From 8e335ea5a63d67b2a5da20fb9a656154961e7caa Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris <43348706+kaelynj@users.noreply.github.com> Date: Tue, 12 Nov 2024 17:08:58 -0500 Subject: [PATCH] Guides pages for OBP (#2248) Closes #2107 and closes #2108 I'll include the files in the toc and satiate CI once #2148 is merged to avoid dealing with conflicts. --------- Co-authored-by: Caleb Johnson Co-authored-by: abbycross --- docs/guides/_toc.json | 13 + docs/guides/optimize-for-hardware.mdx | 6 +- .../qiskit-addons-obp-get-started.ipynb | 486 ++++++++++++++++++ docs/guides/qiskit-addons-obp.mdx | 95 ++++ .../guides/qiskit-addons/obp-diagram.png | Bin 0 -> 415702 bytes qiskit_bot.yaml | 4 + scripts/config/notebook-testing.toml | 1 + scripts/js/commands/checkPatternsIndex.ts | 4 + scripts/nb-tester/requirements.txt | 2 + 9 files changed, 610 insertions(+), 1 deletion(-) create mode 100644 docs/guides/qiskit-addons-obp-get-started.ipynb create mode 100644 docs/guides/qiskit-addons-obp.mdx create mode 100644 public/images/guides/qiskit-addons/obp-diagram.png diff --git a/docs/guides/_toc.json b/docs/guides/_toc.json index 93cd2955232..4cc20558640 100644 --- a/docs/guides/_toc.json +++ b/docs/guides/_toc.json @@ -534,6 +534,19 @@ "url": "/guides/qiskit-addons-sqd-get-started" } ] + }, + { + "title": "Operator backpropagation (OBP)", + "children": [ + { + "title": "OBP addon overview", + "url": "/guides/qiskit-addons-obp" + }, + { + "title": "Getting started with OBP", + "url": "/guides/qiskit-addons-obp-get-started" + } + ] } ] }, diff --git a/docs/guides/optimize-for-hardware.mdx b/docs/guides/optimize-for-hardware.mdx index 515ae1ef7d1..7a20258d02d 100644 --- a/docs/guides/optimize-for-hardware.mdx +++ b/docs/guides/optimize-for-hardware.mdx @@ -59,4 +59,8 @@ can be run on IBM® hardware using IBM Qiskit Runtime. - [IBM Circuit function](/guides/ibm-circuit-function) - [Algorithmiq Tensor-network error mitigation](/guides/algorithmiq-tem) - [Q-CTRL Performance Management](/guides/q-ctrl-performance-management) -- [QEDMA QESEM](/guides/qedma-qesem) \ No newline at end of file +- [QEDMA QESEM](/guides/qedma-qesem) + +### Qiskit Addons +* [Operator Backpropagation (OBP)](./qiskit-addons-obp) + * [Getting started with OBP](./qiskit-addons-obp-get-started) \ No newline at end of file diff --git a/docs/guides/qiskit-addons-obp-get-started.ipynb b/docs/guides/qiskit-addons-obp-get-started.ipynb new file mode 100644 index 00000000000..42b9db77557 --- /dev/null +++ b/docs/guides/qiskit-addons-obp-get-started.ipynb @@ -0,0 +1,486 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f9dcb976-96bf-4016-976a-cb19ace0f526", + "metadata": {}, + "source": [ + "# Get started with OBP\n", + "\n", + "When you prepare a quantum workload with operator backpropagation (OBP), first you must make a selection of \"circuit slices\", and second, you should specify a truncation threshold or \"error budget\" to remove terms with small coefficients in the backpropagated operator as well as set an upper bound to the overall size of the backpropagated operator. During backpropagation, the number of terms in the operator of an $N$-qubit circuit will approach $4^N$ quickly in the worst-case scenario. This guide demonstrates the steps involved in applying OBP to a quantum workload.\n", + "\n", + "The main component of the `qiskit-addons-obp` package is the `backpropagate()` function. It ingests arguments for the final observable to reconstruct, a set of circuit slices to compute classically, and, optionally, a `TruncationErrorBudget` or `OperatorBudget` to provide constraints on the truncation that is done. Once these are specified, the classically computed backpropagated operator $O'$ is calculated iteratively by applying the gates from each slice, $s$, in the following way:\n", + "\n", + "$$ O'^{(s)} = \\mathcal{U}_{S-s+1}^\\dagger O'^{(s-1)} \\mathcal{U}_{S-s+1} $$\n", + "\n", + "where $S$ is the total number of slices and $\\mathcal{U}_{s}$ represents a single slice of the circuit. This example uses the `qiskit-addons-utils` package to prepare the circuit slices as well as generate the example circuit.\n", + "\n", + "\n", + "To begin, consider the time evolution of a Heisenberg XYZ chain. This Hamiltonian has the form\n", + "\n", + "$$ \\hat{H} = \\sum_{(j,k)} \\left( J_xX_jX_k + J_yY_jY_k + J_z Z_jZ_k \\right) + \\sum_{j} \\left(h_xX_j + h_yY_j + h_zZ_j\\right)$$\n", + "\n", + "and the expectation value to measure will be $\\langle Z_0 \\rangle$.\n", + "\n", + "The following code snippet generates the Hamiltonian in the form of a `SparsePauliOp` by using the `qiskit_addons_utils.problem_generators` module and a `CouplingMap`. Set the coupling constants to $J_x=\\pi/8$, $J_y=\\pi/4$, $J_z=\\pi/2$ and external magnetic fields to $h_x=\\pi/3$, $h_y=\\pi/6$, $h_z=\\pi/9$, and then generate a circuit that models its time evolution." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "00f39aa3-60ee-47f1-8e3a-a110ca87c994", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "from qiskit.transpiler import CouplingMap\n", + "from qiskit.synthesis import LieTrotter\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2\n", + "from qiskit_ibm_runtime.fake_provider import FakeMelbourneV2\n", + "from qiskit.primitives import StatevectorEstimator\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "from qiskit_addon_utils.problem_generators import (\n", + " generate_time_evolution_circuit,\n", + " generate_xyz_hamiltonian,\n", + ")\n", + "from qiskit_addon_utils.slicing import slice_by_gate_types\n", + "from qiskit_addon_obp.utils.simplify import OperatorBudget\n", + "from qiskit_addon_obp.utils.truncating import setup_budget\n", + "from qiskit_addon_obp import backpropagate\n", + "from qiskit_addon_utils.slicing import combine_slices\n", + "\n", + "\n", + "coupling_map = CouplingMap.from_heavy_hex(3, bidirectional=False)\n", + "\n", + "# Choose a 10-qubit linear chain on this coupling map\n", + "reduced_coupling_map = coupling_map.reduce(\n", + " [0, 13, 1, 14, 10, 16, 5, 12, 8, 18]\n", + ")\n", + "\n", + "# Get a qubit operator describing the Heisenberg XYZ model\n", + "hamiltonian = generate_xyz_hamiltonian(\n", + " reduced_coupling_map,\n", + " coupling_constants=(np.pi / 8, np.pi / 4, np.pi / 2),\n", + " ext_magnetic_field=(np.pi / 3, np.pi / 6, np.pi / 9),\n", + ")\n", + "\n", + "# we evolve for some time\n", + "circuit = generate_time_evolution_circuit(\n", + " hamiltonian, synthesis=LieTrotter(reps=2), time=0.2\n", + ")\n", + "\n", + "circuit.draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "21b9eba7-3e24-4a14-8cd0-0fe05678104e", + "metadata": {}, + "source": [ + "### Prepare inputs to backpropagate\n", + "\n", + "Next, generate the circuit slices for backpropagation. In general, the choice of how to slice can have an impact on how well backpropagation performs for a given problem. Here, group gates of the same type into slices using the `qiskit_addons_utils.slice_by_gate_types` function." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "67446f03-4ca7-480e-9b85-7bba97f05b57", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Separated the circuit into 18 slices.\n" + ] + } + ], + "source": [ + "slices = slice_by_gate_types(circuit)\n", + "print(f\"Separated the circuit into {len(slices)} slices.\")" + ] + }, + { + "cell_type": "markdown", + "id": "521c51fb-0fb9-41fb-850f-dd4f0d241c97", + "metadata": {}, + "source": [ + "Once the slices have been generated, specify an `OperatorBudget` to provide the `backpropagate()` function with a condition to stop backpropagating the operator and prevent the classical overhead from growing further. You can also specify a truncation error budget for each slice wherein Pauli terms with small coefficients will be truncated from each slice until the error budget is filled. Any leftover budget will then be added to the following slice's budget.\n", + "\n", + "Here, specify that backpropagation should stop when the number of qubit-wise commuting Pauli groups in the operator grows past $8$, and allocate an error budget of $0.005$ for each slice." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "71ee4776-4d89-43d1-b73e-95932ae8c892", + "metadata": {}, + "outputs": [], + "source": [ + "op_budget = OperatorBudget(max_qwc_groups=8)\n", + "truncation_error_budget = setup_budget(max_error_per_slice=0.005)" + ] + }, + { + "cell_type": "markdown", + "id": "c7cf0465-e079-4c95-b245-c72c64201ded", + "metadata": {}, + "source": [ + "### Backpropagate slices\n", + "\n", + "In this step you will define the final observable to measure and run the backpropagation across each slice. The `backpropagate()` function returns three outputs: the backpropagated observable, the remaining circuit slices that were not backpropagated (and which should be run on quantum hardware), and metadata about the backpropagation.\n", + "\n", + "Note that both the `OperatorBudget` and the `TruncationErrorBudget` are optional parameters for the `backpropagate()` method. In general, the best choice for both should be heuristically chosen and requires some amount of experimentation. In this example we will backpropagate both with and without a `TruncationErrorBudget`.\n", + "\n", + "\n", + " By default, `backpropagate()` uses the $L_1$ norm of the truncated coefficients to bound the total error incurred from truncation, but other $L_p$ can be used if you would like to modify how the truncation error is calculated.\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3bd64d98-8650-4ad9-af19-539c19651dbf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Backpropagated 7 slices.\n", + "New observable has 18 terms, which can be combined into 8 groups.\n", + "After truncation, the error in our observable is bounded by 0.000e+00\n", + "Note that backpropagating one more slice would result in 27 terms across 12 groups.\n" + ] + } + ], + "source": [ + "# Specify a single-qubit observable\n", + "observable = SparsePauliOp(\"IIIIIIIIIZ\")\n", + "\n", + "# Backpropagate without the truncation error budget\n", + "backpropagated_observable, remaining_slices, metadata = backpropagate(\n", + " observable,\n", + " slices,\n", + " operator_budget=op_budget,\n", + ")\n", + "\n", + "# Recombine the slices remaining after backpropagation\n", + "bp_circuit = combine_slices(remaining_slices, include_barriers=True)\n", + "\n", + "print(f\"Backpropagated {metadata.num_backpropagated_slices} slices.\")\n", + "print(\n", + " f\"New observable has {len(backpropagated_observable.paulis)} terms, which can be combined into \"\n", + " f\"{len(backpropagated_observable.group_commuting(qubit_wise=True))} groups.\\n\"\n", + " f\"After truncation, the error in our observable is bounded by {metadata.accumulated_error(0):.3e}\"\n", + ")\n", + "print(\n", + " f\"Note that backpropagating one more slice would result in {metadata.backpropagation_history[-1].num_paulis[0]} terms \"\n", + " f\"across {metadata.backpropagation_history[-1].num_qwc_groups} groups.\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6dddb0ce-0cf2-4e13-abe0-0180e37ea091", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The remaining circuit after backpropagation without truncation looks as follows:\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(\n", + " \"The remaining circuit after backpropagation without truncation looks as follows:\"\n", + ")\n", + "bp_circuit.draw(\"mpl\", scale=0.6)" + ] + }, + { + "cell_type": "markdown", + "id": "4443fbef-9d2f-40ac-b465-6822d2a71bcc", + "metadata": {}, + "source": [ + "The below code snippets backpropagates the circuit *with* a truncation error budget." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "bc98019c-3985-4118-8a1e-06018fb0a522", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Backpropagated 10 slices.\n", + "New observable has 19 terms, which can be combined into 8 groups.\n", + "After truncation, the error in our observable is bounded by 4.933e-02\n", + "Note that backpropagating one more slice would result in 27 terms across 13 groups.\n" + ] + } + ], + "source": [ + "# Backpropagate *with* the truncation error budget\n", + "backpropagated_observable_trunc, remaining_slices_trunc, metadata_trunc = (\n", + " backpropagate(\n", + " observable,\n", + " slices,\n", + " operator_budget=op_budget,\n", + " truncation_error_budget=truncation_error_budget,\n", + " )\n", + ")\n", + "\n", + "# Recombine the slices remaining after backpropagation\n", + "bp_circuit_trunc = combine_slices(\n", + " remaining_slices_trunc, include_barriers=True\n", + ")\n", + "\n", + "print(f\"Backpropagated {metadata_trunc.num_backpropagated_slices} slices.\")\n", + "print(\n", + " f\"New observable has {len(backpropagated_observable_trunc.paulis)} terms, which can be combined into \"\n", + " f\"{len(backpropagated_observable_trunc.group_commuting(qubit_wise=True))} groups.\\n\"\n", + " f\"After truncation, the error in our observable is bounded by {metadata_trunc.accumulated_error(0):.3e}\"\n", + ")\n", + "print(\n", + " f\"Note that backpropagating one more slice would result in {metadata_trunc.backpropagation_history[-1].num_paulis[0]} terms \"\n", + " f\"across {metadata_trunc.backpropagation_history[-1].num_qwc_groups} groups.\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6a3d796b-3b4e-48c4-b416-98a4d72ce39d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The remaining circuit after backpropagation with truncation looks as follows:\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(\n", + " \"The remaining circuit after backpropagation with truncation looks as follows:\"\n", + ")\n", + "bp_circuit_trunc.draw(\"mpl\", scale=0.6)" + ] + }, + { + "cell_type": "markdown", + "id": "1fd7563b-a7c1-42f7-be00-c3f338197aa0", + "metadata": {}, + "source": [ + "### Transpile and execute quantum workload\n", + "\n", + "Now that you have backpropagated the operator, you can execute the remaining portion of the circuit on a QPU. The quantum workload, using the Estimator, should include the `bp_circuit_trunc` circuit and must measure the backpropagated operator `backpropagated_observable`\n", + "\n", + "To demonstrate the effectiveness of OBP on its own, the following code snippet transpiles both the original and backpropagated circuit (with and without truncation) and simulates the circuits classically using the `StatevectorEstimator`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "59f7344c-e6aa-4a44-9551-34be0e9bbcec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact expectation value: 0.8854160687717517\n", + "Backpropagated expectation value without truncation: 0.8854160687717538\n", + "Backpropagated expectation value with truncation: 0.8850236647156042\n", + " - Expected Error for truncated observable: 0.000e+00\n", + " - Observed Error for truncated observable: 3.924e-04\n" + ] + } + ], + "source": [ + "# Specify a backend and a pass manager for transpilation\n", + "backend = FakeMelbourneV2()\n", + "# pm = generate_preset_pass_manager(backend=backend, optimization_level=1)\n", + "\n", + "\n", + "pm = generate_preset_pass_manager(backend=backend, optimization_level=3)\n", + "\n", + "# Transpile original experiment\n", + "circuit_isa = pm.run(circuit)\n", + "observable_isa = observable.apply_layout(circuit_isa.layout)\n", + "\n", + "# Transpile backpropagated experiment without truncation\n", + "bp_circuit_isa = pm.run(bp_circuit)\n", + "bp_obs_isa = backpropagated_observable.apply_layout(bp_circuit_isa.layout)\n", + "\n", + "# Transpile the backpropagated experiment with truncated observable terms\n", + "bp_circuit_trunc_isa = pm.run(bp_circuit_trunc)\n", + "bp_obs_trunc_isa = backpropagated_observable_trunc.apply_layout(\n", + " bp_circuit_trunc_isa.layout\n", + ")\n", + "\n", + "\n", + "estimator = StatevectorEstimator()\n", + "\n", + "# Run the experiments using the exact statevector estimator\n", + "result_exact = (\n", + " estimator.run([(circuit, observable)]).result()[0].data.evs.item()\n", + ")\n", + "\n", + "result_bp = (\n", + " estimator.run([(bp_circuit_isa, bp_obs_isa)]).result()[0].data.evs.item()\n", + ")\n", + "result_bp_trunc = (\n", + " estimator.run([(bp_circuit_trunc_isa, bp_obs_trunc_isa)])\n", + " .result()[0]\n", + " .data.evs.item()\n", + ")\n", + "\n", + "print(f\"Exact expectation value: {result_exact}\")\n", + "print(f\"Backpropagated expectation value without truncation: {result_bp}\")\n", + "print(f\"Backpropagated expectation value with truncation: {result_bp_trunc}\")\n", + "print(\n", + " f\" - Expected Error for truncated observable: {metadata.accumulated_error(0):.3e}\"\n", + ")\n", + "print(\n", + " f\" - Observed Error for truncated observable: {abs(result_exact - result_bp_trunc):.3e}\"\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "31eb5da9-26cf-4b7d-b337-64ceeba6ca65", + "metadata": {}, + "source": [ + "Lastly the following code snippet will transpile and execute the backpropagated circuit on a QPU (both with and without truncation)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "189b129b-17fd-44f7-9a39-2c52bf79c21b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact expectation value: 0.8854160687717517\n", + "Backpropagated expectation value without truncation: 0.7970843120444361\n", + "Backpropagated expectation value with truncation: 0.835404112144685\n", + " - Observed Error for observable without truncation: 8.833e-02\n", + " - Observed Error for truncated observable: 5.001e-02\n" + ] + } + ], + "source": [ + "# Specify a backend and a pass manager for transpilation\n", + "service = QiskitRuntimeService()\n", + "backend = service.least_busy()\n", + "pm = generate_preset_pass_manager(backend=backend, optimization_level=3)\n", + "\n", + "# Transpile backpropagated experiment without truncation\n", + "bp_circuit_isa = pm.run(bp_circuit)\n", + "bp_obs_isa = backpropagated_observable.apply_layout(bp_circuit_isa.layout)\n", + "\n", + "# Transpile the backpropagated experiment with truncated observable terms\n", + "bp_circuit_trunc_isa = pm.run(bp_circuit_trunc)\n", + "bp_obs_trunc_isa = backpropagated_observable_trunc.apply_layout(\n", + " bp_circuit_trunc_isa.layout\n", + ")\n", + "\n", + "# Run the experiments using Estimator primitive\n", + "estimator = EstimatorV2(mode=backend)\n", + "\n", + "result_bp_qpu = (\n", + " estimator.run([(bp_circuit_isa, bp_obs_isa)]).result()[0].data.evs.item()\n", + ")\n", + "\n", + "result_bp_trunc_qpu = (\n", + " estimator.run([(bp_circuit_trunc_isa, bp_obs_trunc_isa)])\n", + " .result()[0]\n", + " .data.evs.item()\n", + ")\n", + "\n", + "print(f\"Exact expectation value: {result_exact}\")\n", + "print(f\"Backpropagated expectation value without truncation: {result_bp_qpu}\")\n", + "print(\n", + " f\"Backpropagated expectation value with truncation: {result_bp_trunc_qpu}\"\n", + ")\n", + "print(\n", + " f\" - Observed Error for observable without truncation: {abs(result_exact - result_bp_qpu):.3e}\"\n", + ")\n", + "print(\n", + " f\" - Observed Error for truncated observable: {abs(result_exact - result_bp_trunc_qpu):.3e}\"\n", + ")" + ] + } + ], + "metadata": { + "description": "Get started using the operator backpropagation Qiskit addon (OBP)", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3" + }, + "title": "Get started with OBP" + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/guides/qiskit-addons-obp.mdx b/docs/guides/qiskit-addons-obp.mdx new file mode 100644 index 00000000000..51035737649 --- /dev/null +++ b/docs/guides/qiskit-addons-obp.mdx @@ -0,0 +1,95 @@ +--- +title: Operator backpropagation (OBP) +description: Learn about the operator backpropagation addon to reduce the depth of quantum circuits +--- + +# Operator backpropagation (OBP) + +Operator backpropagation (OBP) is a technique to reduce circuit depth by trimming operations from its end at the cost of more operator measurements. There are a number of ways in which operator backpropagation can be performed, and this package uses a method based on Clifford perturbation theory. + +As one propagates an operator further through a circuit, the size of the observable to measure grows exponentially. This results in both a classical and quantum resource overhead. However, for some circuits, the resulting distribution of additional Pauli observables is more concentrated than the worst-case exponential scaling. This implies that some terms in an observable with small coefficients can be truncated to reduce the quantum overhead. The error incurred by doing so can be controlled to find a suitable tradeoff between precision and efficiency. + +## Installation + +You can install the OBP package in one of two ways: via PyPI or building from source. Consider installing these packages in a [virtual environment](https://docs.python.org/3.10/tutorial/venv.html) to ensure separation between package dependencies. + +### Install from PyPI + +The most straightforward way to install the `qiskit-addon-obp` package is via PyPI. + +```bash +pip install qiskit-addon-obp +``` + +### Build from source + +Users who wish to contribute to this package or who want to install it manually may do so by first cloning the repository: + +```bash +git clone git@github.com:Qiskit/qiskit-addon-obp.git +```_ + +and install the package via `pip`. The repository also contains example notebooks. If you plan on developing in the repository, install the `dev` dependencies. + +Adjust the options to suit your needs: + +```bash +pip install tox notebook -e '.[notebook-dependencies, dev]' +``` + +## Theoretical background + +When using the Estimator primitive, the output of a quantum workload is the estimation of one or more expectation values $\langle O \rangle$ with respect to some state prepared using a QPU. This section summarizes the procedure. + +First, start by writing the expectation value measurement of an observable $O$ in terms of some initial state $|\psi\rangle$ and a quantum circuit $U_Q$: + +$$ \langle O \rangle_{U|\psi\rangle} = \langle\psi | U^\dagger O U |\psi \rangle. $$ + +To distribute this problem across both classical and quantum resources, split the circuit $U$ into two subcircuits, $U_C$ and $U_Q$, classically simulate the circuit $U_C$, then execute the circuit $U_Q$ on quantum hardware and use the results of the classical simulation to reconstruct the measurement of the observable $O$. + +![OBP diagram depicting splitting a circuit into two subcircuits, classically computing one of the subcircuits, then measuring the other circuit using quantum hardware](/images/guides/qiskit-addons/obp-diagram.png) + + +The subcircuit $U_C$ should be selected to be classically simulable and will compute the expectation value + +$$ \langle O' \rangle \equiv U_C^\dagger O U_C, $$ + +which is the version of the initial operator $O$ evolved through the circuit $U_C$. Once $O'$ has been determined, the quantum workload is prepared wherein the state $|\psi\rangle$ is initiated, has the circuit $U_Q$ applied to it, and then measures the expectation value $O'$. You can show that this is equivalent to measuring $\langle O \rangle$ by writing: + +$$ \langle \psi | U_Q^\dagger O' U_Q \psi \rangle = \langle \psi | U_Q^\dagger U_C^\dagger O U_CU_Q \psi \rangle = \langle\psi | U^\dagger O U |\psi \rangle = \langle O \rangle_{U|\psi\rangle}$$ + + +Lastly, in order to measure the expectation value $\langle O' \rangle$, we must require it to be decomposable into a sum of Pauli strings + +$$ O' = \sum_P c_P P, $$ + +where $c_P$ are real coefficients of the decomposition and $P$ is some Pauli string composed of $I$, $X$, $Y$, and $Z$ operators. This ensures that you can reconstruct the expectation value of $O$ by + +$$ \langle \psi | U_Q^\dagger O' |\psi \rangle = \sum_P c_P \langle \psi | U_Q^\dagger P U_Q | \psi \rangle. $$ + + +### Truncating terms + +This scheme offers a tradeoff between the required circuit depth of $U_Q$, the number of circuit executions on quantum hardware, and the amount of classical computing resources needed to compute $O'$. In general, as you choose to backpropagate further through a circuit, the number of Pauli strings to measure as well as the error-mitigation overhead both grow exponentially (alongside the classical resources needed to simulate $U_C$). + +Fortunately, the decomposition of $O'$ can often contain coefficients that are quite small and can be truncated from the final measurements used to reconstruct $O$ without incurring much error. The `qiskit-addon-obp` package possesses functionality to specify an error budget, which can automatically search for terms that can be truncated, to within some error tolerance. + + +### Clifford perturbation theory + +Lastly, the `qiskit-addon-obp` package approaches operator backpropagation based on Clifford perturbation theory. This method has the benefit that the overhead incurred by backpropagating various gates scales with the non-Cliffordness of $U_C$ (i.e. how much of U C is comprised of non-Clifford instructions). + +This approach to OBP begins by splitting the simulated circuit, $U_C$, into *slices*: + +$$ U_C = \prod_{s=1}^S \mathcal{U}_s = \mathcal{U}_S...\mathcal{U}_2\mathcal{U}_1, $$ + +where $S$ represents the total number of slices and $\mathcal{U}_s$ denotes a single slice of the circuit $U_C$. Each of these slices are then analytically applied in sequence to measure the back propagated operator $O'$ and may or may not contribute to the overall size of the sum, depending on if the slice is a Clifford vs non-Clifford operation. If an [error budget](../api/qiskit-addon-obp/utils-truncating#setup_budget) is allocated, truncation will then occur between the application of each slice. + + + +## Next steps + + + - [Get started with OBP.](/guides/qiskit-addons-obp-get-started) + - Become familiar with the [error mitigation techniques](/guides/error-mitigation-and-suppression-techniques) available in Qiskit Runtime. + diff --git a/public/images/guides/qiskit-addons/obp-diagram.png b/public/images/guides/qiskit-addons/obp-diagram.png new file mode 100644 index 0000000000000000000000000000000000000000..ccc25bf48371680aafb294c0d30e61c42d16c32f GIT binary patch literal 415702 zcmd>lgnAz$>_=O&DKX~vUjX!k+5!aF5ghD|2$ zs3_bqnVw4uqMM749}Q*+(2sIuRjXD1o}@^$Jhn@kV#b|Nt3DS}8+ZhMznaeCvrDXq zeIMK2P9K2FWXdfhB!ty1Y^yT%(e_8#iyvOsc_#qd8r;Wzuu(Fp(NN6jet;Qs%5NcaEB72n@MsNKm~U*8QGy=EoFJ}7eV zqekfU5JmVRxhH}KV!GSSo41;e?Tu<(!}L|olWd!Hd12LWcA-CT5=UjF{ejesND$)3L1m& z`(9iiOuo&SL7kn6ny!c3;mcnszeGjdB|9Is5Safk)BLvjx(;e|BT|*Y!Rvz1=k#bI 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