@ -677,7 +677,7 @@ "data": { "text/plain": "0.0056128979765628" }, - "execution_count": 11, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -700,13 +700,13 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 24, "id": "d01e712eb69a686e", "metadata": { "collapsed": false, "ExecuteTime": { - "end_time": "2024-03-09T23:25:47.390809Z", - "start_time": "2024-03-09T23:25:47.388274Z" + "end_time": "2024-03-15T12:25:45.810056Z", + "start_time": "2024-03-15T12:25:45.806688Z" } }, "outputs": [ diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 0514bc78f..7e0a64373 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -60,7 +60,7 @@ def __init__( *, limit: int = 10, threshold: float = 0.9, - sampler: BaseSampler | None = None, + sampler: BaseSampler = Sampler(), ): """ Args: @@ -86,8 +86,6 @@ def __init__( self._circ = circuit self._limit = limit self._threshold = threshold - if sampler is None: - sampler = Sampler() self._sampler = sampler # Label of register mapped to its qubit From 21989fbfffc71968142043f481e75d3ec83dec77 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 15 Mar 2024 17:46:56 +0100 Subject: [PATCH 46/48] Fixed format error release note --- .../notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml index 165cc032f..f226b0027 100644 --- a/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml +++ b/releasenotes/notes/add-quantum-bayesian-inference-92c6025432d9b7e0.yaml @@ -36,5 +36,4 @@ features: For the new :class:`~qiskit_machine_learning.algorithms.QBayesian` class, a tutorial was added. Please refer to: - New `QBI tutorial <../tutorials/13_quantum_bayesian_inference.html>`__ - that introduces a step-by-step approach for how to do quantum Bayesian inference on a Bayesian network. - + that introduces a step-by-step approach for how to do quantum Bayesian inference on a Bayesian network. From a7bbd3ecb7a360c1aab408e87d6ed40a5923a53f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 15 Mar 2024 17:53:58 +0100 Subject: [PATCH 47/48] Removed mutable object as a default parameter --- qiskit_machine_learning/algorithms/inference/qbayesian.py | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 7e0a64373..0514bc78f 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -60,7 +60,7 @@ def __init__( *, limit: int = 10, threshold: float = 0.9, - sampler: BaseSampler = Sampler(), + sampler: BaseSampler | None = None, ): """ Args: @@ -86,6 +86,8 @@ def __init__( self._circ = circuit self._limit = limit self._threshold = threshold + if sampler is None: + sampler = Sampler() self._sampler = sampler # Label of register mapped to its qubit From cb6008ace016826439fabba8187ae2c42033d6ac Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Peter=20R=C3=B6seler?= Date: Fri, 15 Mar 2024 22:42:40 +0100 Subject: [PATCH 48/48] Fixed TypeError --- qiskit_machine_learning/algorithms/inference/qbayesian.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/qiskit_machine_learning/algorithms/inference/qbayesian.py b/qiskit_machine_learning/algorithms/inference/qbayesian.py index 0514bc78f..9621ba5e4 100644 --- a/qiskit_machine_learning/algorithms/inference/qbayesian.py +++ b/qiskit_machine_learning/algorithms/inference/qbayesian.py @@ -11,6 +11,8 @@ # that they have been altered from the originals. """Quantum Bayesian Inference""" +from __future__ import annotations + import copy from typing import Tuple, Dict, Set, List from qiskit import QuantumCircuit, ClassicalRegister