lab-QPE.ipynb

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   "source": [
    "# Quantum Phase Estimation\n",
    "\n",
    "![image.png](Support_files/Support_1.png)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "# The problem\n",
    "![image.png](Support_files/Support_2.png)"
   ]
  },
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   "source": [
    "### Intuition\n",
    "The quantum phase estimation algorithm uses phase kickback to write the phase of $U$ (in the Fourier basis) to the $t$ qubits in the counting register. We then use the inverse QFT to translate this from the Fourier basis into the computational basis, which we can measure.\n",
    "\n",
    "We remember (from the QFT chapter) that in the Fourier basis the topmost qubit completes one full rotation when counting between $0$ and $2^t$. To count to a number, $x$ between $0$ and $2^t$, we rotate this qubit by $\\tfrac{x}{2^t}$ around the z-axis. For the next qubit we rotate by $\\tfrac{2x}{2^t}$, then $\\tfrac{4x}{2^t}$ for the third qubit.\n",
    "\n",
    "![image.png](Support_files/Support_3.png)\n",
    "\n",
    "When we use a qubit to control the $U$-gate, the qubit will turn (due to kickback) proportionally to the phase $e^{2i\\pi\\theta}$. We can use successive $CU$-gates to repeat this rotation an appropriate number of times until we have encoded the phase theta as a number between $0$ and $2^t$ in the Fourier basis. \n",
    "\n",
    "Then we simply use $QFT^\\dagger$ to convert this into the computational basis.\n",
    "\n",
    "\n",
    "**As an application of our quantum Fourier transform algorithm, we'll implement the phase estimation algorithm. The phase estimation algorithm estimates the eigenvalues of a unitary operator and uses the inverse QFT as a subroutine. The total circuit that we are going to implement is shown below.**\n",
    "\n",
    ">![Phase Estimation](https://upload.wikimedia.org/wikipedia/commons/a/a5/PhaseCircuit-crop.svg)"
   ]
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    "### Mathematical Foundation\n",
    "Our objective is to get an $n$-bit approximation to $\\theta$. The first step is to construct the state\n",
    "\n",
    "$$\n",
    "|\\Phi\\rangle = \\frac{1}{2^{n/2}}\\sum_{y=0}^{2^{n-1}} e^{2\\pi i y \\theta}|y\\rangle.\n",
    "$$\n",
    "\n",
    "As mentioned above, this circuit estimates the phase of a unitary operator $U$. It estimates $\\theta$ in $U\\vert\\psi \\rangle =e^{\\boldsymbol{2\\pi i} \\theta }|\\psi \\rangle$, where $|\\psi\\rangle$ is an eigenvector and $e^{\\boldsymbol{2\\pi i}\\theta}$ is the corresponding eigenvalue. The circuit operates in the following steps:\n",
    "\n",
    "i. **Setup**: $\\vert\\psi\\rangle$ is in one set of qubit registers. An additional set of $n$ qubits form the counting register on which we will store the value $2^n\\theta$: \n",
    "\n",
    "\n",
    "\n",
    "$$ |\\psi_0\\rangle = \\lvert 0 \\rangle^{\\otimes n} \\lvert \\psi \\rangle$$\n",
    "\n",
    " \n",
    "\n",
    "ii. **Superposition**: Apply a $n$-bit Hadamard gate operation $H^{\\otimes n}$ on the counting register: \n",
    "\n",
    "\n",
    "\n",
    "$$ |\\psi_1\\rangle = {\\frac {1}{2^{\\frac {n}{2}}}}\\left(|0\\rangle +|1\\rangle \\right)^{\\otimes n} \\lvert \\psi \\rangle$$\n",
    "\n",
    "\n",
    "\n",
    "iii. **Controlled Unitary Operations**: We need to introduce the controlled unitary $CU$ that applies the unitary operator $U$ on the target register only if its corresponding control bit is $|1\\rangle$. Since $U$ is a unitary operator with eigenvector $|\\psi\\rangle$ such that $U|\\psi \\rangle =e^{\\boldsymbol{2\\pi i} \\theta }|\\psi \\rangle$, this means: \n",
    "\n",
    "\n",
    "\n",
    "$$U^{2^{j}}|\\psi \\rangle =U^{2^{j}-1}U|\\psi \\rangle =U^{2^{j}-1}e^{2\\pi i\\theta }|\\psi \\rangle =\\cdots =e^{2\\pi i2^{j}\\theta }|\\psi \\rangle$$\n",
    "\n",
    "\n",
    "\n",
    "Applying all the $n$ controlled operations $CU^{2^j}$ with $0\\leq j\\leq n-1$, and using the relation $|0\\rangle \\otimes |\\psi \\rangle +|1\\rangle \\otimes e^{2\\pi i\\theta }|\\psi \\rangle =\\left(|0\\rangle +e^{2\\pi i\\theta }|1\\rangle \\right)\\otimes |\\psi \\rangle$:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "|\\psi_{2}\\rangle & =\\frac {1}{2^{\\frac {n}{2}}} \\left(|0\\rangle+{e^{\\boldsymbol{2\\pi i} \\theta 2^{n-1}}}|1\\rangle \\right) \\otimes \\cdots \\otimes \\left(|0\\rangle+{e^{\\boldsymbol{2\\pi i} \\theta 2^{1}}}\\vert1\\rangle \\right) \\otimes \\left(|0\\rangle+{e^{\\boldsymbol{2\\pi i} \\theta 2^{0}}}\\vert1\\rangle \\right) \\otimes |\\psi\\rangle\\\\\\\\\n",
    "& = \\frac{1}{2^{\\frac {n}{2}}}\\sum _{k=0}^{2^{n}-1}e^{\\boldsymbol{2\\pi i} \\theta k}|k\\rangle \\otimes \\vert\\psi\\rangle\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $k$ denotes the integer representation of n-bit binary numbers. \n",
    "\n",
    "iv. **Inverse Fourier Transform**: Notice that the above expression is exactly the result of applying a quantum Fourier transform as we derived in the notebook on Quantum Fourier Transform and its Implementation. Recall that QFT maps an n-qubit input state $\\vert x\\rangle$ into an output as\n",
    "\n",
    "$$\n",
    "QFT\\vert x \\rangle = \\frac{1}{2^\\frac{n}{2}}\n",
    "\\left(\\vert0\\rangle + e^{\\frac{2\\pi i}{2}x} \\vert1\\rangle\\right) \n",
    "\\otimes\n",
    "\\left(\\vert0\\rangle + e^{\\frac{2\\pi i}{2^2}x} \\vert1\\rangle\\right) \n",
    "\\otimes  \n",
    "\\ldots\n",
    "\\otimes\n",
    "\\left(\\vert0\\rangle + e^{\\frac{2\\pi i}{2^{n-1}}x} \\vert1\\rangle\\right) \n",
    "\\otimes\n",
    "\\left(\\vert0\\rangle + e^{\\frac{2\\pi i}{2^n}x} \\vert1\\rangle\\right) \n",
    "$$\n",
    "\n",
    "Replacing $x$ by $2^n\\theta$ in the above expression gives exactly the expression derived in step 2 above. Therefore, to recover the state $\\vert2^n\\theta\\rangle$, apply an inverse Fourier transform on the auxiliary register. Doing so, we find\n",
    "\n",
    "$$\n",
    "\\vert\\psi_3\\rangle = \\frac {1}{2^{\\frac {n}{2}}}\\sum _{k=0}^{2^{n}-1}e^{\\boldsymbol{2\\pi i} \\theta k}|k\\rangle \\otimes | \\psi \\rangle \\xrightarrow{\\mathcal{QFT}_n^{-1}} \\frac {1}{2^n}\\sum _{x=0}^{2^{n}-1}\\sum _{k=0}^{2^{n}-1} e^{-\\frac{2\\pi i k}{2^n}(x - 2^n \\theta)} |x\\rangle \\otimes |\\psi\\rangle\n",
    "$$ \n",
    "\n",
    "v. **Measurement**: \n",
    "The above expression peaks near $x = 2^n\\theta$. For the case when $2^n\\theta$ is an integer, measuring in the computational basis gives the phase in the auxiliary register with high probability: \n",
    "\n",
    "\n",
    "\n",
    "$$ |\\psi_4\\rangle = | 2^n \\theta \\rangle \\otimes | \\psi \\rangle$$\n",
    "\n",
    "\n",
    "\n",
    "For the case when $2^n\\theta$ is not an integer, it can be shown that the above expression still peaks near $x = 2^n\\theta$ with probability better than $4/\\pi^2 \\approx 40\\%$ [1]."
   ]
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   "source": [
    "# Let's take this example: T-Gate\n",
    "Let’s take a gate we know well, the $T$-gate, and use Quantum Phase Estimation to estimate its phase. You will remember that the $T$-gate adds a phase of $e^\\frac{i\\pi}{4}$ to the state $|1\\rangle$:\n",
    "\n",
    "$$ T|1\\rangle = \n",
    "\\begin{bmatrix}\n",
    "1 & 0\\\\\n",
    "0 & e^\\frac{i\\pi}{4}\\\\ \n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "0\\\\\n",
    "1\\\\ \n",
    "\\end{bmatrix}\n",
    "= e^\\frac{i\\pi}{4}|1\\rangle $$\n",
    "\n",
    "Since QPE will give us $\\theta$ where:\n",
    "\n",
    "\n",
    "\n",
    "$$ T|1\\rangle = e^{2i\\pi\\theta}|1\\rangle $$\n",
    "\n",
    "\n",
    "\n",
    "We expect to find:\n",
    "\n",
    "\n",
    "\n",
    "$$\\theta = \\frac{1}{8}$$\n",
    "\n",
    "\n",
    "\n",
    "In this example we will use three qubits and obtain an _exact_ result (not an estimation!)"
   ]
  },
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   "id": "de4fa4d0-b06d-4bfb-a479-e933c41ded5c",
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   "source": [
    "# Creating a circuit\n",
    "Let's first prepare our environment for this:\n"
   ]
  },
  {
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   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, Aer, transpile, assemble\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "\n",
    "# import basic plot tools and circuits\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.circuit.library import QFT"
   ]
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   "cell_type": "markdown",
   "id": "77e87a65-c9f0-4d6d-a111-139c953e3d2f",
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   "source": [
    "Now, set up the quantum circuit. We will use four qubits -- qubits 0 to 2 as counting qubits, and qubit 3 as the eigenstate of the unitary operator ($T$). \n",
    "\n",
    "We initialize $\\vert\\psi\\rangle = \\vert1\\rangle$ by applying an $X$ gate:"
   ]
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       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">          \n",
       "q_0: ─────\n",
       "          \n",
       "q_1: ─────\n",
       "          \n",
       "q_2: ─────\n",
       "     ┌───┐\n",
       "q_3: ┤ X ├\n",
       "     └───┘\n",
       "c: 3/═════\n",
       "          </pre>"
      ],
      "text/plain": [
       "          \n",
       "q_0: ─────\n",
       "          \n",
       "q_1: ─────\n",
       "          \n",
       "q_2: ─────\n",
       "     ┌───┐\n",
       "q_3: ┤ X ├\n",
       "     └───┘\n",
       "c: 3/═════\n",
       "          "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "qpe = QuantumCircuit(4, 3)\n",
    "qpe.x(3)\n",
    "qpe.draw()"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Next, we apply Hadamard gates to the counting qubits:"
   ]
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       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐\n",
       "q_0: ┤ H ├\n",
       "     ├───┤\n",
       "q_1: ┤ H ├\n",
       "     ├───┤\n",
       "q_2: ┤ H ├\n",
       "     ├───┤\n",
       "q_3: ┤ X ├\n",
       "     └───┘\n",
       "c: 3/═════\n",
       "          </pre>"
      ],
      "text/plain": [
       "     ┌───┐\n",
       "q_0: ┤ H ├\n",
       "     ├───┤\n",
       "q_1: ┤ H ├\n",
       "     ├───┤\n",
       "q_2: ┤ H ├\n",
       "     ├───┤\n",
       "q_3: ┤ X ├\n",
       "     └───┘\n",
       "c: 3/═════\n",
       "          "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for qubit in range(3):\n",
    "    qpe.h(qubit)\n",
    "qpe.draw()"
   ]
  },
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   "source": [
    "Next we perform the controlled unitary operations.\n",
    "\n",
    "We'll use Qiskit's [`PhaseGate`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PhaseGate.html) to create the $T$ operation. The phase gate does the transformation $P|1\\rangle = e^{i\\lambda}|1\\rangle$, where $\\lambda$ is the angle we provide. Since we want to implement $T$, which performs $T|1\\rangle = e^{2\\pi i \\theta}|1\\rangle$, we need to set $\\lambda = \\tfrac{2 \\pi}{8} = \\pi/4$.\n",
    "\n",
    "Also remember that Qiskit orders its qubits the opposite way round to the circuit diagram in the overview."
   ]
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       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                               \n",
       "q_0: ┤ H ├─■─────────────────────────────────────────────────────────────\n",
       "     ├───┤ │                                                             \n",
       "q_1: ┤ H ├─┼────────■────────■───────────────────────────────────────────\n",
       "     ├───┤ │        │        │                                           \n",
       "q_2: ┤ H ├─┼────────┼────────┼────────■────────■────────■────────■───────\n",
       "     ├───┤ │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4) \n",
       "q_3: ┤ X ├─■────────■────────■────────■────────■────────■────────■───────\n",
       "     └───┘                                                               \n",
       "c: 3/════════════════════════════════════════════════════════════════════\n",
       "                                                                         </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                               \n",
       "q_0: ┤ H ├─■─────────────────────────────────────────────────────────────\n",
       "     ├───┤ │                                                             \n",
       "q_1: ┤ H ├─┼────────■────────■───────────────────────────────────────────\n",
       "     ├───┤ │        │        │                                           \n",
       "q_2: ┤ H ├─┼────────┼────────┼────────■────────■────────■────────■───────\n",
       "     ├───┤ │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4) \n",
       "q_3: ┤ X ├─■────────■────────■────────■────────■────────■────────■───────\n",
       "     └───┘                                                               \n",
       "c: 3/════════════════════════════════════════════════════════════════════\n",
       "                                                                         "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repetitions = 1\n",
    "for counting_qubit in range(3):\n",
    "    for i in range(repetitions):\n",
    "        qpe.cp(math.pi/4, counting_qubit, 3); # controlled-T\n",
    "    repetitions *= 2\n",
    "qpe.draw()"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "We apply the inverse quantum Fourier transformation to convert the state of the counting register, then measure the counting register:"
   ]
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    {
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       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                                ░ »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────────░─»\n",
       "     ├───┤ │                                                              ░ »\n",
       "q_1: ┤ H ├─┼────────■────────■────────────────────────────────────────────░─»\n",
       "     ├───┤ │        │        │                                            ░ »\n",
       "q_2: ┤ H ├─┼────────┼────────┼────────■────────■────────■────────■────────░─»\n",
       "     ├───┤ │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  ░ »\n",
       "q_3: ┤ X ├─■────────■────────■────────■────────■────────■────────■────────░─»\n",
       "     └───┘                                                                ░ »\n",
       "c: 3/═══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       "«     ┌──────────┐ ░ ┌─┐      \n",
       "«q_0: ┤0         ├─░─┤M├──────\n",
       "«     │          │ ░ └╥┘┌─┐   \n",
       "«q_1: ┤1 IQFT_dg ├─░──╫─┤M├───\n",
       "«     │          │ ░  ║ └╥┘┌─┐\n",
       "«q_2: ┤2         ├─░──╫──╫─┤M├\n",
       "«     └──────────┘ ░  ║  ║ └╥┘\n",
       "«q_3: ─────────────░──╫──╫──╫─\n",
       "«                  ░  ║  ║  ║ \n",
       "«c: 3/════════════════╩══╩══╩═\n",
       "«                     0  1  2 </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                                ░ »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────────░─»\n",
       "     ├───┤ │                                                              ░ »\n",
       "q_1: ┤ H ├─┼────────■────────■────────────────────────────────────────────░─»\n",
       "     ├───┤ │        │        │                                            ░ »\n",
       "q_2: ┤ H ├─┼────────┼────────┼────────■────────■────────■────────■────────░─»\n",
       "     ├───┤ │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  │P(π/4)  ░ »\n",
       "q_3: ┤ X ├─■────────■────────■────────■────────■────────■────────■────────░─»\n",
       "     └───┘                                                                ░ »\n",
       "c: 3/═══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       "«     ┌──────────┐ ░ ┌─┐      \n",
       "«q_0: ┤0         ├─░─┤M├──────\n",
       "«     │          │ ░ └╥┘┌─┐   \n",
       "«q_1: ┤1 IQFT_dg ├─░──╫─┤M├───\n",
       "«     │          │ ░  ║ └╥┘┌─┐\n",
       "«q_2: ┤2         ├─░──╫──╫─┤M├\n",
       "«     └──────────┘ ░  ║  ║ └╥┘\n",
       "«q_3: ─────────────░──╫──╫──╫─\n",
       "«                  ░  ║  ║  ║ \n",
       "«c: 3/════════════════╩══╩══╩═\n",
       "«                     0  1  2 "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpe.barrier()\n",
    "# Apply inverse QFT\n",
    "qpe = qpe.compose(QFT(3, inverse=True), [0,1,2])\n",
    "# Measure\n",
    "qpe.barrier()\n",
    "for n in range(3):\n",
    "    qpe.measure(n,n)\n",
    "\n",
    "qpe.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab85a344-f62f-4ad5-9766-17ed10a74fd5",
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   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "04b697b4-8f8d-411e-bf4c-80730c2008ea",
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   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "shots = 2048\n",
    "t_qpe = transpile(qpe, aer_sim)\n",
    "results = aer_sim.run(t_qpe, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0377bd0-b290-4bd1-9cd3-e5dde0914bb2",
   "metadata": {},
   "source": [
    "We see we get one result (`001`) with certainty, which translates to the decimal: `1`. We now need to divide our result (`1`) by $2^n$ to get $\\theta$:\n",
    "\n",
    "\n",
    "\n",
    "$$ \\theta = \\frac{1}{2^3} = \\frac{1}{8} $$\n",
    "\n",
    "\n",
    "\n",
    "This is exactly the result we expected!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e35e1f1-e9d1-4570-835c-bdea2fa4641d",
   "metadata": {
    "tags": []
   },
   "source": [
    "## What if $\\theta$ is not an integer?\n",
    "\n",
    "Instead of a $T$-gate, let’s use a gate with $\\theta = \\frac{1}{3}$.\n",
    "\n",
    "In the cell below, we set up our circuit as we did with the last example.\n",
    "\n",
    "We'll use Qiskit's [`PhaseGate`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PhaseGate.html) again, which does $P|1\\rangle = e^{i\\lambda}|1\\rangle$. Since we want to implement $U|1\\rangle = e^{2\\pi i \\tfrac{1}{3}}|1\\rangle$, we need to set $\\lambda = \\tfrac{2 \\pi}{3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "63384e36-ad21-49d4-b213-fdea1a014c2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                            »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────»\n",
       "     ├───┤ │                                                          »\n",
       "q_1: ┤ H ├─┼─────────■─────────■──────────────────────────────────────»\n",
       "     ├───┤ │         │         │                                      »\n",
       "q_2: ┤ H ├─┼─────────┼─────────┼─────────■─────────■─────────■────────»\n",
       "     ├───┤ │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "q_3: ┤ X ├─■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "     └───┘                                                            »\n",
       "c: 3/═════════════════════════════════════════════════════════════════»\n",
       "                                                                      »\n",
       "«               ┌──────────┐┌─┐      \n",
       "«q_0: ──────────┤0         ├┤M├──────\n",
       "«               │          │└╥┘┌─┐   \n",
       "«q_1: ──────────┤1 IQFT_dg ├─╫─┤M├───\n",
       "«               │          │ ║ └╥┘┌─┐\n",
       "«q_2: ─■────────┤2         ├─╫──╫─┤M├\n",
       "«      │P(2π/3) └──────────┘ ║  ║ └╥┘\n",
       "«q_3: ─■─────────────────────╫──╫──╫─\n",
       "«                            ║  ║  ║ \n",
       "«c: 3/═══════════════════════╩══╩══╩═\n",
       "«                            0  1  2 </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                            »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────»\n",
       "     ├───┤ │                                                          »\n",
       "q_1: ┤ H ├─┼─────────■─────────■──────────────────────────────────────»\n",
       "     ├───┤ │         │         │                                      »\n",
       "q_2: ┤ H ├─┼─────────┼─────────┼─────────■─────────■─────────■────────»\n",
       "     ├───┤ │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "q_3: ┤ X ├─■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "     └───┘                                                            »\n",
       "c: 3/═════════════════════════════════════════════════════════════════»\n",
       "                                                                      »\n",
       "«               ┌──────────┐┌─┐      \n",
       "«q_0: ──────────┤0         ├┤M├──────\n",
       "«               │          │└╥┘┌─┐   \n",
       "«q_1: ──────────┤1 IQFT_dg ├─╫─┤M├───\n",
       "«               │          │ ║ └╥┘┌─┐\n",
       "«q_2: ─■────────┤2         ├─╫──╫─┤M├\n",
       "«      │P(2π/3) └──────────┘ ║  ║ └╥┘\n",
       "«q_3: ─■─────────────────────╫──╫──╫─\n",
       "«                            ║  ║  ║ \n",
       "«c: 3/═══════════════════════╩══╩══╩═\n",
       "«                            0  1  2 "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create and set up circuit\n",
    "qpe2 = QuantumCircuit(4, 3)\n",
    "\n",
    "# Apply H-Gates to counting qubits:\n",
    "for qubit in range(3):\n",
    "    qpe2.h(qubit)\n",
    "\n",
    "# Prepare our eigenstate |psi>:\n",
    "qpe2.x(3)\n",
    "\n",
    "# Do the controlled-U operations:\n",
    "angle = 2*math.pi/3\n",
    "repetitions = 1\n",
    "for counting_qubit in range(3):\n",
    "    for i in range(repetitions):\n",
    "        qpe2.cp(angle, counting_qubit, 3);\n",
    "    repetitions *= 2\n",
    "\n",
    "# Do the inverse QFT:\n",
    "qpe2 = qpe2.compose(QFT(3, inverse=True), [0,1,2])\n",
    "\n",
    "# Measure of course!\n",
    "for n in range(3):\n",
    "    qpe2.measure(n,n)\n",
    "\n",
    "qpe2.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e546e2f8-810d-4ce7-a88e-a01e2911df17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AgB3BEAAAAJIIhgAAALAjGAIAAEASwRAAAAB2BEMAAABIIhgCAADAjmAIAAAASQRDAAAA2BEMAQAAIIlgCAAAADuCIQAAACQRDAEAAGBHMAQAAIAkgiEAAADsCIYAAACQRDAEAACAHcEQAAAAkgiGAAAAsCMYAgAAQBLBEAAAAHYEQwAAAEgiGAIAAMCOYAgAAABJBEMAAADYEQwBAAAgiWAIAAAAO4IhAAAAJBEMAQAAYEcwBAAAgCSCIQAAAOwIhgAAAJBEMAQAAIAdwRAAAACSCIYAAACwIxgCAABAEsEQAAAAdgRDAAAASPoLwXDDhg06efLkTftERERow4YNWf0VAAAAyEVZDoahoaGaP3/+TfssXLhQoaGhWf0VAAAAyEVZDobGmFv2sdlssiwrq78CAAAAuShHzzEMDw+Xn59fTv4KAAAAZBOPzHR+5plnnH7+5ptvdPz48TT9kpKSHOcXPvTQQ3+pQAAAAOSOTAXD1OcUWpalsLAwhYWFpdvXsiw1bNhQ77777l+pDwAAALkkU8Hw2LFjkpLPL6xcubIGDx6sf/zjH2n6ubu7y9/fX97e3tlTJQAAAHJcpoJhhQoVHP9/3rx5qlu3rlMbAAAA8q5MBcPU+vTpk511AAAAwMWyHAxTbN++XTt27NDly5eVlJSUZrtlWRo1atRf/TUAAADIYVkOhhcvXtQjjzyiTZs23XRNQ4IhAABA3pDlYDh06FBt3LhRLVu2VJ8+fXTXXXfJw+MvH4AEAACAi2Q5yS1fvlyNGjXSjz/+yN1NAAAA8oEs3/nk2rVrat68OaEQAAAgn8hyMKxTp066dz3JDp9++qkGDBigBg0ayMvLS5ZlOS2unZ5jx46pf//+qlChgry8vFS6dGmFhoZqyZIl6fb/7LPP1KhRI3l7e8vf318PP/ywdu7cmeHz79ixQx07dlTx4sXl7e2txo0ba/HixX9lmAAAAHeULH+VPHr0aHXp0kVbt25V48aNs7MmjRw5UidOnFDJkiVVpkwZnThx4qb9V69erUceeUSS1LlzZ1WuXFmXLl3Snj17tGbNGnXv3t2p//jx4zVy5EhVqFBBL7zwgq5cuaIvv/xSTZs21Y8//qhmzZo59V+3bp3at2+vwoUL6/HHH5evr6+WLl2qnj17KiIiQq+88kq2jh8AAMAVLHOzS4pvYuHChfrPf/6j5cuX66mnnlK9evVUrFixdPv27t07U8+9Zs0aVa1aVRUqVNDEiRM1fPhwzZs3T3379k3T9+TJk6pVq5ZKly6tNWvWqHz58k7bExMTnS6KCQ8PV40aNVS5cmVt375dfn5+kqSwsDA1btxYlStX1r59++Tm5uZ4fEhIiE6dOqWtW7eqTp06kqSoqCg1atRIx48f16FDhzK10Hd0dLT8/PwUFRWV4ZwByF79p7m6Aumjwa6uAEBBlJnckeUjhn379pVlWTLGaP78+Zo/f36a8w2NMbIsK9PBsE2bNrfdd8KECYqOjtayZcvShEJJaa6UnjdvnhITE/X66687QqGU/NX4E088ofnz52vjxo1q3ry5JGnt2rU6cuSI+vXr5wiFkuTn56cRI0aob9++WrBggd54441MjREAAOBOk+VgOG/evOysI0uMMVqyZIkCAgLUqlUr/frrr/rpp59ks9lUp04dtWrVynHkL8X69eslSe3atUvzfO3bt9f8+fP1008/OYLhrfpL0k8//ZSNowIAAHCNPH1LvGPHjunixYtq0KCBBgwYoNmzZzttr1u3rr799lvdddddjrbw8HD5+PgoKCgozfNVrVrV0Sd1/9TbUgsKCpKPj49TfwAAgLwqT69Ife7cOUnSrl27dODAAc2bN09du3ZVVFSUJkyYoI8++kjdunXT1q1bHY+JiopSYGBgus+X8r17VFSUU39JTl873/iY1P3TExcXp7i4OMfP0dHRkqSEhAQlJCRIktzc3OTu7q6kpCTZbDZH35T2xMREpzvMuLu7y83NLcP2lOdNkfKVemJi4m21e3p6ymazOd3m0LIseXh4ZNieUe2MiTHdGWPylKulnhv+ToyJMTGm3BpTZmQ5GJ48efK2+6Z37l92SBl4UlKSxo0b57g4xd/fX7Nnz9aePXu0bds2bdy4UQ888ECO1HA73n77bb355ptp2letWqWiRYtKSp6junXras+ePU5zW716dYWEhGj79u06f/68o71OnTqqUKGCNmzYoCtXrjjamzRposDAQK1atcppxwsNDVWRIkW0YsUKpxo6duyoa9euad26dY42Dw8PderUSRcuXNCWLVsc7b6+vmrVqpUiIiIUFhbmaC9VqpSaNm2q8PBwHTx40NHOmBjTnTWmrnK11HPA34kxMSbGlFtjCg4O1u3K8lXJbm5ut7W4tWVZaZJxZtzsquT9+/fr3nvvlSQdOXJElStXdtqesizNu+++q8GDB0tKntDr1687/WFT/Prrr2rQoIF69eqlhQsXSpK6d++ur776Sr/88ovq16+f5jG+vr7y9/e/aVBO74hhuXLldOHCBcdRyoL26YUxMabcHtOLM1x/xPCDgRwxZEyMiTHl/phiY2Nz/qrk3r17pxsMo6KitHv3bh07dkwtWrRQxYoVs/orbunuu+92TELx4sXTbE9pu3btmqOtatWq2rJliyIjI9OcZ5je+YSpzzu8MRhGRkYqJiZGjRo1ummdXl5e8vLyStPu6ekpT0/nNyt3d3e5u7un6ZvRfagzar/xebPS7ubmlu4h6IzaM6qdMTGmzLbn9JhcJTNj5e/EmDKqMbPtjIkxZUaWg+HN7kRijNGUKVP0r3/9S3Pnzs3qr7ilwoULq2nTpvr555/122+/pfm6+LfffpMkp3DaokULbdmyRatWrUqzjM7KlSsdfVL3f/vtt7Vq1So9/vjjt+wPAACQV2X5lng3Y1mW/vnPf6pmzZp69dVXc+JXOPz973+XJI0ZM8bp69oDBw5o/vz58vX1VYcOHRzt/fr1k4eHh8aPH+900UhYWJi++OIL3XPPPU4Bs3Xr1qpcubI+//xzp+/4Uy5wKVSoUKbXaQQAALgT5ehVyQ0aNNCcOXMy/bg5c+Zo48aNkqS9e/c62lLWFHzggQf03HPPSZIef/xxff311/rqq69Uu3ZttW/fXlFRUVq6dKmuX7+uhQsXyt/f3/Hc1apV05gxYzRy5EjVrl1bjz32mOOWeJL00UcfOR2y9fDw0Jw5c9S+fXs1b97c6ZZ4J06c0OTJk3P063IAAIDckqPB8MiRI1m68GTjxo1asGCBU9umTZu0adMmx88pwdCyLH3xxRdq2rSp5s6dq1mzZsnLy0tNmzbViBEj0v2a9/XXX1fFihU1bdo0ffjhhypUqJAefPBBjRs3TvXq1UvTPzQ0VBs3btTo0aO1aNEiJSQkqFatWpo0aZJ69uyZ6fEBAADcibJ8VXJGbDabTp8+rfnz52vMmDFq3bq1Vq1alZ2/Is/jXslA7uNeyQAKqly5V/Ktlqsxxsjf319TpkzJ6q8AAABALspyMGzevHm6wdDNzU3+/v5q2LCh+vXrl+FdRgAAAHBnyXIwTLkQBAAAAPlDjixXAwAAgLwnW65K3rRpk8LCwhQdHa1ixYqpTp06atasWXY8NQAAAHLJXwqGmzdvVr9+/XT48GFJyRecpJx3WLVqVc2bN09NmjT561UCAAAgx2U5GO7fv1/t2rXT1atX1bZtW4WGhqpMmTKKjIzUunXrtGrVKrVv315bt25VjRo1srNmAAAA5IAsB8OxY8cqPj5eK1ascLrlnCS99tpr+uGHH9SlSxeNHTvWcVcRAAAA3LmyfPHJ+vXr1a1btzShMEWHDh3UrVs3rVu3LsvFAQAAIPdkORhGRUWpUqVKN+1TqVIlRUVFZfVXAAAAIBdlORgGBwdr69atN+2zbds2BQcHZ/VXAAAAIBdlORh26dJF69ev16hRo3T9+nWnbdevX9fo0aO1bt06de3a9S8XCQAAgJxnGWNMVh74559/6v7779exY8cUEBCgRo0aqXTp0vrjjz+0Y8cOnT9/XpUrV9b27dtVokSJ7K47T8vMzawBZI/+01xdgfTRYFdXAKAgykzuyPJVyQEBAdq6dav+7//+T19++aVWrFjh2Fa4cGH169dPkyZNIhQCAADkEX9pgeuSJUvq448/1qxZs3TgwAHHnU9CQkLk6emZXTUCAAAgF2Q6GI4fP16xsbF68803HeHP09NTtWrVcvSJj4/X66+/Ll9fXw0bNiz7qgUAAECOydTFJ2vWrNEbb7yhgICAmx4RLFSokAICAvT666+zjiEAAEAekalguHDhQvn7+2vQoEG37Dtw4ECVKFFC8+bNy3JxAAAAyD2ZCoabN29WmzZt5OXldcu+Xl5eatOmjTZt2pTl4gAAAJB7MhUMz5w5o8qVK992/0qVKuns2bOZLgoAAAC5L1PB0M3NTQkJCbfdPyEhQW5uWV5DGwAAALkoU6ktODhY+/btu+3++/btU9myZTNdFAAAAHJfpoLhgw8+qLVr1+r48eO37Hv8+HGtXbtWzZs3z2ptAAAAyEWZCoYDBw5UQkKCunXrpgsXLmTY788//1T37t2VmJiov//973+5SAAAAOS8TC1wXa9ePQ0ePFjTpk1TjRo19MILLyg0NFR33XWXJOn06dP68ccfNXv2bJ0/f15Dhw5VvXr1cqRwAAAAZK9M3/lkypQpKly4sN555x2NHz9e48ePd9pujJG7u7uGDx+ut956K9sKBQAAQM7KdDC0LEsTJkzQs88+q3nz5mnz5s2KjIyUJAUFBalZs2bq27ev7r777mwvFgAAADkn08Ewxd13380RQQAAgHyERQYBAAAgiWAIAAAAO4IhAAAAJBEMAQAAYEcwBAAAgCSCIQAAAOwIhgAAAJBEMAQAAIAdwRAAAACSCIYAAACwIxgCAABAEsEQAAAAdgRDAAAASCIYAgAAwI5gCAAAAEkEQwAAANgRDAEAACCJYAgAAAA7giEAAAAkEQwBAABgRzAEAACAJIIhAAAA7AiGAAAAkEQwBAAAgB3BEAAAAJIIhgAAALAjGAIAAEASwRAAAAB2BEMAAABIIhgCAADAjmAIAAAASQRDAAAA2BEMAQAAIIlgCAAAADuCIQAAACQRDAEAAGBHMAQAAIAkgiEAAADsCIYAAACQRDAEAACAHcEQAAAAkgiGAAAAsCMYAgAAQBLBEAAAAHYEQwAAAEgiGAIAAMCOYAgAAABJBEMAAADYEQwBAAAgiWAIAAAAO4IhAAAAJBEMAQAAYEcwBAAAgCSCIQAAAOwIhgAAAJBEMAQKpIoVK8qyrDT/DRw4UJI0e/ZstWzZUsWKFZNlWbp8+XKa59i5c6fatm2r4sWLKyAgQM8//7xiYmJyeSQAgOyUL4KhMUZff/21QkNDVaZMGRUtWlTVq1fXgAEDdPTo0TT9o6OjNXToUFWoUEFeXl6qWLGiXn311Qzf1Gw2m95//33VqlVLRYoUUalSpfTEE0+k+9xAXrBjxw6dPXvW8d/q1aslSd27d5ckXb16VR06dNCIESPSffyZM2fUpk0bValSRdu2bdMPP/yg/fv3q2/fvrk1BABADrCMMcbVRfxVr7zyiqZOnaoyZcqoa9euKlasmHbv3q1Vq1bJx8dHmzdv1r333itJio2N1QMPPKCwsDC1a9dOdevW1a5du7Rq1So1bNhQGzZsUOHChZ2ev3///pozZ45q1qypTp066cyZM1q8eLF8fHy0detWVa1aNVP1RkdHy8/PT1FRUSpWrFi2zQOQVYMHD9by5csVHh4uy7Ic7evXr1doaKguXbqk4sWLO9pnz56tUaNG6ezZs3JzS/58uXfvXt13330KDw9XlSpVcnsIt9R/mqsrkD4a7OoKABREmckdHrlUU46JjIzUtGnTVKFCBe3evVt+fn6Obe+++66GDh2qqVOn6uOPP5Yk/etf/1JYWJhee+01TZw40dF32LBhmjRpkt59910NHz7c0b5u3TrNmTNHzZs31+rVq1WoUCFJ0pNPPqmOHTtq0KBBWrlyZS6NFsh+8fHx+vTTTzV06FCnUHgzcXFxKlSokCMUSlKRIkUkSRs3brwjgyEA4Nby/FfJx48fl81mU7NmzZxCoSQ9/PDDkqTz589LSv7Kec6cOfLx8dGoUaOc+o4aNUo+Pj6aM2eOU/tHH30kSRo3bpwjFErSQw89pJYtW2rVqlU6efJkto8LyC3ffPONLl++nKmvgVu1aqXIyEi98847io+P16VLlzRs2DBJ0tmzZ3OoUgBATsvzwbBq1aoqVKiQNm3apOjoaKdty5cvlyS1bt1akhQeHq4zZ86oWbNm8vb2durr7e2tZs2a6ejRo4qIiHC0r1+/3rHtRu3bt5ck/fTTT9k6JiA3zZ07Vw899JCCg4Nv+zE1a9bUggULNGXKFBUtWlRBQUGqVKmSSpcu7XQUEQCQt+T5r5IDAgI0ceJEvfLKKwoJCXE6x3Dt2rV68cUXNWjQIEnJwVBShucEVq1aVStXrlR4eLjKlSun2NhYnT17Vvfee6/c3d3T7Z/6eYG85sSJE1qzZo2+/vrrTD/2ySef1JNPPqk//vhD3t7esixLU6dOVeXKlXOgUgBAbsjzwVCShgwZorJly+q5557TzJkzHe0PPPCAnnzySXl4JA8zKipKktJ85Zwi5YTMlH6Z7Z+RuLg4xcXFOX5OObKZkJCghIQESZKbm5vc3d2VlJQkm83m6JvSnpiYqNTXCbm7u8vNzS3D9pTnTZEyB4mJibfV7unpKZvNpqSkJEebZVny8PDIsD2j2hnTnTumOXPmKDAwUJ06dUp3TClS76s3jqlEiRKSpAULFqhw4cJq2bKl07junL+Tp1wt9bwU9H2PMTEmxpR7Y8qMfBEMx44dq7feektjx47V008/reLFiyssLExDhgxRy5YttXTpUnXp0sVl9b399tt6880307SvWrVKRYsWlSSVL19edevW1Z49e5zOWaxevbpCQkK0fft2x7mSklSnTh1VqFBBGzZs0JUrVxztTZo0UWBgoFatWuW044WGhqpIkSJasWKFUw0dO3bUtWvXtG7dOkebh4eHOnXqpAsXLmjLli2Odl9fX7Vq1UoREREKCwtztJcqVUpNmzZVeHi4Dh486GhnTHf2mGw2m2bNmqVOnTrJw8NDu3btcozp0qVL8vPz059//ikp+VzblKWaHnzwQVWoUEFDhw5VxYoVVbhwYe3evVuffPKJJk6cqO3bt9+hf6eucrXUc1CQ9z3GxJgYU+6OKTOnCuX55WrWrFmjtm3basiQIZo6darTtsjISFWuXFlly5ZVeHi4vvvuOz388MMaNGiQ3n///TTP9dJLL2n69On68ccf1apVK8XGxsrHx0f33nuv9u7dm6b/0qVL1a1bN40aNUpjx47NsMb0jhiWK1dOFy5ccBx1LGifXhiT68e0evVqderUSb/99pvuuecepzGlfNi60Zw5c9SvXz+5ubnp6aef1vfff6+YmBhVr15dr7zyivr06XPH/p1enOH6I4YfDOSIIWNiTIwp98cUGxtbcJar+f777yUlp/MbBQUFKSQkRLt27VJMTMwtzwm88RxEb29vlSlTRseOHVNSUlKa8wxvdc5iCi8vL3l5eaVp9/T0lKen85uVu7t7uuczpuxMt9t+4/Nmpd3NzS3dQ9AZtWdUO2O6M8fUsWPHNC9wKWMaN26cxo0bl24NKT799NO/XHtG7Tn9d3KVzIw1P+97t9vOmBhTRu2MKede9/L85YPx8fGS5HTIN7Xz58/Lzc1Nnp6eqlq1qoKDg7Vp0ybFxsY69YuNjdWmTZtUqVIllStXztHeokULx7Ybpaxf2Lx58+waDgAAgMvk+WCYsozM1KlT01wEMnPmTJ06dUpNmjSRl5eXLMvSc889p5iYmDRHQ8aNG6eYmBj179/fqf3555+XlLzOYUoIlZKPVK5fv17t2rVThQoVcmJoAAAAuSrPn2OYlJSkVq1aacOGDQoMDFSXLl1UvHhx7dy5U2vXrlWRIkW0fv16NWrUSFLykcFmzZpp9+7dateunerVq6edO3c6bon3008/Oe7gkOLGW+KdPXtWixYtko+Pj7Zs2aJq1aplqmZuiQfkPm6JB6CgykzuyPPBUEq+uOPdd9/V4sWLdfDgQcXHx6t06dIKDQ3ViBEjdM899zj1j4qK0pgxY7R06VJFRkaqTJky6t69u0aPHi1fX980z2+z2TR9+nTNnj1bhw8flo+Pj9q0aaPx48fr7rvvznS9BEMg9xEMARRUBS4Y5jUEQyD3EQwBFFSZyR15/hxDAAAAZA+CIQAAACTlg3UMAdwaX6MCAG4HRwwBAAAgiWAIAAAAO4IhAAAAJBEMAQAAYEcwBAAAgCSCIQAAAOwIhgAAAJBEMAQAAIAdwRAAAACSCIYAAACwIxgCAABAEsEQAAAAdgRDAAAASCIYAgAAwI5gCAAAAEkEQwAAANgRDAEAACCJYAgAAAA7giEAAAAkEQwBAABgRzAEAACAJIIhAAAA7AiGAAAAkEQwBAAAgB3BEAAAAJIIhgAAALAjGAIAAEASwRAAAAB2BEMAAABIIhgCAADAjmAIAAAASQRDAAAA2BEMAQAAIIlgCAAAADuCIQAAACQRDAEAAGBHMAQAAIAkgiEAAADsCIYAAACQRDAEAACAHcEQAAAAkgiGAAAAsCMYAgAAQBLBEAAAAHYEQwAAAEgiGAIAAMCOYAgAAABJBEMAAADYEQwBAAAgiWAIAAAAO4IhABRwGzZsUOfOnRUcHCzLsvTNN984bf/jjz/Ut29fBQcHq2jRourQoYPCw8PTPM+WLVvUqlUreXt7q1ixYmrevLmuXbuWS6MAkB0IhgBQwMXGxqp27dqaMWNGmm3GGD3yyCM6evSo/vOf/2jXrl2qUKGC2rRpo9jYWEe/LVu2qEOHDmrXrp22b9+uHTt2aNCgQXJz420GyEs8XF0AAMC1HnroIT300EPpbgsPD9fWrVu1b98+1axZU5L04YcfKigoSF988YWee+45SdKQIUP08ssva9iwYY7HVq9ePeeLB5Ct+CgHAMhQXFycJKlw4cKONjc3N3l5eWnjxo2SpHPnzmnbtm0KDAxU06ZNVbp0abVo0cKxHUDeQTAEAGQoJCRE5cuX1/Dhw3Xp0iXFx8dr0qRJOnXqlM6ePStJOnr0qCRpzJgx6t+/v3744QfVq1dPrVu3TvdcRAB3LoIhACBDnp6e+vrrr3Xo0CGVKFFCRYsW1bp16/TQQw85zh+02WySpAEDBqhfv36qW7eu3n33XVWvXl0ff/yxK8sHkEmcYwgAuKn69esrLCxMUVFRio+PV6lSpXT//ferQYMGkqQyZcpIkmrUqOH0uHvuuUcnT57M9XoBZB1HDFHg3GppjjFjxigkJETe3t7y9/dXmzZttG3bNqc+O3fuVNu2bVW8eHEFBATo+eefV0xMTC6OAsh9fn5+KlWqlMLDw/XLL7+oa9eukqSKFSsqODhYBw8edOp/6NAhVahQwRWlAsgigiEKnJstzSFJ1apV0/Tp07V3715t3LhRFStWVLt27XT+/HlJ0pkzZ9SmTRtVqVJF27Zt0w8//KD9+/erb9++uTgKIPvExMQoLCxMYWFhkqRjx44pLCzMcbRvyZIlWr9+vWPJmrZt2+qRRx5Ru3btJEmWZenVV1/Ve++9p6+++kqHDx/WqFGjdODAAT377LOuGhaALOCrZBQ4N1uaQ5KefPJJp5+nTp2quXPnas+ePWrdurWWL18uT09PzZgxw3GO1cyZM3Xffffp8OHDqlKlSo7WD2S3X375RaGhoY6fhw4dKknq06eP5s+fr7Nnz2ro0KH6448/VKZMGfXu3VujRo1yeo7Bgwfr+vXrGjJkiC5evKjatWtr9erVuvvuu3N1LAD+GoIhcBPx8fGaPXu2/Pz8VLt2bUnJy3cUKlTIaeHeIkWKSJI2btxIMESe07JlSxljMtz+8ssv6+WXX77l8wwbNsxpHUMAeQ9fJQPpWL58uXx8fFS4cGG9++67Wr16tUqWLClJatWqlSIjI/XOO+8oPj5ely5dcrwZpizfAQBAXkQwBNIRGhqqsLAwbd68WR06dFCPHj107tw5SVLNmjW1YMECTZkyRUWLFlVQUJAqVaqk0qVLc/svAECexrsYkA5vb29VqVJFjRs31ty5c+Xh4aG5c+c6tj/55JOKjIzU6dOn9eeff2rMmDE6f/68Kleu7MKqAQD4azjHELgNNpvNcWuw1EqXLi1J+vjjj1W4cGG1bds2t0sDMqX/NFdXIH002NUV3J6kpCSNGTNGn376qSIjIxUcHKy+fftq5MiRsixLUvLyVl9++aUiIiJUqFAh1a9fX+PHj9f999/v4uqBrCEYosCJiYnR4cOHHT+nLM1RokQJBQQEaPz48erSpYvKlCmjCxcuaMaMGTp9+rS6d+/ueMz06dPVtGlT+fj4aPXq1Xr11Vc1ceJEFS9e3AUjApATJk2apA8//FALFixQzZo19csvv6hfv37y8/NzXIyTsrxV5cqVde3aNb377rtq166dDh8+rFKlSrl4BEDmEQxR4NxsaY6ZM2fqwIEDWrBggS5cuKCAgAA1bNhQP//8s2rWrOl4zPbt2zV69GjFxMQoJCREs2bNUq9evXJ9LAByzubNm9W1a1d16tRJUvJC3l988YW2b9/u6HOr5a2AvIZgiALnVktzfP3117d8joULF2ZnSQDuQE2bNtXs2bN16NAhVatWTbt379bGjRs1derUdPunt7wVkNcQDAEASMewYcMUHR2tkJAQubu7KykpSePHj9dTTz3l1G/58uV6/PHHdfXqVZUpU8ZpeSsgr+GqZDhMnDhRlmVp8ODBjrYjR47o0UcfValSpVSsWDH16NFDf/zxh+uKBIBcsnjxYn322Wf6/PPPtXPnTi1YsECTJ0/WggULnPrdbHkr5E83vl8eP35clmWl+9+SJUtcW2wmEQwhSdqxY4dmzZql++67z9EWGxurdu3aybIsrV27Vps2bVJ8fLw6d+4sm83mwmoBIOe9+uqrGjZsmB5//HHVqlVLvXr10pAhQ/T222879bvV8lZ52Ycffqj77rtPxYoVU7FixdSkSRN9//33ju2RkZHq1auXgoKC5O3trXr16mnp0qUurDjnpfd+Wa5cOZ09e9bpvzfffFM+Pj43vQXrnYivkqGYmBg99dRT+uijj/TWW2852jdt2qTjx49r165dKlasmCRpwYIF8vf319q1a9WmTRtXlXzbWJoDQFZdvXo1zaL17u7ut/xgnNHyVnnRXXfdpYkTJ6pq1aoyxmjBggXq2rWrdu3apZo1a6p37966fPmyvv32W5UsWVKff/65evTooV9++UV169Z1dfnZLqP3S3d3dwUFBTn1XbZsmXr06CEfH5/cLvMv4YghNHDgQHXq1ClN0IuLi5NlWfLy8nK0FS5cWG5ubtq4cWNulwkAuapz584aP368vvvuOx0/flzLli3T1KlT9eijj0pK/lZlxIgR2rp1q06cOKFff/1VzzzzTJrlrfKyzp07q2PHjqpataqqVaum8ePHy8fHR1u3bpWUfOX2Sy+9pEaNGqly5coaOXKkihcvrl9//dXFleeMjN4vb/Trr78qLCxMzz77bC5Vln04YljAffnll9q5c6d27NiRZlvjxo3l7e2t1157TRMmTJAxRsOGDVNSUhL3BAaQ773//vsaNWqUXnzxRZ07d07BwcEaMGCA3njjDUnJR4luZ3mr/CIpKUlLlixRbGysmjRpIin5yu1FixapU6dOKl68uBYvXqzr16+rZcuWri02B9zs/fJGc+fO1T333KOmTZvmQmXZi2BYgEVEROgf//iHVq9ercKFC6fZXqpUKS1ZskR///vf9d5778nNzU1PPPGE6tWrxz2BAeR7vr6+mjZtmqZNm5bu9sKFC9/W8lZ53d69e9WkSRNdv35dPj4+WrZsmWrUqCEp+QKdnj17KiAgQB4eHipatKiWLVumKlWquLjq7HWr98vUrl27ps8//1yjRo3KpeqyF8GwAPv111917tw51atXz9GWlJSkDRs2aPr06YqLi1O7du105MgRXbhwQR4eHipevLiCgoK4JzAAFBDVq1dXWFiYoqKi9NVXX6lPnz766aefVKNGDY0aNUqXL1/WmjVrVLJkSX3zzTfq0aOHfv75Z9WqVcvVpWeb23m/dHd3lyR99dVXunr1qnr37u2qcv8SgmEB1rp1a+3du9eprV+/fgoJCdFrr73m2MklOdbkWrt2rc6dO6cuXbrkaq0AANcoVKiQ4whg/fr1tWPHDv373//W//3f/2n69Onat2+f46vz2rVr6+eff9aMGTM0c+ZMV5adrTLzfjl37lx16dIlz94SkWBYgPn6+uree+91avP29lZAQICjfd68ebrnnntUqlQpbdmyRf/4xz80ZMgQVa9e3RUlAwBcLOWq66tXr0pSlq7czmtu5/1Skg4fPqwNGzZoxYoVuV1itiEY4qYOHjyo4cOH6+LFi6pYsaJef/11DRkyxNVlAcBfwlJWt2f48OF66KGHVL58eV25ckWff/651q9fr5UrVyokJERVqlTRgAEDNHnyZAUEBOibb77R6tWrtXz5cleX7hIff/yx7rrrLrVr187VpWQZwRBO1q9f7/TzxIkTNXHiRNcUAwBwqXPnzql37946e/as/Pz8dN9992nlypVq27atJGnFihUaNmyYOnfurJiYGFWpUkULFixQx44dXVx5zrvx/VKSJkyYoAkTJuR+MdmIYAgAANJ1qzu4VK1aNd/f6aSgYc0RAAAASOKIYabs2LFDo0eP1ubNm5WQkKBatWpp6NCh6tGjh6tLS4PzZwAAuDXeL50RDG/TunXr1L59exUuXFiPP/64fH19tXTpUvXs2VMRERF65ZVXXF0iAACZQijCjfgq+TYkJiaqf//+cnNz04YNGzR79mxNmTJFu3fvVrVq1TRixAidOHHC1WUCAAD8JQTD27B27VodOXJETz75pOrUqeNo9/Pz04gRIxQfH68FCxa4rkAAAIBsQDC8DSmXpKe3LlH79u0lST/99FNulgQAAJDtOMfwNoSHh0tKviz/RkFBQfLx8XH0SU9cXJzi4uIcP0dFRUmSLl68qISEBEnJK8e7u7srKSnJacX4lPbExEQZYxzt7u7ucnNzy7A9/noWB5uNLl1KytYxpcxVCg+P5N03MTExw/b4657ZPq7Mio5Wto4pNU9PT9lsNiUlJTnaLMuSh4eHU/udMA9//nl7Y73dMaVuz2gfS91+p81Bdowpdfvt/nu6k+Yhu1/3MvPvKf66le3jyqw//0zIkde91G717yn+uuuPD0VFJY87u1/3Urff7N9T/HV3uVp0tHLkdS+lPTY2VpKc9rGMWOZ2ehVw7dq10+rVqxUeHu64X2RqZcuWVUxMjCPw3WjMmDF68803c7pMAACADEVEROiuu+66aR+OGOaC4cOHa+jQoY6fbTabLl68qICAAFmW6z+1pic6OlrlypVTRESEihUr5upyXII5SMY8JGMekjEPzEEK5iFZXpgHY4yuXLmi4ODgW/YlGN4GPz8/ScrwiGB0dLT8/f0zfLyXl5e8vLyc2ooXL55t9eWkYsWK3bE7em5hDpIxD8mYh2TMA3OQgnlIdqfPQ0qWuRXXn1yQB6ScW5jeeYSRkZGKiYlJ9/xDAACAvIRgeBtatGghSVq1alWabStXrnTqAwAAkFcRDG9D69atVblyZX3++ecKCwtztEdFRWnChAkqVKiQevfu7boCc4CXl5dGjx6d5ivwgoQ5SMY8JGMekjEPzEEK5iFZfpsHrkq+TRndEu/EiROaPHkyt8QDAAB5HsEwE7Zv367Ro0dr8+bNSkhIUK1atTR06FD17NnT1aUBAAD8ZQRDAAAASOIcQwAAANgRDAEAACCJYAgAAAA7giEAAAAkEQyRjoyuR+I6JQAA8jeCIdKwLEunT5+WJMXHx+vq1auOdhQsfEgAcDO8FuQ/LFcDB2OMli9frrlz52rv3r2KiYnRfffdp1q1aql+/fqqU6eOqlSpIi8vLxljCIoFRHh4uAIDA3XlyhUVKVJEAQEBri4JdyBeE5CCfSFvIxjC4Y033tDkyZNVtGhRlStXTgkJCYqPj1dERISMMapdu7a6deum3r17q3Tp0q4uN0clJSXJzc2twL64xcXFacmSJfrggw+0a9cuubm5qWrVqqpSpYrq16+vpk2bql69evL19XV1qTnOGKOkpCS5u7sX2P0htXPnzun8+fMKCAjQlStXVKpUKRUvXtzVZSGXJSUlKTw8XJcuXZKU/O/k7rvvzvfvDQUBwRCSpOPHj6tmzZpq2bKlpkyZopCQEF24cEERERE6cuSINmzYoJUrVyo8PFy1a9fWhAkT9NBDD8lms8nNLf+ckRAREaFy5co5frbZbDLGyN3d3YVV5b5XXnlF//73v1WhQgVVrVpVnp6eunz5svbu3avo6GiVK1dODz/8sJ555hnVr1/f1eXmmCNHjujuu+92/Gyz2WSz2eTh4eHCqlzj7Nmzev3117V69WqdPn1avr6+qlSpku655x7df//9euCBB1SrVq18c7/YG6UcBSvI+0CKgwcPavjw4VqxYoXi4+Pl5eUlf39/VaxYUU2aNFGHDh3UtGlTeXt7u7pUZAHBEJKkcePGadq0aVq8eLFat26txMREpxe+6Oho7d+/X4sXL9a///1vlS5dWt9//73q1KnjuqKz2fHjx1W5cmW1a9dOTzzxhB5++GGnr02TkpJkWZbc3NwcbxLx8fEqVKiQC6vOfseOHVONGjXUuXNnzZgxQ6VKldKVK1d0+fJlnT17Vhs2bNCyZcu0Y8cOlS1bVm+++aZ69+6d774+OnLkiKpWraqQkBA988wzevrppxUUFOTYnpSUJElyd3d3jD02NlYxMTEKCAjIV8EhMjJSjz76qLZt26YOHTrIx8dHbm5uOnHihPbs2aNr166pRo0a6tGjh/r3768yZcq4uuRsFx0drcuXL6t8+fKOttT7QEFx5swZdejQQfv371evXr1UsmRJeXh4aP/+/fr5558VHR2t4sWL69FHH9WAAQPUqFEjV5ecIy5duqQ9e/aocePG+e/DkAGMMb179zZlypQxkZGRxhhjbDab0/+m9uWXXxo/Pz/TuHHjXK0xp02YMMFYluX4r2TJkqZPnz7mu+++MwkJCU594+LijDHGzJw507Ru3docPHjQFSXniPHjx5sSJUqYH3/80RhjTGJiotP2hIQEc/ToUTNt2jRTqlQpY1mW+eGHH1xRao6aNGmS0/5gWZZp2bKl+fTTT018fLxT39T7Q6NGjczOnTtdUXKOeeONN4yfn5+ZNm2ao+3SpUsmIiLCbNiwwYwcOdLUqFHDuLm5mSZNmpiNGzcaY9J//cirhg4daizLMg8++KD5+OOPTWxsrNP2hIQEk5SU5NR29uxZ88cff+SreRg5cqTx9/c3c+bMcbTFxcWZ+Ph4c/LkSTNr1izTrFkz4+bmZmrUqGGWL19ujMlf+4Ixxvzzn/80lmWZevXqmXHjxpl9+/Zl2Ddl7IcOHTJhYWFpXj/uNARDGGOMmTx5srEsyyxZssTRduOLXOp/2P369TMlS5Y0Bw4cyLUac9rDDz9sfH19zZw5c0yfPn1M0aJFHYGgSpUq5p///KfZvn2702P+9re/GcuyTExMjIuqzn4vvviiKV68uImIiDDG3PwFfdWqVaZMmTKmevXq5vr167lVYq547LHHTJEiRcznn39u3njjDVOjRg3H/uDp6Wkef/xxR3hOkR/3B2OMqVGjhnn44YfNuXPnjDFp94nr16+b3bt3O8JTSEiI+eOPP1xRao6pVatWmg8Kjz76qPnuu++c+qXMTXR0tHnqqadM+/bt03ywzMtq165tOnTo4Pj7pvf6cP78efP++++bEiVKGF9fX/Pbb7/ldpk5rk6dOsbNzc2UKFHCsT+EhoaaWbNmmVOnTqXpHxMTY5544gnTuHFjgiHyhg0bNhgfHx8TEhJiduzY4bTNZrM5QmLK/06YMMF4e3unCUp51blz50yjRo1M2bJlHW3Xrl0zn332mWndurXTm0HDhg3Ne++9ZxYvXmzKlCljOnfu7MLKs9/cuXONZVlmxowZjhf9xMTEDAPi8OHDjY+PT746Snb+/HnTtGlTExQU5GiLi4sz33//vXn22WdNmTJlHPtDqVKlzLBhw8ynn36aL/eHyMhIc88995i2bdvesm9CQoJ57733jGVZ5rXXXsuF6nLHkSNHTKlSpUyLFi3Mhg0bzN///ndTvnx5xz7g7+9vXnzxRad/A7t27TL+/v6mRYsWris8m124cME0aNDgtr4tSkhIMF9++aWxLMsMGDAgF6rLPceOHTPBwcGmcePGJiwszIwbN840b97cFC5c2FiWZXx9fU2PHj3MsmXLzJ9//mmMMWb79u2mRIkSJjQ01MXV3xrBEI43/I8++si4u7sby7LM888/b9asWWOio6PT9L969ap54oknTEBAQG6XmmNOnjxpHnzwQdOpUydjzP++Gkxx5swZM3nyZKejBikvAjceMcjr9u7da8qWLWtKlChh/vvf/zpts9lsjq+WUz4kTJ061RQuXNhs3rw512vNKZGRkaZDhw6mbdu2JiEhIc0n/PPnz5uFCxeaLl26GG9vb6cPDvlpf0j5UNitWzdTrFgxs23bNkf7jacYpFarVi3TqlUrc+XKldwqNUetWrXKWJZlXnnlFUfb5cuXzaJFi0z37t2Nn5+f4+9/9913m4kTJ5rXXnvNWJbl+Co1r0t5n+jfv7+xLMv897//dXxgvNkR0WbNmpmGDRs6AlJ+sHbtWuPm5mZefvllR9uVK1fMypUrzZAhQ8x9993n2B/Kli1rBg8ebAYMGJBn9geCIRxiYmLMhx9+aAIDA41lWSYwMNB07drVTJgwwaxZs8ZcvHjRbNu2zQwYMMAUKlTI6UUyr4uPjzdr1641mzdvdgSelDe/G79SP3jwoBk4cKCxLMuUKFHCFeXmmJQX/++//97cddddxrIs0759e7N48WJz8eLFNP1jYmJMjx498tWHhBTh4eFm3759afaHG4+cnjx50owdO9YULVrU+Pv7u6LUHDd79mzH+XU3nkuVlJTkNC9RUVGmY8eO5t5773VFqTli8+bNply5cmb27NnGGJMmCJ04ccK8//77pmXLlk4fEvLj/rBixQpjWZapVq2aWblypdO2xMREp33h8uXL5pFHHjHVqlVzRak5JiwszFStWtW89957xpi052GfPXvWfPHFF6ZPnz6mUqVKeW5/IBgizRtdTEyMmTZtmmnSpInx8PBw7NRubm6mUKFCxrIs069fv3TPo8jrbgyBKVI+Fae8AGzfvt0ULVrUPP/887lZXq5JSEgwX331ldMn39q1a5uBAweapUuXmt9//918/fXXpmfPnsbd3d0MGzbM1SXnqpSQmLI/bNmyJV/vD8YYM3HiROPm5mYsyzJ9+vQxK1euNNeuXXNsT3kdWbNmjSlbtqzp37+/q0rNdvHx8Wb//v2Oi/OMyfio6aFDh8zTTz9tLMsyAwcOzM0yc81nn31mSpcu7TivbtGiRU7n1absC999950JDg7OV/tCiujo6DQfltN7/zh9+rQZNGiQsSzLvPjii7lV3l/CcjXI0IULF3To0CFt3bpVP//8s5KSklStWjXdc889evbZZ11dXrZKWcDYGCObzXbL5SdeeuklzZgxQzt27MjX6/hJ0jfffKM5c+Zo5cqVjuU5LMuSMUaenp4aOHCgXnvttQK9sO2gQYP0wQcf5Mv9wdiX4rl8+bI+/vhjTZo0SefPn5e7u7vq16+vZs2aKTQ0VH5+ftqxY4emT5+uK1euaO3atapVq5ary88VN75ujB07VmPGjMmX+4OUvAD+0qVLNXXqVO3cuVOSFBgYqBYtWqht27by8vLSvn37NHfuXHl5eWnVqlWqWbOmi6vOPTfuD6NHj9a4cePyzP5AMCzgzp07p7179+rQoUOKiYlRo0aNFBISopIlS6YJR3FxcU7rNZl8tm7d7YqOjtaAAQO0bt06RUZGurqcHJFeQI6MjNS6deu0adMmeXp6Kjg4WCEhIercubMLK3W92NhYDRw4UCtWrNC5c+dcXU62u/Hf+fXr17VgwQItXLhQW7ZsSdO/Ro0aGj58uJ566qncLDNHpSzkn/IBMj0p83To0CF17txZiYmJOnLkSC5XmruMMfrvf/+r2bNna9WqVUpMTHTa3qRJE40cOVIPPfSQiyp0vaNHj+qRRx7RlStXdOzYMVeXc1sIhgXY999/r7feeivNi3uJEiXUunVr9ezZU507d5anp6djW36704mUcThOvUjxjW8IcXFxOnfunNNdUvK6zPxtb5yP/PQhIav7eHR0tIoVK5YDFd25Tp48qTVr1mjfvn0KCgpSYGCgHnjgAVWpUsXVpbnMwYMH9cgjj6hz587617/+5epycoRJPg3N6d9JVFSU1q9fr6NHjyo4OFg+Pj5q2LChAgMDXVip6x07dkwDBgxQixYt9Prrr7u6nNtCMCygIiIi1LJlS8XGxqpv374KDQ3V0aNHtWvXLu3evVt79uxRXFycatSooREjRqhbt24qVKhQvgoA0s3DcZs2bRzhOD/dxeJ2ZBSOUt9D+sa74+RHtxMSExMTZVlWvrz7xQ8//KB9+/YpLCxMpUuXVoMGDVSlShWVK1dOAQEBTh8a86vUcxAYGKiGDRuqSpUqqlChggICApzufJNafvv3kdHR0tR3hCoIbnbUOCce5xK5eD4j7iCvv/668ff3N0uXLk2zLSIiwixatMg89dRTjgsPJk2a5IIqc9bJkydN5cqVTenSpc1rr71mfvjhB/PBBx+Y/v37m0aNGjmWo7n33nvNZ5995ljCJqMLVPKqyMhIM3ToUPPDDz+YS5cuOW2z2Wz57o4FGWEe/ufSpUvm//7v/4xlWU4XoFmWZQICAkyXLl3MvHnz0ixBkp/m6Hbn4MZ95WbL+ORF6d3oIL3XwNTtt1rCJi+63Xm40Y1Ln+UFBMMC6v777zctW7Y058+fN8YYpytuU1u7dq2pW7eu8fLyMnPnzs3tMnMU4TjZG2+8YSzLMpUqVTKdOnUy77zzjtm+fXuaO5mkLEtijDHr1q0z33//vSvKzTHMw//861//MkWLFjWPPvqoWbdunTl48KD58ssvzZtvvmkefvhhx60Q69WrZ5YtW+bqcnMEc5Dsgw8+MD169DDLly9Psy5lUlJSvvugnJGCNA8EwwLoypUrpk2bNiYkJMRxv8/UO/WNn4R27txp/P39TZcuXRzb8wPCcbI6deqYQoUKmcaNGzuWI6pYsaJ56qmnzJw5c8zvv//u1D82NtZ06dLFuLm5OS1XktcxD/9ToUIF06lTJ3PhwoU0206fPm2WL19unn/+eceRtI8++sgFVeYs5iBZxYoVHQv633///WbUqFFmy5Ytad4HUo4QxsbGmnfffdesXbvWFeXmmII0DwTDAiplVf70gk7qHT0lIHbt2tVUq1bNHD9+PNdqzEmE42QnT540FStWNPXr1zfx8fFmy5YtZtSoUaZ27drGsizj7u5u7rvvPjNo0CCzePFiExUVZbZv326CgoLy1a3fmIf/+f33342Pj48ZMWKEoy29IyJxcXHmu+++M5UrVzYlSpTIV3e+YQ6S7du3z1iWZRo0aGDatm3r+PbEx8fHtG/f3vz73/9O84Hp559/NpZlmWbNmrmo6uxX0OaBYFhAnTp1ynF7t5deesn8+uuvaY56pHzyiYqKMt27dzfly5d3Rak5pqCHY2OM2bZtmylRooTp06ePMcY47vTyxx9/mO+//9688MILpkKFCsayLFO0aFHTvHlzx72jb7xdXl7GPPzPb7/9Zu666y7Ts2dPY0zy68CNH5pS//v45ptv8t2pFsxBsi+++MJYlmWmTp1qjEm+69OkSZNMnTp1HOGoTJky5oknnjALFy40Fy9eNFOmTMkzt367XQVtHgiGBdiyZcsct+tp0KCBGTdunFm3bp05fvy4U0j89NNPTalSpfLdjdAJx8m3ffvb3/5mPvvss3S3x8fHm+PHj5tPPvnE9OjRw5QoUSJP3drpdjEPzu6//37j6+trVqxYkWZbSiBKCUp//vmnqVSpkunWrVuu1pjTmANjZs2aZSzLSncOtm/fboYMGWLKlSvnCEfVqlUzQUFBxs/PL/eLzUEFbR4IhgXMjV+B/vnnn+af//ynKV++vOP+yK1atTJPP/20ef75502vXr2Ml5eXCQkJMQcOHHBR1TmnoIdjY5LvZ5reeVSppbwBzpw5M0/d2ikzmIf/vT5s27bNlC1b1liWZQYPHmy2bduW5kNTykU5mzdvNsHBwebll1/O9XpzAnOQzGazmS1btpghQ4aYw4cPO7Wndu3aNbN8+XLTp08f4+fnZyzLMoMGDcrtcnNMQZwHgmEBlLJDR0REON7o9u7da95++23Tvn17R0i0LMuUKFHCtGrVyuzbt8+VJWcrwnGy9M6TTPkKNSOvvvqqsSzL/PrrrzlZWq5iHtJKTEw08+fPN2XKlDGWZZmaNWuaIUOGmCVLlpj9+/c75ubUqVPmiSeeMB4eHvluLpiDZFeuXMlwyZUb/+0MHDjQWJZldu3alQuV5a6CNA8scF2AJCYmatOmTfr444916NAhWZalokWLqmHDhurRo4fq1q0rY4wiIiJ07do1HT16VCEhISpXrpw8PDzy1eLWKWM5deqUgoOD5ebmpn379mn58uVav369fv/9d0VEREiS/P39VadOHb333nv57n6fKfMQGRmpwMBAp0VqUy9mLUmnTp1Sp06ddObMGZ0/f95VJecI5iF958+f1/Tp07V48WIdOnRIRYsWVdmyZeXj46MSJUrowIEDOn/+vPr166cPPvjA1eXmCObg5lL+7Rw5ckQ9e/ZUVFSUwsPDXV1WrstP80AwLEAmT56scePG6cqVK6pSpYrc3d118OBBx/YaNWroxRdfVLdu3fLtbYwIx8lunAc3NzcVKVJEtWvX1mOPPaamTZumecyFCxf0ySefKDg4WD179nRB1dmPeUifSXWv7GvXrik8PFw7duzQpk2btG3bNh04cEClSpVSuXLl9Nxzz+npp5+Wt7e3q8vOVsxB5ixfvlxdunTRq6++qkmTJrm6HJfJF/PggqOUcIGjR48ab29v8+CDD5qjR4+aU6dOmYSEBBMREWE++OADExoa6vj6uFWrVmbHjh2uLjlHvPPOO6ZYsWLGsixTtWpVExIS4nRHg5o1a5oZM2aYP/74w9Wl5qhbzcM999xjpk6das6ePev0uLi4uHy1kCvzcPuSkpJMbGysSUhIMBcuXMhXp5fcroI4B7e7NFdkZKSZP39+mrvh5BcFaR4IhgXEqFGjTGBgoFmzZo2j7cYdfc+ePaZ3796mcOHCpnr16uaXX37J7TJzFOE4WWbmoXXr1vnyvCljmIfUrl69ag4cOGCuXr2aZltSUpLTa8WNrxv5JSAzB8luNg+3kp9uB1iQ54FgWED87W9/M5UrVzYnTpwwxvxvGRabzZZmJ542bZqxLMv07ds31+vMSYTjZH9lHvLLwt7GMA+pvf3226ZBgwZmwoQJZu3ateb06dNpXhduXLvv3Llz+ep+uMxBstuZhxsxD8nyyzwQDAuIcePGGcuyzP79+zPsk/oF77HHHjPly5c3R44cyY3ycgXhOBnzkIx5+J+UZVk8PDxMQECA6dy5s3n//ffN9u3b013CJyYmxvzzn/80/fr1yzdHy5iDZH9lHvL6kbLUCvI8EAwLiI0bNxrLskydOnXMjz/+mO5l96nfEEeMGGGKFi1qdu/endul5hjCcTLmIRnzkOzgwYPGx8fHNG3a1EyfPt107drVBAYGGsuyTIUKFUyfPn3MJ598Yvbt22cuXbpkjDFm69atxs/Pz3Tt2tWltWcX5iAZ85CsoM8DwbCASExMNK+88orjhPrp06ebyMjIdPtevHjR9O7d25QqVSqXq8xZhONkzEMy5iHZf//7X+Ph4WHGjBljjDHm+PHjZuXKlWbMmDGmefPmxsfHx3h4eJj77rvPDB482Pzwww+OdRzz4u2+0sMcJGMekhX0eSAYFjAzZ840d999t7Esy5QtW9YMGjTIfPfdd2bPnj1m//795vTp02bYsGGmcOHCZujQoa4uN1sRjpMxD8mYh2RLliwxlmWZRYsWObXHx8eb8PBw89VXX5l//OMfpnbt2qZQoULG29vbFC1aNF/dDpA5SMY8JCvo80AwLGBsNps5dOiQefXVV53u7Vi6dGlz1113GXd3d2NZlnnyySdNRESEq8vNEQU5HKfGPCQr6PNgs9nMb7/9Zo4ePer4+UYxMTFm586d5osvvjDt2rVz3F88v2AOkjEPyQr6PBAMC7CYmBizdu1aM3jwYNOjRw/TsmVL06VLF/Ppp5+muSdofkI4TsY8JGMeMpbeG+JLL71kLMsyO3fudEFFuY85SMY8JCsI88CdTyBJSkhIkKenp6vLyHWxsbHavn27vv32W505c0bnzp1TsWLF1KNHDz322GMqXLiwq0vMFcxDMuYhfTabTW5ubjp+/Li6du2qS5cu6eTJk64uK1cxB8mYh2T5eR48XF0A7gwFMRRKkre3t0JDQxUaGlpgw7HEPKRgHtKXcu/o06dPKyEhQS+++KKLK8p9zEEy5iFZfp4HjhgCAG6LMUanTp1SiRIlCux9gZmDZMxDsvw4DwRDAAAASJLcXF0AAAAA7gwEQwAAAEgiGAIAAMCOYAgAAABJBEMAAADYEQwBAAAgiWAIAAAAO4IhAAAAJBEMAQAAYPf/0ovAS2fvZ8wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the results!\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "shots = 4096\n",
    "t_qpe2 = transpile(qpe2, aer_sim)\n",
    "results = aer_sim.run(t_qpe2, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72fc1570-7574-4f67-9c89-3afd94c22952",
   "metadata": {},
   "source": [
    "We are expecting the result $\\theta = 0.3333\\dots$, and we see our most likely results are `010(bin) = 2(dec)` and `011(bin) = 3(dec)`. These two results would tell us that $\\theta = 0.25$ (off by 25%) and $\\theta = 0.375$ (off by 13%) respectively. The true value of $\\theta$ lies between the values we can get from our counting bits, and this gives us uncertainty and imprecision.\n",
    "\n",
    "### The Solution <a id='the_solution'></a>\n",
    "To get more precision we simply add more counting qubits. We are going to add two more counting qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cc0d51f5-1933-4f46-9a0e-5a7905d3e2e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                            »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────»\n",
       "     ├───┤ │                                                          »\n",
       "q_1: ┤ H ├─┼─────────■─────────■──────────────────────────────────────»\n",
       "     ├───┤ │         │         │                                      »\n",
       "q_2: ┤ H ├─┼─────────┼─────────┼─────────■─────────■─────────■────────»\n",
       "     ├───┤ │         │         │         │         │         │        »\n",
       "q_3: ┤ H ├─┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "     ├───┤ │         │         │         │         │         │        »\n",
       "q_4: ┤ H ├─┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "     ├───┤ │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "q_5: ┤ X ├─■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "     └───┘                                                            »\n",
       "c: 5/═════════════════════════════════════════════════════════════════»\n",
       "                                                                      »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ─■────────────────────────────────────────────────────────────────────»\n",
       "«      │                                                                    »\n",
       "«q_3: ─┼─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │         │         │         │         │         │         │        »\n",
       "«q_4: ─┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_3: ─■─────────■──────────────────────────────────────────────────────────»\n",
       "«      │         │                                                          »\n",
       "«q_4: ─┼─────────┼─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_3: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_4: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                             ┌──────────┐ ░ ┌─┐            \n",
       "«q_0: ────────────────────────────────────────┤0         ├─░─┤M├────────────\n",
       "«                                             │          │ ░ └╥┘┌─┐         \n",
       "«q_1: ────────────────────────────────────────┤1         ├─░──╫─┤M├─────────\n",
       "«                                             │          │ ░  ║ └╥┘┌─┐      \n",
       "«q_2: ────────────────────────────────────────┤2 IQFT_dg ├─░──╫──╫─┤M├──────\n",
       "«                                             │          │ ░  ║  ║ └╥┘┌─┐   \n",
       "«q_3: ────────────────────────────────────────┤3         ├─░──╫──╫──╫─┤M├───\n",
       "«                                             │          │ ░  ║  ║  ║ └╥┘┌─┐\n",
       "«q_4: ─■─────────■─────────■─────────■────────┤4         ├─░──╫──╫──╫──╫─┤M├\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) └──────────┘ ░  ║  ║  ║  ║ └╥┘\n",
       "«q_5: ─■─────────■─────────■─────────■─────────────────────░──╫──╫──╫──╫──╫─\n",
       "«                                                          ░  ║  ║  ║  ║  ║ \n",
       "«c: 5/════════════════════════════════════════════════════════╩══╩══╩══╩══╩═\n",
       "«                                                             0  1  2  3  4 </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                            »\n",
       "q_0: ┤ H ├─■──────────────────────────────────────────────────────────»\n",
       "     ├───┤ │                                                          »\n",
       "q_1: ┤ H ├─┼─────────■─────────■──────────────────────────────────────»\n",
       "     ├───┤ │         │         │                                      »\n",
       "q_2: ┤ H ├─┼─────────┼─────────┼─────────■─────────■─────────■────────»\n",
       "     ├───┤ │         │         │         │         │         │        »\n",
       "q_3: ┤ H ├─┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "     ├───┤ │         │         │         │         │         │        »\n",
       "q_4: ┤ H ├─┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "     ├───┤ │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "q_5: ┤ X ├─■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "     └───┘                                                            »\n",
       "c: 5/═════════════════════════════════════════════════════════════════»\n",
       "                                                                      »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ─■────────────────────────────────────────────────────────────────────»\n",
       "«      │                                                                    »\n",
       "«q_3: ─┼─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │         │         │         │         │         │         │        »\n",
       "«q_4: ─┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_3: ─■─────────■──────────────────────────────────────────────────────────»\n",
       "«      │         │                                                          »\n",
       "«q_4: ─┼─────────┼─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                                                           »\n",
       "«q_0: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_1: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_2: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_3: ──────────────────────────────────────────────────────────────────────»\n",
       "«                                                                           »\n",
       "«q_4: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) »\n",
       "«q_5: ─■─────────■─────────■─────────■─────────■─────────■─────────■────────»\n",
       "«                                                                           »\n",
       "«c: 5/══════════════════════════════════════════════════════════════════════»\n",
       "«                                                                           »\n",
       "«                                             ┌──────────┐ ░ ┌─┐            \n",
       "«q_0: ────────────────────────────────────────┤0         ├─░─┤M├────────────\n",
       "«                                             │          │ ░ └╥┘┌─┐         \n",
       "«q_1: ────────────────────────────────────────┤1         ├─░──╫─┤M├─────────\n",
       "«                                             │          │ ░  ║ └╥┘┌─┐      \n",
       "«q_2: ────────────────────────────────────────┤2 IQFT_dg ├─░──╫──╫─┤M├──────\n",
       "«                                             │          │ ░  ║  ║ └╥┘┌─┐   \n",
       "«q_3: ────────────────────────────────────────┤3         ├─░──╫──╫──╫─┤M├───\n",
       "«                                             │          │ ░  ║  ║  ║ └╥┘┌─┐\n",
       "«q_4: ─■─────────■─────────■─────────■────────┤4         ├─░──╫──╫──╫──╫─┤M├\n",
       "«      │P(2π/3)  │P(2π/3)  │P(2π/3)  │P(2π/3) └──────────┘ ░  ║  ║  ║  ║ └╥┘\n",
       "«q_5: ─■─────────■─────────■─────────■─────────────────────░──╫──╫──╫──╫──╫─\n",
       "«                                                          ░  ║  ║  ║  ║  ║ \n",
       "«c: 5/════════════════════════════════════════════════════════╩══╩══╩══╩══╩═\n",
       "«                                                             0  1  2  3  4 "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create and set up circuit\n",
    "qpe3 = QuantumCircuit(6, 5)\n",
    "\n",
    "# Apply H-Gates to counting qubits:\n",
    "for qubit in range(5):\n",
    "    qpe3.h(qubit)\n",
    "\n",
    "# Prepare our eigenstate |psi>:\n",
    "qpe3.x(5)\n",
    "\n",
    "# Do the controlled-U operations:\n",
    "angle = 2*math.pi/3\n",
    "repetitions = 1\n",
    "for counting_qubit in range(5):\n",
    "    for i in range(repetitions):\n",
    "        qpe3.cp(angle, counting_qubit, 5);\n",
    "    repetitions *= 2\n",
    "\n",
    "# Do the inverse QFT:\n",
    "qpe3 = qpe3.compose(QFT(5, inverse=True), range(5))\n",
    "\n",
    "# Measure of course!\n",
    "qpe3.barrier()\n",
    "for n in range(5):\n",
    "    qpe3.measure(n,n)\n",
    "\n",
    "qpe3.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f6c02baf-6489-487c-855d-cfd6eb2aee77",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the results!\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "shots = 4096\n",
    "t_qpe3 = transpile(qpe3, aer_sim)\n",
    "results = aer_sim.run(t_qpe3, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "495d9944-3c49-4ff2-bbee-2983eac811ad",
   "metadata": {},
   "source": [
    "The two most likely measurements are now `01011` (decimal 11) and `01010` (decimal 10). Measuring these results would tell us $\\theta$ is:\n",
    "\n",
    "$$\n",
    "\\theta = \\frac{11}{2^5} = 0.344,\\;\\text{  or  }\\;\\; \\theta = \\frac{10}{2^5} = 0.313\n",
    "$$\n",
    "\n",
    "These two results differ from $\\frac{1}{3}$ by 3% and 6% respectively. A much better precision!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f27e8868-ad8a-4019-9ca4-0b52af36b984",
   "metadata": {},
   "source": [
    "## Exercises <a id='exercises'></a>\n",
    "1. Try the experiments above with different gates ($\\text{CNOT}$, Controlled-$S$, Controlled-$T^\\dagger$). What results do you get?\n",
    "\n",
    "2. Try the experiment with a Controlled-$Y$-gate. What do you notice?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2388b8e-abc8-46cf-9400-f12e950f1538",
   "metadata": {},
   "source": [
    "## Looking Forward <a id='looking_forward'></a>\n",
    "\n",
    "The quantum phase estimation algorithm may seem pointless, since we have to know $\\theta$ to perform the controlled-$U$ operations on our quantum computer. We will see in later chapters that it is possible to create circuits for which we don’t know $\\theta$, and for which learning theta can tell us something very useful (most famously how to factor a number!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1773b039-b8dc-4ac1-8ed9-6c87014fb22a",
   "metadata": {},
   "source": [
    "## References <a id='references'></a>\n",
    "\n",
    "[1] Michael A. Nielsen and Isaac L. Chuang. 2011. Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.). Cambridge University Press, New York, NY, USA.\n",
    "\n",
    "[2] https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm\n",
    "\n",
    "[3] https://quantumai.google/cirq/experiments/textbook_algorithms#phase_estimation"
   ]
  }
 ],
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