{ "cells": [ { "cell_type": "markdown", "id": "bc8aecb7", "metadata": {}, "source": [ "# Learning Outcomes\n", "- QFT's counting perspective \n", "- Quantum Phase Estimation\n", "- Shor's Algorithm\n", "- Grover's Algorithm" ] }, { "cell_type": "markdown", "id": "4491e382", "metadata": {}, "source": [ "## 2. Intuition \n", "\n", "The quantum Fourier transform (QFT) transforms between two bases, the computational (Z) basis, and the Fourier basis. The H-gate is the single-qubit QFT, and it transforms between the Z-basis states $|0\\rangle$ and $|1\\rangle$ to the X-basis states $|{+}\\rangle$ and $|{-}\\rangle$. In the same way, all multi-qubit states in the computational basis have corresponding states in the Fourier basis. The QFT is simply the function that transforms between these bases.\n", "\n", "$$\n", "|\\text{State in Computational Basis}\\rangle \\quad \\xrightarrow[]{\\text{QFT}} \\quad |\\text{State in Fourier Basis}\\rangle\n", "$$\n", "\n", "$$\n", "\\text{QFT}|x\\rangle = |\\widetilde{x}\\rangle\n", "$$\n", "\n", "(We often note states in the Fourier basis using the tilde (~)).\n", "\n", "### 2.1 Counting in the Fourier basis: \n", "\n", "In the computational basis, we store numbers in binary using the states $|0\\rangle$ and $|1\\rangle$:\n", "\n", "![zbasiscounting](images/zbasis-counting.gif)\n", "Note the frequency with which the different qubits change; the leftmost qubit flips with every increment in the number, the next with every 2 increments, the third with every 4 increments, and so on. In the Fourier basis, we store numbers using different rotations around the Z-axis:\n", "\n", "![fbasiscounting](./images/fourierbasis-counting.gif)\n", "\n", "The number we want to store dictates the angle at which each qubit is rotated around the Z-axis. In the state $|\\widetilde{0}\\rangle$, all qubits are in the state $|{+}\\rangle$. As seen in the example above, to encode the state $|\\widetilde{5}\\rangle$ on 4 qubits, we rotated the leftmost qubit by $\\tfrac{5}{2^n} = \\tfrac{5}{16}$ full turns ($\\tfrac{5}{16}\\times 2\\pi$ radians). The next qubit is turned double this ($\\tfrac{10}{16}\\times 2\\pi$ radians, or $10/16$ full turns), this angle is then doubled for the qubit after, and so on. \n", "\n", "Again, note the frequency with which each qubit changes. The leftmost qubit (`qubit 0`) in this case has the lowest frequency, and the rightmost the highest. \n" ] }, { "cell_type": "markdown", "id": "5933ba9b", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Let's say we are using 3 qubits to represent numbers between 0-7. Answer the following:\n", "- How do we represent $|3\\rangle$ in z basis?\n", "- How do we represent $|\\widetilde{3}\\rangle$? That is how much do we rotate each qubit?\n", "- How do we represent $|6\\rangle$ in z basis?\n", "- How do we represent $|\\widetilde{6}\\rangle$? That is how much do we rotate each qubit? " ] }, { "cell_type": "markdown", "id": "6e431f51", "metadata": {}, "source": [ "### Answer\n", "\n", "?" ] }, { "cell_type": "markdown", "id": "d9aca03e", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "# Quantum Phase Estimation" ] }, { "cell_type": "markdown", "id": "6fd2ca96", "metadata": {}, "source": [ "## Contents\n", "\n", "1. [Overview](#overview) \n", " 1.1 [Intuition](#intuition) \n", " 1.2 [Mathematical Basis](#maths)\n", "2. [Example: T-gate](#example_t_gate) \n", " 2.1 [Creating the Circuit](#creating_the_circuit) \n", " 2.2 [Results](#results) \n", "3. [Getting More Precision](#getting_more_precision) \n", " 3.1 [The Problem](#the_problem) \n", " 3.2 [The Solution](#the_solution) \n", "4. [Experimenting on Real Devices](#real_devices) \n", " 4.1 [With the Circuit from 2.1](#circuit_2.1) \n", "5. [Exercises](#exercises) \n", "6. [Looking Forward](#looking_forward)\n", "7. [References](#references)\n", "8. [Contributors](#contributors)" ] }, { "cell_type": "markdown", "id": "14c076ec", "metadata": {}, "source": [ "Quantum phase estimation is one of the most important subroutines in quantum computation. It serves as a central building block for many quantum algorithms. The objective of the algorithm is the following:\n", "\n", "Given a unitary operator $U$, the algorithm estimates $\\theta$ in $U\\vert\\psi \\rangle =e^{\\boldsymbol{2\\pi i} \\theta }|\\psi \\rangle$. Here $|\\psi\\rangle$ is an eigenvector and $e^{\\boldsymbol{2\\pi i}\\theta}$ is the corresponding eigenvalue. Since $U$ is unitary, all of its eigenvalues have a norm of 1." ] }, { "cell_type": "markdown", "id": "85b72760", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Prove that given a unitary operator $U$, its eigenvalues have norm 1.\n", "Hint: $U |n\\rangle = n | n \\rangle $" ] }, { "cell_type": "markdown", "id": "2cf1d71f", "metadata": {}, "source": [ "### Answer\n" ] }, { "cell_type": "markdown", "id": "cf4a9c4f", "metadata": {}, "source": [ "## 1. Overview " ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "7f69303a", "metadata": {}, "source": [ "The general quantum circuit for phase estimation is shown below. The top register contains $t$ 'counting' qubits, and the bottom contains qubits in the state $|\\psi\\rangle$:\n", "\n", "![image.png](attachment:image.png)\n", "\n" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "cefc9f3c", "metadata": {}, "source": [ "### 1.1 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](attachment:image.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" ] }, { "cell_type": "markdown", "id": "b77da0d0", "metadata": {}, "source": [ "### 1.2 Mathematical Foundation \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", "$$ \\psi_0 = \\lvert 0 \\rangle^{\\otimes n} \\lvert \\psi \\rangle$$\n", "\n", " \n", "\n", "ii. **Superposition**: Apply a $n$-bit Hadamard gate operation $H^{\\otimes n}$ on the counting register: \n", "\n", "\n", "\n", "$$ \\psi_1 = {\\frac {1}{2^{\\frac {n}{2}}}}\\left(|0\\rangle +|1\\rangle \\right)^{\\otimes n} \\lvert \\psi \\rangle$$\n", "\n", "\n", "\n", "iii. **Controlled Unitary Operations**: We need to introduce the controlled unitary $C-U$ that applies the unitary operator $U$ on the target register only if its corresponding control bit is $|1\\rangle$. Since $U$ is a unitary operatory 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 $C − U^{2^j}$ 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", "\\begin{aligned}\n", "\\psi_{2} & =\\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", "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 Qiskit Implementation](https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html). 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]." ] }, { "cell_type": "markdown", "id": "b97903c7", "metadata": {}, "source": [ "## 2. Example: T-gate " ] }, { "cell_type": "markdown", "id": "3815729a", "metadata": {}, "source": [ "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!)" ] }, { "cell_type": "markdown", "id": "d2687138", "metadata": {}, "source": [ "### 2.1 Creating the Circuit \n", "Let's first prepare our environment:" ] }, { "cell_type": "code", "execution_count": 1, "id": "b9eda711", "metadata": {}, "outputs": [], "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\n", "from qiskit.visualization import plot_histogram" ] }, { "cell_type": "markdown", "id": "1e67d426", "metadata": {}, "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:" ] }, { "cell_type": "code", "execution_count": 2, "id": "3fd7e692", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qpe = QuantumCircuit(4, 3)\n", "qpe.x(3)\n", "qpe.draw()" ] }, { "cell_type": "markdown", "id": "2780ca27", "metadata": {}, "source": [ "Next, we apply Hadamard gates to the counting qubits:" ] }, { "cell_type": "code", "execution_count": 3, "id": "2e06194a", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "for qubit in range(3):\n", " qpe.h(qubit)\n", "qpe.draw()" ] }, { "cell_type": "markdown", "id": "12fa595f", "metadata": {}, "source": [ "Next we perform the controlled unitary operations. **Remember:** Qiskit orders its qubits the opposite way round to the image above." ] }, { "cell_type": "code", "execution_count": 4, "id": "fa15fc6f", "metadata": {}, "outputs": [ { "data": { "image/png": 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HsCwrpK2gIL/Z9X/615/rlZnxDbbDReua/TwFBfkh1xkJW3N7z0avI2Gj122zjcrMDul1MlAr3XB9D8/rjeTt3u9MDanXlWfqPK810rc5M0O4ntCWincd9rzWSN/m/+wFBYLNANjS2g82eF5rc7dQheWFtwkJCZKkoqIiTZgwoX58wYIFOnLkiDIzMxv9vhdffFGTJk1yo8QmjZg4t9ELbwEAoTlbFdpi+0CgTpXnK9q4GrOF2utz1eVtXIn5zoZwEYltB1QRylsraNK56i9lWU3PZQcCdaqoLHOpIveFZchPSkpSenq6cnNz1a1bNyUmJiovL08rVqyQpEZD/rPPPqs9e/bogw8+COkYdoj3BHtppbTXo9taZWVlK2++OfcuW7XQ+W+ovce1o9fuoddtw7al9f8R5MJaS+qR7FfV+XOu1WWiulpp7SvBl5Gkjozn57yFzp+T1r7a9DISy/Ip555bZL9Ar1vi7Enpozeb3sfn8+v7P7xLP37dzF6H5XIdn8+nJUuWKC0tTbNmzdL06dOVkJCgOXPmyO/3Kz09vcH+8+fP17vvvqv3339fnTpx3ykAiHSWJd00MshOtnTT11wpx2j+KKnf8Kb38fmlftzUrsViOkmJ6U3sYElRsUH2QUg63yB1H9TEDpYUGyf1utm1klwXljP5kpSSkqLVq1c3GJs2bZpuueUWdezYsX7s2Wef1YoVK7Ry5UrFx8e7XCUAoK30vlWq+tK5Bd5XWZZ0y3gpvo/7dZlowEipukIqLZRkqcEFz74o5z75nW/wqjqzpORI1WedWzh+tddRMdLQyU74RMuljZe2/EU6fUhX9Dq2szRsiuQ3+D75YRvyG7NhwwaNHHlpamfHjh165plnNHDgQGVnZ9ePb9myxf3iLvju0/nNGgcANM6ypIFfl3qmOLdvLCl0xm+63Znp5MOZWo9lSTePcU6sSrZIR3Y44wO/IfW+zQlEaB0+v3PSVHbIuYvO0Qu3y0zJkW5Mk6I7eFufSaJipcwp0oli505cx3c74zffJd042OyAL0VQyK+oqFBRUZFmz55dP5aWlsb6QAAwXFx355fyxZA/6Jve1mMqy5Kuv9HZLob8AcGWTOGaWJbUrZ+zXQz5/Rq/pwhayPJJ3Qc628VrqPpkeFuTWyIm5MfFxamujpshAwAAAMGE5YW3AAAAAK4dIR8AAAAwDCEfAAAAMAwhHwAAADAMIR8AAAAwDCEfAAAAMAwhHwAAADBMxNwn3yuJXdvnsQEAABC5CPlB3Dvc6woAAACA5mG5DgAAAGAYQj4AAABgGEI+wkJ+fr769++v7OxsTZw4UVVVVQ0eX7hwoTZv3nzV7y8tLdVjjz1W//WvfvUrfeMb35AkFRYWasGCBW1SdySi1+6h1+6h1+6h1+6h1+4xsdeEfISNadOmKT8/X6NHj1ZeXl79eCAQ0IcffqihQ4de9XtXrlypu+66S5JUXV2tLVu21D+WkZGhjz76SLZtt1ntkYZeu4deu4deu4deu4deu8e0XhPyEXaGDBmikpKS+q8LCws1aNAgSc6ZdteuXZWdna3+/ftr4sSJkqSCggJlZWVJkn7/+9/rwQcfbPCcycnJTZ6Bt1f02j302j302j302j302j2m9JqQj7CzZs0apaSk1H+9e/du3XTTTZKkO+64QyNGjFB+fr6ysrL029/+VrZt6+zZs4qLi1NNTY3y8/N15513NnjOpKQk7dy5082/RkSg1+6h1+6h1+6h1+6h1+4xpdeEfISNP/zhD8rJydHp06frz4y/at++fUpKSpIkHTp0SImJiSosLFRGRkb9c3zve99zreZIRa/dQ6/dQ6/dQ6/dQ6/dY1qvCfkIG9OmTdPq1av18ssvy+/3148nJydr//79kqQdO3YoLS1NdXV18vmcH9/L18Ht2rVLr7zyisaNG6cdO3bopZdekuT8o7z55pvd/QuFMXrtHnrtHnrtHnrtHnrtHtN6TchH2MvIyFBRUZGkS/+4qqurdezYMR05ckQbNmzQ8OHOp5Y9//zz+tvf/qb3339faWlpevTRRyVJRUVFGjJkiFd/hYhBr91Dr91Dr91Dr91Dr90Tqb3mE28RFrKzs5Wdnd3oYz6fT9/85je1efNm/fSnP60f37ZtmyRp8uTJ9WfTl1u3bp0k54KZUaNGNbpPe0Sv3UOv3UOv3UOv3UOv3WNiry2beyfBJasWOv8d85S3dbQH9No99No99No99No99No97a3XnL4BAAAAhiHkAwAAAIZhTX4QT+76TIXl5Z4cO6NLF/2f1Fs8OTYAAAAiFyE/iMLycq0pO+V1GQAAAEDIWK4DAAAAGIaQDwAAABiGkA8AAAAYhpAPAAAAGIaQDwAAABiGkA8AAAAYhpAPAAAAGIaQDwAAABiGkA/XBQJeV2A2277sz/S6TTXotX31/dBy9No9vG64J1DndQXtR3vsdViH/EAgoIULFyo5OVkdOnRQRkaGCgoKlJqaqpkzZ3pdXqPsmhrV/OsPVffa7xqM1y37i2q+/6DsigqPKvPO0SLpn3+89PXa30p71ko1ld7VZCLblg5vkz55+9LYutel4o+luvPe1WWiQEA6uEla//tLY+v/Qzq4sX3+ImlLdTXS/k+cn+WLPn5LKt1K2G9tNVXS3nXSmlcujX36X9LRnfS6tVWflYpWSwUvXxrb+N/SiX3e1WSqytPS5yul/JcujW1ZJp0u8awk10R5XUBTZsyYoaVLl2revHnKzMzU+vXrNXXqVB0/flxPPPGE1+U1yoqOVtRPfqTaRx+TNeJr8g0dIru4WIE33pL/5/9bVlyc1yW6au86J2TKujRWU+X80j66Sxo+VYrt7Fl5xrBt6fO/OyH/8l5XVzj/D47tljLvl6JiPCvRGIE6aety6cTehuOVZ5xf2ieKpSH3SD6/N/WZpO68tClPOnO44fjZE87Pe1mJlDZesqzGvx+hO39O2vAn6dyphuNffiFte1fqf1RKzvKmNtNUnpE2LHZeny9XViKVHZKSs6X+wz0pzTjlx6WNf5JqqxuOn9jnvIanTZBuvMWb2twQtjP5ixcv1qJFi7R8+XI99dRTysnJ0dy5czVq1CjV1tZq2LBhXpd4VdZN/eV7+EHVLfyV7FOnVPuLF+Sb+B350m/zujRXnTpwIeBLUiOzQJWnpZ0r3azIXF98fiHgS432uvyotGeNqyUZ6+DGKwP+5U7tl/Z/6lo5Rtvz4ZUB/3JffCYd3u5ePSbb9Y8rA76k+teTA/9klrm17FjhzORf4UKvd+c7J1doGduWtv5Vqm3snewLvf7sPanqS1fLclXYhvzc3FyNGzdOWVkNpw4GDRqk6OhopaenS5ImTZqk9PR0DR06VCNGjNCqVau8KPcKvkkTZfXrq9pH5kh+v3wPTvO6JNcd2qwGs8qNOb7H7H9gbjm0SUF7fXj7lbMZaB47cOHnOoiSzSzbaam689LhrUF2sqRDG1lK0lLVFc6yyiZZF15n0CIVx6XTpWp0MuZyJVvcqMZspw44k4lN9dq2pZJgrzMRLCxDfklJibZv364pU6Zc8djBgweVlpam2NhYSdKiRYu0detWbd68Wa+99pomT56surrgv10tywppy8/Pv6a/g2VZstJvk86cke9/3CkrOrrZz5Gfnx9yneG4Hdj+ZdAXMkn6dva/eF5rJG+x0R2dWZ8gvQ7USl9Lu9PzeiN56909SdXlwX+mz5+TBvQe7Hm9kbxlpH5ddTVBGm1LFSekLp3iPa83kre7Rn83+Gu1LR3ZU+V5rZG+ff+eR4O/gEjavPaA57VG+vbvs3JlB7mK3LZtvbv4Q89rbe4WqrAN+ZLUq1evBuOVlZUqKChosFQnPj6+/s9nzpyRZVmyw2Baxy4uVuCPf5Lv/ikK/OcfZR875nVJrvOFuCg51P3QuOb0j163jL85vbbodUs0p3/8XLdMyK/V/Ey3WKg9bM5rDRrn8/mDnrtalmV0r8PywtuEhARJUlFRkSZMmFA/vmDBAh05ckSZmZkN9p8zZ47ee+89nTlzRu+8846iooL/tUI9ERiz4ROtKWtsoWITz32+xlmHf+8k+ac/KLusTHUv/FL+53Nl+UI/r8rOztaqMDhhuVYb/hTa25LL3n9bcQlvN70Trsq2nbu8VJ4OsqMlrd+8kgudWyBQK615Vaqtano/f4y059B2+Zv/Bh4uOF8prX0l+O0cO3SRzlScVDMmt/AV58oa3imqUZbULTE6LCbRItnpEud3Y5MsaXBmH3rdQkd3OheNB3PXxJGyXzKz12E5k5+UlKT09HTl5ubq7bff1j/+8Q/NmjVLb7zxhiRdEfJffvll7du3T0uXLtWPfvQjVXh8m8rAG2/KioqSb9q/SJL8s/9V9hdHFXhnmad1ua3vEDUd8C0pPlGKS3CpIENZltR3aLCdpJ4p3MmopXxRUmJ68P163yYCfgvFdJR63ayg15r0GcrddVqqU1epa3813Ws7hNcZBHV9otT5BgXtdR963WLdk6Xojgr+GjLEjWq8EZYh3+fzacmSJUpLS9OsWbM0ffp0JSQkaM6cOfL7/fUX3X5VVlaWfD6fPvzwQ5crviSweYsCK96X/yf/LuvCOwpWp07y//gpBd7+T9nFxZ7V5rYeqVLP1Ks8aDm3cxw81tWSjNVniNS171UetJxwn5ztYkEGG3C7FNf96o93vkFKGuVePSYblOXM1F/tl3R8otQ3fG+0FlEGj5GiY3XVXndPlnoNdrUkI1mWc9tXn19X7XVihtStn6tlGcnnl26dcGES4Cq9Thpt9kSjZUfQ+0HTpk1TYWGhtm51LoWuqKjQyZMn1b9/f0nS5s2bdeedd6qwsFD9+rXOv5BrWa7TWu7o2k2rht/uybFbix1wbid4aJNzMaIkyZK6D5IGfVPq3M3T8oxSVyvtWy+VFl66i47lk3reLCXfIcW2r49oaFO11c4Huh3e7izhkZxZ/hvTnJ/r6A7e1meS6rPO7V+/+PzS0h1/jPOOysCv845Jazp32un1sd2qfxc2uqMzg3/TSKkZq00RRPlxp9cnL5v3i42T+n/NOXHl3anWc7pU2rNOOn3o0ljHeGnASKn3rZ6V5YqICvmDBw/WyJEj9eabb0qSjh49qokTJ6qiokJRUVHq0KGD5s2bp29/+9utdkxCfusI1Enlx5xA1KkrgbMt1dU4v0AUkDp1k2I6eV2RuWqrnbu7SM5sUFSst/WYrKZSOntSkk/q0p1w35aqzzrr9H1+qUsPPtitLVV96Xw4lj/a6bXFiVSbOXdaqi53XqfjurePE6mwvPC2MRUVFSoqKtLs2bPrx3r27KmPP/64ie9CuPD5petv9LqK9sEfLcX39rqK9iEq1lkygrYX3VGK7+N1Fe1DbGeu33FLh+ucDW2vU7yztScRE/Lj4uJCuv89AAAA0N7xxhAAAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgmIi5T75XMrp0aZfHBgAAQOSybNu2vS4CAAAAQOthuQ4AAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgGEI+AAAAYBhCPgAAAGAYQj4AAABgGEI+AAAAYBhCPgAAAGCYKK8LCFdjx47VsWPHVFdXp9TUVL3xxhu67rrrvC4LAAAACMqybdv2uohwdObMGV1//fWSpMcee0zx8fF65plnvC0KAAAACAHLda7iYsAPBAKqqqqSZVkeVwQAAACEhpDfhHvuuUc9evTQrl279OSTT3pdDgAAABASQn4Tli1bpsOHD6tPnz7Ky8vzuhwAAAAgJIT8IGJiYvTAAw9o2bJlXpcCAAAAhISQ34jy8nIdOXJEkrMmf/ny5UpLS/O4KgAAACA03EKzEeXl5Zo4caKqq6sVCAR0++236+mnn5Yk2bbNRbgAAAAIa9xCs5nyP96i0i+O6/7v3Kkov9/rcgAAAIArsFynGaqrz2vNJ4U6X1NLwAcAAEDYiviQv23bNk2ePFkJCQnq0KGDkpOTNXfu3DY51vpNO3Suqlpjvp7ZJs8PAAAAtIaIXpO/ceNG3XHHHerbt69eeOEF9e/fX8XFxVq/fn3Q7/3J869f83Ff/sNfrvl7AQAAgGv1ix/PDGm/iA75Tz75pDp37qxPPvmk/hNqJWnGjBkeVgUAAAB4K2IvvD137py6dOmiH/7wh/r1r3/dpseqrj6v519drL69e2j6lPFteiwAAACgpSJ2Jr+srEyBQEB9+vS5pu+/luU6u/YdatEyHwAAAKAlQl2uE7EX3nbt2lU+n0+lpaVelwIAAACElYhdriNJOTk5+uyzz7R7925dd911bXKM1R9t1t/W/FNzpk1S39492uQYAAAAQGuK2Jl8SVq4cKEqKio0cuRILVq0SKtXr9Zbb72lH/zgB63y/NXV57X2061KTepLwAcAAEDEiNg1+ZKUmZmpjz76SPPmzdPjjz+uqqoq9e3bVw888ECrPP+pM+Xq2DGW++IDAAAgokT0ch03BAIB+XwR/YYHAAAA2hlCPgAAAGAYpqgBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADDEPIBAAAAwxDyAQAAAMMQ8gEAAADD/H/VBGakKp/3+wAAAABJRU5ErkJggg==\n", 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" ] }, "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); # This is C-U\n", " repetitions *= 2\n", "qpe.draw()" ] }, { "cell_type": "markdown", "id": "3d073d47", "metadata": {}, "source": [ "We apply the inverse quantum Fourier transformation to convert the state of the counting register. Here we provide the code for $QFT^\\dagger$:" ] }, { "cell_type": "code", "execution_count": 5, "id": "2bc691f1", "metadata": {}, "outputs": [], "source": [ "def qft_dagger(qc, n):\n", " \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n", " # Don't forget the Swaps!\n", " for qubit in range(n//2):\n", " qc.swap(qubit, n-qubit-1)\n", " for j in range(n):\n", " for m in range(j):\n", " qc.cp(-math.pi/float(2**(j-m)), m, j)\n", " qc.h(j)" ] }, { "cell_type": "markdown", "id": "5103e4d9", "metadata": {}, "source": [ "We then measure the counting register:" ] }, { "cell_type": "code", "execution_count": 6, "id": "949685c4", "metadata": {}, "outputs": [], "source": [ "qpe.barrier()\n", "# Apply inverse QFT\n", "qft_dagger(qpe, 3)\n", "# Measure\n", "qpe.barrier()\n", "for n in range(3):\n", " qpe.measure(n,n)" ] }, { "cell_type": "code", "execution_count": 7, "id": "6463515f", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qpe.draw()" ] }, { "cell_type": "markdown", "id": "52a77e04", "metadata": {}, "source": [ "### 2.2 Results " ] }, { "cell_type": "code", "execution_count": 8, "id": "b70b5294", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAc0AAAFCCAYAAACTo4YQAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAaTElEQVR4nO3df7SdVZ3f8feXREBMUBKGkJtLxBiqNRFBjgh4gegyQ4FVVLAiC0xTKimxEpE6M7oGqXEQp+owME4Zh8wsIWhbFDtaJUAYJUYhXLyJjYI2SQfMmJDckCEYlZAAfvvHc5I5vdwf+yQ3957kvF9rnZVz9t7Pvt/nD/is59d+IjORJElDO2S0C5Ak6UBhaEqSVMjQlCSpkKEpSVIhQ1OSpEJjR7uA0XT00Ufn8ccfP9plSJJayMqVK7dm5u/119fWoXn88cfT09Mz2mVIklpIRKwfqM/Ts5IkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE3pIHT55ZdzzDHHMHPmzH77M5MFCxYwffp0TjzxRFatWrWn7/bbb+eEE07ghBNO4Pbbb9/TvnLlSt74xjcyffp0FixYQGbu9/2QWo2hKR2E5s6dy7333jtg/z333MO6detYt24dt956K/Pnzwfg6aefZuHChXR3d/PII4+wcOFCtm3bBsD8+fNZtGjRnu0Gm186WBma0kHorLPOYsKECQP2f+tb32LOnDlEBKeddhrPPPMMmzZt4r777mP27NlMmDCBo446itmzZ3PvvfeyadMmtm/fzmmnnUZEMGfOHL75zW+O3A5JLcLQlNrQxo0bOe644/b87uzsZOPGjYO2d3Z2vqRdajeGpiRJhQxNqQ1NmTKFX/7yl3t+b9iwgSlTpgzavmHDhpe0S+3G0JTa0AUXXMDixYvJTB5++GFe+cpXMnnyZM455xyWLl3Ktm3b2LZtG0uXLuWcc85h8uTJHHnkkTz88MNkJosXL+Zd73rXaO+GNOLGjnYBkobfJZdcwrJly9i6dSudnZ0sXLiQ559/HoArr7yS8847jyVLljB9+nSOOOIIvvzlLwMwYcIEPvnJT/KWt7wFgOuuu27PDUW33HILc+fOZceOHZx77rmce+65o7Nz0iiKdn7WqlarZU9Pz2iXIUlqIRGxMjNr/fV5elaSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUqERDc2IOCsi/ldEbIyIjIi5Bdu8MSK+HxE76ttdFxHRZ8xFEfGziNhZ//c9+20nJElta6SPNMcBjwIfAXYMNTgijgTuB3qBt9S3+wPgmoYxpwN3Al8FTqr/+/WIeOsw1y5JanMjuvZsZi4BlgBExG0Fm1wKHAH828zcATwaEa8HromIG7NaA/Bq4IHM/Ex9m89ExNvr7ZcM7x5IktpZq1/TPB34QT0wd7sP6ACObxiztM929wFn7PfqJEltpdXfcnIssKFPW29D3xP1f3v7GXNsfxNGxDxgHkBHRwfLli0DYNq0aYwfP57Vq1cDMHHiRGbMmMHy5csBGDt2LF1dXaxatYrt27cDUKvV6O3t5U+//dp92UdJ0jD49MWbWLNmDVC9M7azs5Pu7m4Axo0bR61WY8WKFezcuROArq4u1q5dy5YtWwCYOXPmnr6BjNpbTiLiN8CHM/O2QcYsBTZk5uUNbVOB9cAZmbkiInYBH8zMxQ1j5gCLMvOwwWoYrrecXHHTPk8hSdpHi64ennkO5LecbAYm9Wmb1NA32JjNSJI0jFo9NFcAZ0bE4Q1ts4EngV80jJndZ7vZwEP7vTpJUlsZ6ec0x0XESRFxUv1vT63/nlrv/2xEfLdhk/8GPAvcFhEzI+JC4OPA7jtnAW4G3hERH4+I10fEJ4C3AzeN0G5JktrESB9p1oAf1z8vBxbWv3+63j8Z2HNXTWb+iuqosQPoAf4r8GfAjQ1jHgLeD8wFfgLMAS7OzO79uyuSpHYz0s9pLgNikP65/bT9FDhriHnvAu7ax/IkSRpUq1/TlCSpZRiakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklSoqdCMiEMi4pCG38dGxAcj4m3DX5okSa2l2SPNu4GrACJiHNADfB5YFhFzhrk2SZJaSrOhWQO+V/9+IbAdOAa4AvhYyQQR8aGIeCIinouIlRFx5iBjb4uI7Ofz24YxswYY8/om902SpEE1G5rjgGfq338f+LvMfJ4qSF871MYRcTFwM3ADcDLwEHBPREwdYJOPAJP7fB4HvtbP2Bl9xq0r2iNJkgo1G5r/CLwtIl4BnAPcX2+fADxbsP01wG2ZuSgzf56ZVwGbgPn9Dc7MX2Xm5t0fqmCeBizqZ/iWxrGZ+WKT+yZJ0qDGNjn+RuAO4DfAemB5vf0s4KeDbRgRhwKnAF/o07UUOKPw718BPJaZD/XT1xMRhwE/A67PzAcGqGMeMA+go6ODZcuWATBt2jTGjx/P6tWrAZg4cSIzZsxg+fJqF8eOHUtXVxerVq1i+/btANRqNXp7eyk4yJYk7WebNm1izZo1AEyZMoXOzk66u7sBGDduHLVajRUrVrBz504Aurq6WLt2LVu2bAFg5syZe/oGEpnZVFERUQOOA+7PzN/U284HnsnMBwfZrgPYCJydmcsb2q8DLs3M1w3xd19JdVT6icy8uaH9dcDbgR8BhwIfAK6s/50fDDZnrVbLnp6ewYYUueKmfZ5CkrSPFl09PPNExMrMrPXX1+yRJpnZQ3XXbGPb3XtZWzMuozqdfEefv70GWNPQtCIijgf+ABg0NCVJakbTixvU7359LCKejYhp9bY/ioj3DbHpVuBFYFKf9knA5oI/fQXwjcx8umBsN3BCwThJkoo1u7jB1cC1wK1ANHQ9CXx4sG0zcxewEpjdp2s21V20g/3dU4E30f8NQP05iepUriRJw6bZ07NXAldk5t0RcX1D+yqqRz6GciNwR0Q8AjxYn68D+BJARCwGyMy+CyXMA9Zl5rK+E9aD/BfAY1TXNC8D3g1cVLhPkiQVaTY0Xw082k/788DLh9o4M++MiIlUR6uT63Odl5nr60Ne8rxmRIwH3g98eoBpD6ValagT2EEVnudn5pKh6pEkqRnNhubjwJupHjdpdB7Vox5DysxbgFsG6JvVT9uvqRZVGGi+zwGfK/nbkiTti2ZD8wvAX0bEEVTXNE+PiA8AfwhcPtzFSZLUSpoKzcz8ckSMpVoG7wiqxz+eBBZk5p37oT5JklrG3jynuQhYFBFHA4dk5pbhL0uSpNbTdGjulplbh7MQSZJa3ZChGRE/oVqSbltE/BQYcN29zDxxOIuTJKmVlBxpfgPY2fC9ucVqJUk6SAwZmpm5sOH7p/ZrNZIktbBml9H7XkS8qp/2IyPie8NWlSRJLajZBdtnUa3A09fhwJn7XI0kSS2s6O7ZiHhzw88TI6LxTSNjgHOo3pUpSdJBq/SRkx6qG4ASWNpP/w7gquEqSpKkVlQamq+hWjbvceBU4KmGvl3Alsx8cZhrkySppRSFZsNbSJp+abUkSQeLksUNLgS+nZnP178PKDP/57BVJklSiyk50rwLOBbYUv8+kKS6KUiSpINSyeIGh/T3XZKkdmMISpJUqPSaZhGvaUqSDmal1zRLeE1TknRQa+qapiRJ7cxAlCSpkM9pSpJUyOc0JUkq5HOakiQVMgQlSSrUdGhGxJsjYnFE9NQ/d/R536YkSQelpkIzIi4FfgRMBpbUP5OARyLisuEvT5Kk1lH6Ps3dPgN8MjNvaGyMiE8A1wNfGa7CJElqNc2env094Gv9tH8dOGbfy5EkqXU1G5oPALP6aZ8FfH9fi5EkqZU1u2D7PcBnI6IGPFxvOw24EPjUsFcnSVIL2dsF2+fVP42+CNyyzxVJktSiXLBdkqRCBqIkSYWafeSEiDgKOBeYChza2JeZnx6muiRJajlNhWZEnAbcDeykevxkI9VCBzuBXwCGpiTpoNXs6dnPA18FpgDPAe+gOuLsAf7L8JYmSVJraTY0TwT+MjMTeBE4LDN7gT/CR04kSQe5ZkNzV8P3XuDV9e+/ATqGpSJJklpUszcCrQLeAqwFlgHXR8Qk4DLgJ8NbmiRJraXZI80/Bp6sf78WeIpqUYOjeOliB5IkHVSaOtLMzJ6G709RPXoiSVJbaPo5TYCIeC3wL+s/f5aZjw9fSZIktaZmn9OcCPwtcAHwu39uju8Al2fmPw1zfZIktYxmr2n+DTAdOBM4vP45C3gNsGh4S5MkqbU0G5rnAFdk5oOZ+UL98yDwH+p9Q4qID0XEExHxXESsjIgzBxk7KyKyn8/r+4y7KCJ+FhE76/++p8n9kiRpSM2G5lPAb/tpfxYY8tRsRFwM3AzcAJwMPATcExFTh9h0BtVyfbs/6xrmPB24k2qlopPq/349It46VD2SJDWj2dD8NHBTREzZ3VD//meUrTt7DXBbZi7KzJ9n5lXAJmD+ENttyczNDZ8XG/quBh7IzM/U5/wM1TOkVxfvlSRJBYa8ESgifgpkQ9NrgF9ExMb6793r0B5Ddc1zoHkOBU4BvtCnaylwxhBl9ETEYcDPgOsz84GGvtOpnhVtdB/w4SHmlCSpKSV3z941TH/raGAM1fJ7jXqBdw6wze6j0B9RvYbsA8B3I+LszPxBfcyxA8x5bH8TRsQ86gsxdHR0sGzZMgCmTZvG+PHjWb16NQATJ05kxowZLF++HICxY8fS1dXFqlWr2L59OwC1Wo3e3l7gtUPuvCRp/9q0aRNr1qwBYMqUKXR2dtLd3Q3AuHHjqNVqrFixgp07dwLQ1dXF2rVr2bJlCwAzZ87c0zeQqNZe3/8iooPqVWJnZ+byhvbrgEsz83WF8ywBXsjMC+q/dwEfzMzFDWPmAIsy87DB5qrVatnT0zPYkCJX3LTPU0iS9tGiq4dnnohYmZm1/vr2dnGDdwBvoDpt+1hmLivYbCvVm1Em9WmfBGxu4s93A+9v+L15GOaUJGlITd0IFBFTIuIR4H6q14F9nOp0aXf9SHJAmbkLWAnM7tM1m+ou2lInUZ223W3FMMwpSdKQmj3S/Auqo8XpmfkEQERMA75S73vvENvfCNxRD94HgSupXin2pfpciwEyc07999XAL4DHqK5pXga8G7ioYc6bgeUR8XHgm8B7gLcDXU3umyRJg2o2NGcDs3YHJkBmPh4RC4DvDrVxZt5ZX4rvWqrnLR8FzsvM9fUhfZ/XPBT4PNAJ7KAKz/Mzc0nDnA9FxPuB66kee/kH4OLM7G5y3yRJGtTeXNPs786h4ruJMvMW4JYB+mb1+f054HMFc97F8N3lK0lSv5pd3OC7wBcj4rjdDfXVfG6i4EhTkqQDWbOhuQB4BfB4RKyPiPVUp0NfUe+TJOmg1ezp2X8CTgVmAbsXTf95Zv79cBYlSVIrKg7NiBgD/Ap4U2beT/XYiSRJbaP49Gx9kfT1VHe0SpLUdpq9pvknwJ9GxNH7oxhJklpZs9c0P0b1lpONEbGBPu/WzMwTh6swSZJaTbOheRfVM5mxH2qRJKmlFYVmRBxBtTLPu4GXUT2TeVVmbt1/pUmS1FpKr2kuBOYCdwP/ner9l3+1n2qSJKkllZ6evRD495n5PwAi4qvAgxExpn5XrSRJB73SI83jgB/s/pGZjwAvUL2hRJKktlAammOAXX3aXmAvX2ItSdKBqDT0AvhKROxsaDscWBQRz+5uyMwLhrM4SZJaSWlo3t5P21eGsxBJklpdUWhm5r/b34VIktTqml1GT5KktmVoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFRjw0I+JDEfFERDwXESsj4sxBxl4YEUsj4qmI+HVEdEfEBX3GzI2I7Odz+P7fG0lSOxnR0IyIi4GbgRuAk4GHgHsiYuoAm5wNfA84vz5+CfB3/QTts8Dkxk9mPjf8eyBJamdjR/jvXQPclpmL6r+vioh/BcwHPtF3cGZ+pE/Twog4H3g38IP/f2hu3g/1SpK0x4gdaUbEocApwNI+XUuBM5qYajywrU/byyNifURsiIjvRMTJ+1CqJEn9GskjzaOBMUBvn/Ze4J0lE0TEfwQ6gTsamtcAlwOrqQL1I8CDEfGmzFzXzxzzgHkAHR0dLFu2DIBp06Yxfvx4Vq9eDcDEiROZMWMGy5cvB2Ds2LF0dXWxatUqtm/fDkCtVqO3txd4bUn5kqT9aNOmTaxZswaAKVOm0NnZSXd3NwDjxo2jVquxYsUKdu7cCUBXVxdr165ly5YtAMycOXNP30AiM/fjLjT8oYgOYCNwdmYub2i/Drg0M183xPYXUYXlxZn57UHGjQH+N/BAZi4YbM5arZY9PT3lOzGAK27a5ykkSfto0dXDM09ErMzMWn99I3kj0FbgRWBSn/ZJwKDXIyPivVSBOWewwATIzBeBHuCEvS9VkqSXGrHQzMxdwEpgdp+u2VR30fYrIt5HFZhzM/Ouof5ORARwIrBp76uVJOmlRvru2RuBOyLiEeBB4EqgA/gSQEQsBsjMOfXf76cKzI8ByyPi2Po8uzLz6fqY/ww8DKwDjgQWUIXm/BHaJ0lSmxjR0MzMOyNiInAt1fOUjwLnZeb6+pC+z2teSVXjTfXPbt8HZtW/vwq4FTgW+BXwY+CszHxk2HdAktTWRvpIk8y8BbhlgL5Zg/0eYJuPAh8djtokSRqMa89KklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFRjw0I+JDEfFERDwXESsj4swhxp9dH/dcRDweEVfu65ySJO2NEQ3NiLgYuBm4ATgZeAi4JyKmDjD+NcCS+riTgc8CX4yIi/Z2TkmS9tZIH2leA9yWmYsy8+eZeRWwCZg/wPgrgScz86r6+EXA7cDH9mFOSZL2yoiFZkQcCpwCLO3TtRQ4Y4DNTu9n/H1ALSJetpdzSpK0V8aO4N86GhgD9PZp7wXeOcA2xwJ/38/4sfX5otk5I2IeMK/+8zcRsaakeKkNHA1sHe0ipL31Nx8dtqlePVDHSIZmS8jMW4FbR7sOqdVERE9m1ka7DqmVjWRobgVeBCb1aZ8EbB5gm80DjH+hPl/sxZySJO2VEbummZm7gJXA7D5ds6nueO3PigHG92Tm83s5pyRJe2WkT8/eCNwREY8AD1LdHdsBfAkgIhYDZOac+vgvAR+OiJuAvwbeBswFLimdU1IxL1tIQxjR0MzMOyNiInAtMBl4FDgvM9fXh0ztM/6JiDgP+HOqR0ieBBZk5jeamFNSgfr1fkmDiMwc7RokSToguPasJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JRERIyJCP9/IA3B/0ikNhYRpwBk5ouZ+bt625iIiNGtTGpNhqbUpiLiBOBHEfFoRNwYESfDngDNqLwsIk6tv4ZPanuGptS+LgH+AbgfOA34TkQ8HBF/GBHHZbXyyTHAw/V/pbbnikBSm4qIr1K9LeizwESgBpwJnApMAH5M9Sah12TmjNGqU2olbfc+TUkQEWOBu4FXZ+ZmqlfpPRYR3wZeB5wCnAW8F7hi1AqVWoxHmpKIiJdl5vN92i4E7gLGZeazo1OZ1Fq8pim1ob6Pl+wOzIgY23Dn7BnAcgNT+meenpXaU0dETKe6Zvk7YE1mbs7MFwDqwflD4M5RrFFqOZ6eldpMRMwHLgfeBPwW+L/ABqq7ZL+ZmWtGsTyppXl6Vmoj9Re23wB8i+ql7acDtwMvAnOAv4iIN9THjhmtOqVW5ZGm1EYi4irgssx8az99XVSPn0wBTs3MrSNdn9TqPNKU2ssuYHxEzASIiMN2r/aTmT8ELgWeA35/9EqUWpehKbWXu6hu/Lk6IsZn5s7M3LX7btrM/EfgGaBzFGuUWpahKbWJ+h2xTwPXArOBJyPib3cv2h4RUyPiMuCNwNdGr1KpdXlNU2ozEfEqYCrVc5jvAd5W79pM9QjKHZn5qVEpTmpxhqbUBiLiGOADwH+iWm92B9Vp2B9SPWryMmA6cG9mrh2lMqWWZ2hKbSAibgNmAN+mOkU7geo07L8AtgDXZmb3qBUoHSAMTekgV7+W+WvgvMxc3tA2FXgr8EFgGvC+zFw1aoVKBwBvBJIOfm8AnqB63ASArKzPzK8B/5rqVO2/GZ3ypAOHoSkd/B6nOgX75xFxQj+Lte+kWhXo3NEoTjqQGJrSQS4zdwB/DLwcWAzMiYjjImIcQEQcAZwNPDp6VUoHBq9pSm2ivgrQJ4ELqBZqXwE8BbwT2AR8MDN/OnoVSq3P0JTaTP3xk/OBd1Mtmfco8PXM/D+jWZd0IDA0pTYWEYdk5u9Guw7pQGFoSpJUyBuBJEkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYX+Hx5jP9a08jRgAAAAAElFTkSuQmCC\n", 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" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qasm_sim = Aer.get_backend('qasm_simulator')\n", "shots = 2048\n", "t_qpe = transpile(qpe, qasm_sim)\n", "qobj = assemble(t_qpe, shots=shots)\n", "results = qasm_sim.run(qobj).result()\n", "answer = results.get_counts()\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "eef555fe", "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": "f0d19ff4", "metadata": {}, "source": [ "## 3. Example: Getting More Precision \n", "### 3.1 The Problem \n", "\n", "Instead of a $T$-gate, let’s use a gate with $\\theta = \\frac{1}{3}$. We set up our circuit as with the last example:" ] }, { "cell_type": "code", "execution_count": 9, "id": "5604f18f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 9, "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", "qft_dagger(qpe2, 3)\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": 10, "id": "cd20598c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the results!\n", "qasm_sim = Aer.get_backend('qasm_simulator')\n", "shots = 4096\n", "t_qpe2 = transpile(qpe2, qasm_sim)\n", "qobj = assemble(t_qpe2, shots=shots)\n", "results = qasm_sim.run(qobj).result()\n", "answer = results.get_counts()\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "2595487c", "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", "### 3.2 The Solution \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": "f9b5e175", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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J761+XQBAbdTtW9mZM2fmwgsv3BV+7TR27Nj07t07TU1NWbduXT70oQ9l/PjxmTx5ci644II8/fTTNaoYgAPpqdZ3hl9vtX5l8sLDVS2psJ64e0f4tZdev/xs8tLjVS2pkMrl5LG7doRfe+n1i48ma5+valmF1L49eexHqfR5L71een+yYU01qwIAaqkuA7Dly5dn8eLFueyyy96xbdmyZZk0aVL69u2bUqmUz3/+81myZEkWLVqUD33oQ5kxY0YNKgbgQNr6RrLqyez1wHWnFxZaz6e7Nq6trK3WYa9LlVl3dM+ry5M31kavq2D108m2TZ3vt3zhQS8FAKgTdXkK5PLly5Mkw4YN221806ZNaW1tzUUXXZQkOfLII3P++efv2n7uuefmpptu6tJjlLp4bsFHb5ibEadM69K+Oz34r3+Yh+6ctdvYts0bMurU8/dyjz1rbW3J71wwfZ/uU8/uvrnyjr+rvWf/6XX16PXBcdqJ78vXr7mn0/22vJ4cMfCovP7G2ipUVUzNkz+eL33q+x3vVE7WvbgtpZJF17rjP7/3v+eaS77R8U7l5ImHl+eMS0dWpaai+uzFX8tl0/7vNJQ6/qz37jvuzykXnFOlqgCAWqrLAGzo0KFJkiVLluTiiy/eNX7TTTdl5cqVmTp16h7v941vfCMf+chHqlFih8665IY9LoIPQNe0tXf98oPtLp/XLV3tdXtZn7urvYu9bnP5zW5rb29LZx9LlMvltHn9AIBDRl0GYGPGjElTU1NmzpyZIUOGZPjw4Zk9e3buvPPOJNljAPblL385Tz/9dH72s5916THKXTxn5s/vTp5Z3fXaD6Tm5mmZ/dXinNvzkx2T4rrae/afXlePXh8cbduSe/4qadvawU6lZODQ5PU3XrVgeDds2Zjc+9fp9LS848b38zzvpg0vJ/ff2vl+ZzSfkPJMve6OV55PFtze8T6lUikfvvw9+fwteg0APc20adP2+T51uQZYQ0NDbr/99kyaNClXX311ZsyYkaFDh+baa69NY2Njmpqadtv/q1/9an74wx/mrrvuyoABA2pUNQAHSmPvZHhTJzuVk1FTXC2vu/oelgw7uZOdysnIM6pSTqENHJocOTLpbGrSiNOrUU2xDRmVDBicDntdakiGT65aSQBAjdXlDLAkGT9+fObOnbvb2BVXXJGJEyemf//+u8a+/OUv584778zdd9+dI488sspVAnCwnPSeypUeX13xtg2lJOXk+FOT406tRWXFM+H9yeurk42vvG3Djl6f8O5k6Im1qKx4Tr0omX9bsvn1t23Y0evx708GHVuLyoqlVEqaLkke+qdk2+a3b6z8M+nipN/hVS8NAKiRug3A9mT+/Pk5++yzd33/2GOP5Q/+4A9y0kkn7Tb9beHChdUvboePfalln8YB2LPG3skZlyXLF1Suird5fWX88KOTkVOS4yaZ/XWg9O6fvOs3kmUPV66Kt3VjZfzI4cmoqckx42paXqH0G5Sc9alk2UPJ8keS7TvCmaNGJ6PeVfmXA2Pg0OTd/yV5/pfJi4srp1Ynlefz6DOTI46vbX0AQHX1mABsw4YNWbJkSa655ppdY5MmTbIeCUCBNfZKRr8rGXVm8tM/qYy9+7/Utqai6tU3GXNOcuLZb/b6zE/Wtqai6nNYMva85KT3Jj/9emXsjI/Vtqai6jcomfBrybjpyc929Lrp12tbEwBQGz0mABs4cGDa2lypB+BQZKZX9eh19ZTqciXWYmrQawA45Hk7AAAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAAqtV60LqHfDBx+ajw0AAABQFAKwTlx6Zq0rAAAAAKA7nAIJAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUWq9aF1Dv5sxPVqyrzWMPH5xcemZtHhsAAACgKARgnVixLnlmda2rAAAAAGB/OQUSAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFFqvWhfQkfb29nz961/PN7/5zbzwwguZMGFC/uzP/ixXXXVVmpub861vfavWJb7D7K9Oy6hTz89ZH/lSl8YBAKCna9+erFqSrHws2bIh6TMgOW5icuzJSWPvWldXLNu3Ji/9qnLbtinpd3hy3KnJMeOShsZaV1cs2zYnLy5OVi9Jtm9J+h+ZDG9Khp6YlEwlOaC2bExefDRZ83TStj0ZeFQyfHIyeGRSKtW6umLZ9Fqy4pHkleeSclty+LHJiNOTQcOK3+u6DsCuvPLKzJkzJzfeeGOmTp2aefPm5fLLL8+aNWty/fXX17o8AAA45G3ZkDx8e7LxlSSlJOVk49pk3QvJ0geSKZcl/Y+odZXF8Ma65KH/k2x5Pbv1+pXnksOPSc74WCV8pPvWv5QsmF0JwXbauDZ5+Zlk8Kjk9I8kjX1qVl6hvPJ8suifK0H6ThtfSVY9mRw7IZl0sXD3QFn1RLL4zqTc/ubYhlcqH16MPCMZ//5ih2B1m1vfdtttufXWW3PHHXfkC1/4QqZPn54bbrgh55xzTrZv354pU6bUukQAADiklcvJwn+uBAOVgd3/3fRasuAHux9ssX/at1eCxi0bdgy8rdevr04euaMWlRXP1k3Jw7OTbVvetmFHr9ctSx7/j6qXVUhvvLoj/Gp724YdvV71ZPLMvdWuqpjWv5Q8+u97eD3e0esXFiTLHqp6WVVVtwHYzJkzc+GFF6a5uXm38bFjx6Z3795pampKknzkIx9JU1NTzjjjjJx11ln5yU9+UotyAQDgkLPuheT1VXkzjHm7cvLG2uTlZ6tZVTGtWpJsXp+99zrJq8uT11ZWraTCWrk42b45HfZ61ROVgJfuWb5gx8yvDnr9wsLKKah0z/Pzu7DPg3sIIwukLk+BXL58eRYvXpzrrrvuHduWLVuWSZMmpW/fvkmSW2+9NUceeWSSZMGCBZk2bVrWrl2bxsaO50iWujiv76M3zM2IU6btU/0P/usf5qE7Z+02tm3zhow69fx9+jmtrS35nQum79N96tndN1de1brae/afXlePXlePXlePXlePXlePXh8cv3PpX+Y/vfuqNHRwflJb+/bMuvEfc9M//VYVKyueP/itf87ZEz+Uxoa9H8K1l9vzhc/enL+984tVrKx4/uJ3Hsi44WemoaHj+SK/+aHP559//qdVqqqYbvvS8gw9YniH+7RvT85/9yfSuuj/VKmq4imVSvn3mZvTu1fH5+1ufSM5fdx5eXRpMafd1W0AliTDhg3bbXzTpk1pbW3NRRddtGtsZ/iVJK+99lpKpVLK5Q7i4yo465Ib9rgIPgAAFMmAvoO69N57QN9BVaim2Ab0G5SGUscf8pfL7RnQT6+767B+R3YaflX20+vuGtD38C7up9fd0buxb6fh105Ffg2pywBs6NChSZIlS5bk4osv3jV+0003ZeXKlZk6depu+1977bX50Y9+lNdeey0/+MEP0qtX579WV0OyP787eWb1PhR/ADU3T8vsr9Y2zDuQfrJjUlytA8pDgV5Xj15Xj15Xj15Xj15Xj14fHE/fmzz3QMf7NDb0yiev+Ej+v1v1vjse+1Gy8vF0eKpYY0OvfP73rs6f/uDqqtVVRA/fnqxdlg57nSR//L/+Z7576v+sSk1Fdd93dlxAoxPf/ae/yVEn/s3BL6igyuXknlt2v6jD3tzd+sMcfvTBr6m7pk2bts/3qcsAbMyYMWlqasrMmTMzZMiQDB8+PLNnz86dd96ZJO8IwG655ZYkSWtra6677rrcc889GThwYNXrBgCAQ8nxp3YegCXJ8acd/FqKbvhplSu1daiUHD+pKuUU2vCmZO3zHe/T2Ds5Znx16imy4ZOTJT/reJ++A5Mho6tTT1GVSpXn9XMPdrRT5WqyPSH82l91uQh+Q0NDbr/99kyaNClXX311ZsyYkaFDh+baa69NY2PjrgXw3665uTkNDQ35xS9+UeWKAQDg0DNgcDLi9I73GTaxclBF9xwxPDl6bMf7jD6zEhbQPUePTY44vuN9Tnpv0sUzyujA8acmA4Z0vM+4aUmpLpOLnmXk1B2vDx0shTmuee/biqAuZ4Alyfjx4zN37tzdxq644opMnDgx/fv3T5Js2LAhr7zySkaPrsTBCxYsyDPPPJNTTjml6vXu9LEvtezTOAAA9GQT3p80NCYvLEjK7W/ZUEpGNCXj31+z0gqlVEpO/VDyxN3vnAlWakhGn5Wc9J7a1FY0DY3JGR9NHrszWfPM27b1qoRfI6fUprai6dUnmfqJ5NF/q1zF9O3bxv9aMuzk2tRWNH0PS6Z+MnnkjmTD25Z56t0/mXRhMmRUbWqrlroNwPZk/vz5Ofvss3d9v3HjxnziE5/Ihg0b0qtXr/Tr1y/f+973MmpUwf+rAQBAnSg1JOOnVwKYVU++eTrT+z5nNtKB1tgrmXRRJej6+bcqYxN+LTn25KRP/9rWVjS9+iaT/3OycW1y399Vxk65IDl2QmUbB07fw5IzP5m8vjp54O8rY5MuTo4ZVznVlANnwJHJu69IXluZzP/HythpH67MeuzgYr6F0WMCsA0bNmTJkiW55pprdo0de+yxuf/++2tYFQAAkFQOYkdNeTMAE34dPG+9SNvIM2pXx6HgsLecnjd8zyvxcIC89VTp4ybWro6iK5WSI99yiu+xE2pXS7X1mABs4MCBaWtrq3UZAAAAAPQwlpIDAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACi0XrUuoN4NH3xoPjYAAABAUQjAOnHpmbWuAAAAAIDucAokAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaL1qXUC9mzM/WbGuNo89fHBy6Zm1eWwAAACAohCAdWLFuuSZ1bWuAgAAAID95RRIAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGh1HYC1t7dn1qxZGTduXPr165fJkyentbU1EyZMyFVXXVXr8gAAAADoAeo6ALvyyivzla98JZ/73Ofyox/9KB//+Mdz+eWX59lnn83UqVNrXd4ezf7qtDz4L1/t8jgAAAAAB1evWhewN7fddltuvfXWtLS0pLm5OUkyffr0PPzww5kzZ06mTJlS4woBAAAA6AnqdgbYzJkzc+GFF+4Kv3YaO3Zsevfunaampt3Gv/Wtb6VUKmX27NnVLBMAAACAOleXAdjy5cuzePHiXHbZZe/YtmzZskyaNCl9+/bdNfbUU0/lO9/5Ts4+++xqlgkAAABAD1CXp0AuX748STJs2LDdxjdt2pTW1tZcdNFFu8a2b9+ez3zmM/mrv/qrfP7zn+/yY5RKpS7t99Eb5mbEKdO6/HOT5MF//cM8dOes3ca2bd6QUaeev08/p7W1Jb9zwfR9uk89u/vmcpKu9579p9fVo9fVo9fVo9fVo9fVo9fVo9fVoc/Vo9fVo9fVcyj2ui4DsKFDhyZJlixZkosvvnjX+E033ZSVK1futgD+V77ylVx00UU5/fTTq13mXp11yQ056yNf2m1s9len1aYYAAAAgENcXQZgY8aMSVNTU2bOnJkhQ4Zk+PDhmT17du68884k2RWAPfDAA/nZz36WlpaWfX6Mcrncpf3+/O7kmdX7/OMPiObmaZn91a7V2RP8ZMekuK72nv2n19Wj19Wj19Wj19Wj19Wj19Wj19Whz9Wj19Wj19XT03s9bdq0fb5PXa4B1tDQkNtvvz2TJk3K1VdfnRkzZmTo0KG59tpr09jYuGsB/Llz5+aZZ57JSSedlBNOOCH3339/rrnmmvzJn/xJjX8DAAAAAOpFXc4AS5Lx48dn7ty5u41dccUVmThxYvr3758k+eIXv5gvfvGLu7ZPmzYtv/3bv52PfexjVa0VAAAAgPpVtwHYnsyfP7/ur/T4sS+17NM4AAAAAAdXjwnANmzYkCVLluSaa67Z6z77sxYYAAAAAMXWYwKwgQMHpq2trdZlAAAAANDD1OUi+AAAAABwoAjAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKrVetC6h3wwcfmo8NAAAAUBQCsE5cematKwAAAACgO5wCCQAAAEChCcCoCy0tLRk9enSmTZuWSy65JJs3b95t+6xZs7JgwYI88MADOffcc/Pe97431113XYc/c8WKFfn85z+fxYsX59xzz8373ve+zJgxI+VyOYsWLcpNN910MH+luqXX1aPX1aPX1aPX1aPX1aPX1aPX1aHP1aPX1aPX1VPUXgvAqBtXXHFFWlpacu6552b27Nm7xtvb2/OLX/wiZ5xxRkaPHp2f/exn+fnPf57Vq1fn0Ucf3evPu/vuu/OBD3wgEyZMyLx583LvvfcmSebPn5/JkyfnvvvuS7lcPui/Vz3S6+rR6+rR6+rR6+rR6+rR6+rR6+rQ5+rR6+rR6+opYq8FYNSd008/PcuXL9/1/aJFizJ27NgkybBhw9KvX78kSe/evdPY2JiWlpYMHjw406ZNy+jRo3PJJZckSVpbW9Pc3JzevXvv+ll9+/bNyJEjkyTjxo3LggULqvVr1SW9rh69rh69rh69rh69rh69rh69rg59rh69rh69rp4i9VoARt255557Mn78+F3fP/XUUznhhBN22+eRRx7JmjVrMnHixJx33nk566yz0tLSkubm5vzlX/5lyuVyNm7cmIEDByZJ7rjjjpx66qlZtWpVjjrqqCTJmDFj8sQTT1Tt96pHel09el09el09el09el09el09el0d+lw9el09el09Req1AIy68d3vfjfTp0/Pq6++uisl3pO1a9fmt3/7t/Ptb387SfLss89mzJgxSZIXXnghw4cPz6JFizJ58uRd9/n1X//1LF68OCNGjMgPf/jDg/uL9AB6XT16XT16XT16XT16XT16XT16XR36XD16XT16XT1F7LUAjLpxxRVXZO7cubnlllvS2Ni4a3zcuHF57rnnkiTbt2/Ppz71qcyaNSvDhg1Lkjz22GOZNGlS2tra0tBQeUrvPL84SbZs2bLrZw0aNCj9+/dPUvkf8+STT67Gr1Z39Lp69Lp69Lp69Lp69Lp69Lp69Lo69Ll69Lp69Lp6ithrARh1b/LkyVmyZEmS5Pbbb88vf/nL/N7v/V6mTZuW++67b9f/YFu2bMnq1auzcuXKzJ8/P2eeeWaS5K677kpzc3Oam5uzatWqXHDBBUmSJUuW5PTTT6/Vr1WX9Lp69Lp69Lp69Lp69Lp69Lp69Lo69Ll69Lp69Lp6enSvy1Ald99cue2Pm2++ufzwww93ef/vf//7HW5fuHBh+Wtf+9r+FdMD6HX16HX16HX16HX16HX16HX16HV16HP16HX16HX19PReNzc3l5ubm/fpPqVy+RC9pidV95NZlX/P/0Jt6zgU6HX16HX16HX16HX16HX16HX16HV16HP16HX16HX19PReT5s2LUnS0tLS5fs4BRIAAACAQhOAAQAAAFBovWpdQL373Scfz6LXX6/JY08+/PD8yYSJNXlsAAAAgKIQgHVi0euv5551a2tdBgAAAAD7ySmQAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUWl0HYO3t7Zk1a1bGjRuXfv36ZfLkyWltbc2ECRNy1VVX1bq8PSpv25Zt//W30/bNv9ltvO2f/yXbPvVbKW/YUKPKamfDy8kTd7/5/fx/Sl76VdLeVruaiuq1lcljd775/YLZyZqnk3K5djUV1dplySN3vPn9on9J1j6v1wdauZy8/Eyy4Advji3+9+S1F2tXU1G1tyernkjmf//NsV/9R/L6mtrVVFTt25MXFycP/sObY0/OTd5YV7uaimr71uSFBcn9//vNsafvTTa/Xruaimrb5uS5B5P7/u7NsaX3J1vfqF1NRbVlY/LsvDe/v+/WZNlDyfYtNSupsDa9ljzV+ub3D3w3WfFI0ratdjUV1cZXkid+8ub3v7wtWfm4Y8aDYf1LyWN3vfn9w7cnq586NI5jSuVy/f6aM2bMyJw5c3LjjTdm6tSpmTdvXm655ZasWbMmf/EXf5HPfe5zB72G8+c/kHvWrd2n+5Sfez7b/9vn0/g//780nHF6ykuXZvvvXJ/GP/yfaWg6rcs/57zBQ/KTM9+9ryXXlZd+lSy+M8lbn2WlyvdDRieTP5I09q5NbUWz7KFkydzs6m/y5tfHnpycenFSquvIu2col5Nn7q28yd9Tr0dNTcZNS0qlmpVYGOVy8vhdycrHssdej31fckLPfomsG+3bK4Huy89m916n8v3EDybHn1qj4gpm+5bk4dnJ+pV5R69LjUnTrydHn1Sr6oply8bkoe8nb6zNO3rd2Ds542PJkcNrVV2xvLGu0uste/ict8+AZMplycCjq19XEa1/qfIasn3zO7f1PyKZ+omk36Dq11VErzyfLPrnyt/IXXa8lhx+THLGZUmf/rWqrlhWPVE5Ziy3v2VwR68Hj0xOv9Qx44HywoLkyZ9mj++tjxmfnPqhpKGHHDNOmzYtSdLS0tLl+9Ttr3bbbbfl1ltvzR133JEvfOELmT59em644Yacc8452b59e6ZMmVLrEveqdMLoNHzmt9I263+lvHZttn/t5jRc8uF9Cr+K4PXVewi/8ub3a59PnmqpclEF9crzO8KvZPd+7/h61RPJ0geqXVUxvfT4jvAr2WOvlz2UvPhotasqpud/uSP8SvbY66fvrcwOo/ueundH+JXs8TX78bsqM0zpvsf/Y0f4lbyj1+W2ShD5xqvVrqqYHrljR/iVvKPXbduThT9Itm2qelmFU26vzNLdsnHP27duqmw3i6P72rZWerm3mV6b1icL//nQmMVxsG3ZsCP8evvzdkdvX1+9+1kX7L8NL+8h/Ep29XrdC8mTP6t6WYW0dtmO8CvZ43vr1UuSpfPefq9iqdsAbObMmbnwwgvT3Ny82/jYsWPTu3fvNDU1JamkfieeeGJOP/30nH766fniF79Yi3LfoeEjl6Q0amS2f+7apLExDb91Ra1LqroXHs47D6TeZsVibz4PhGW/TCW578ALD7/tEyz2WblcCWU66/Xzv/Tms7va25Jl8zvZqZQ839k+dGr7lmTFok52Ku14TadbNq9PVj/Z8T7ltmTFwqqUU2jrX0peW9HBDuXK6ZEvPtbBPnTJy0uTTa9m7+/5ypUwYfVTVSyqoFb+asf75g56vWFN8uryalZVTCse2fG+uYP3c68srZy2R/e8sGAP4dfbrHzM6dQHwrKH0vkx44LKh0RFVZcB2PLly7N48eJcdtll79i2bNmyTJo0KX379t01dvPNN2fhwoVZuHBhvva1r3XpMUqlUpdu+zKd7h0/v+m05LXX0vBr70+p977P2WxpaelynfV4e+LBzk8dLbcl55/98ZrX2pNvvXv1yZql7Z2Gjds2JZPHv6/m9fbk27GDR2bDy+m012+sS0YcPbbm9fbk28QTz+r8jU658qlg/74Da15vT76dN/WSzsPxcrJ04Yaa19rTb5d98L920uikXC5n3l1P17zWnn77b7/15XS2ykd7uT23f3tuzWvt6bc/+uLfpK2TF5G29u35s6/8Y81r7em3W//0h2nrZCpde3t7/p9r/qTmtfb023/cvqDT15Ak+fRHv1DzWnv6bfHPV3Xa53J7ctF7f7PmtfbkW2NDY1Y/1dbpccz2LcmZJ7+/5vV25dba2prW1taOf6G3qdsALEmGDRu22/imTZvS2tpa16c/7lReujTt//hPafjEZWn/3j+mvHp1rUuqur69u3ZSfL8+Aw5yJcXWp1e/NHRxca9+vfW6O/ruw3N1X/blnfruw3O1q6817FlXXxf69O53kCspvq68LpRKJc/pA6Bv7wGdHrw2lBrSv89hVaqouPr2HtDpAdWu/eiWvn0GpKHU8fSNctq9BzkA+vU5LKVOep14b30gdPVvnteQ7unV2CcNDY1d2rfIryF1uQj+008/nXHjxuV//a//lc9//vO7xr/85S/nD/7gD3LLLbfkmmuuSVI5BXLlypXp06dPxowZk6985Su7To88EPZrEfyt27L9v/33NJz97jTO+K1sn/X1ZNXqNP7xzJT2YUW5nr4I/v23Vs7p7syZl1uEtjvK5eSev+zaqaTnfjYZcORBL6mwtm9N7rml83VMSg3Jedck8oL9t/n15Off7Hy/Xn2T867tOYt11qP1LyUPfq/z/QYMTs698uDXU2RrnqmsKdOhUjJ4RGUha/bf8kW7X4F6j0rJsJOTU/9TVUoqrGfn7X5Fwr0ZfWblIjHsv1/dXTk1r7PAcdy0Sr/Zfwv/ecfamJ30+tT/lAw7pSolFdYD362sqdZZr6d8PBkyqiolFVK5nNz718nWvazX+FbnfCY5bMjBr6m7phVlEfwxY8akqakpM2fOzN///d/npz/9aa6++ur83d9Vrqs8derUXfv+/d//fZ544ok8+uijufzyy/PBD34wGzd24b/qQdT+d99JqVevNFzxm0mSxmv+a8ovrUr7Dzp711ssI07vZIdSMmBIcsTx1aimuEqlZMTkznZKBo8SfnVXrz7JsInp+Nz5UuWqm8Kv7ul3eHLUmHS6TsHwJuFXdx1+7I6rs3XS605f0+nUUScmnU44KifDO3tNp1PDTk4aenWyk14fEF29QuzxB+7z6UPW8KZ0GhKUGpLjJlalnEIb0YVe9+qXHD2uKuUU2ojJ6bjXpaT/kZWrQbL/SqWuHZ8fOaJnhF/7qy4PGxoaGnL77bdn0qRJufrqqzNjxowMHTo01157bRobG3eb4TVq1Khd01M/+clPpk+fPnnyyU5WmD2I2hcsTPudd6Xxi7+XUq/KO6/SgAFp/B9fSPvffy/lpUtrVlu1HTcpGTSs431O/rXK/4x0z6iplT8Me1RKGhqTcc172c4+GXPOjkte7+l5W0p6903GnFvtqopp3PuSxl7Za6/7DUpGv6vaVRVPqZRMeP+O1+K9vB4PPDo5/tC6kPFB0dBQ+bvXkcGjkmMcUHVbr77J+Gkd73PsBDPQD4R+g5ITz+l4n1FTi31AVS2Djt0RgnXgpPcmBT57qWqOGpMMPanjfSa8f8f7FLpl2MRk0HF72bjjfYljxgNj5BmVGf17VKq8T+nsb2dPV5enQO7NFVdckUWLFuWRRx5JkmzevDkbNmzI0KFDkyQ//elPc9lll+W5557LoEGDDshj7s8pkAdKTz8FMqksovf4f7zzqlf9j0hO/kBy1Ak1KauQtmxMHv9R8spzu48fNjSZ+MHkiL39YWGfvfFq8tiP3nmFsUHHJZMu8ib/QFq/Knn8rspVrd5q8Ohk0oWVmWIcGGuXVU4Ze2Pd7uNHj6u8hpjVeOCsfqpySfctr785tnPWxoRfSxr3/bo57MWKR5On79l9mYCGxsqn4GPPq3xN95XLlSv3Pntf0rb1zfHG3snos5ITz3bweqCU25NnflG5mttbrz3Qq19y0nsqB7gcGO3bkyVzK68jb71KYZ/DKiGBUx8PnO1bKqf4rnoyu80G6zeocsw49MSalVY4Wzcmj/94xym+b3HYUTuOGXvQ2Vn7cwpkjwrATjnllJx99tn5zne+kyRZvXp1LrroomzdujUNDQ0ZNGhQ/uiP/ijvfe97D9hjCsAOjM2vV4KZ9u2V/7kGj/RG6GB5Y13lQDblZOAxleBLrw+O19ckr72YpFz5Y3H4MbWuqJjK5co6Va+vSuV03pFCxoOlXE5eXV5Zv7GhsfIhRb8D83kSb1NuT9Y+XwnUG3tVZhv0tR77QdHelryyNNm8vhISDB0j0D1Y2rZVDqq2bkx6D6j0ulefWldVTNu3VHq9bVPSd2Cl152e9st+2fpGpddt25L+g5IhJ1p+4WDZ7ZhxSGVWtOOYg+ONV5N1yyp/Iw8/pnIs09N6vT8BWI95mdywYUOWLFmya/H7JDnmmGPy0EMP1bAquqrf4clwp89UxYDBHUxt5YA6/OjKjYOrVKoEuWYxHnylHQGjdTYOvlJDZU2wo2pdyCGgoTE5emytqzg0NPaunFrKwderrxlI1dJnQNfXuqN7HDNWz4AjD831oXtMADZw4MC0tXVy6TUAAAAAeBuTNwEAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACq1XrQuod5MPP/yQfGwAAACAohCAdeJPJkysdQkAAAAAdINTIAEAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAAqtV60LqFcnnHBCDjvssPTu3TtJ8t3vfjennXZajasCAAAAYF8JwDrw4x//OCNGjKh1GQAAAAB0g1MgAQAAACg0AVgHPvzhD+f000/PDTfckG3bttW6HAAAAAD2gwBsL+69994sWLAgv/jFL/Lkk09m1qxZtS4JAAAAgP0gANuLkSNHJkkOO+ywfPazn828efNqXBEAAAAA+0MAtgcbN27M+vXrkyRtbW35wQ9+kKamphpXBQAAAMD+cBXIPVi1alUuvfTStLe3p62tLeecc05uuOGGWpcFAAAAwH4QgO3BmDFjsnDhwj1uW/j403l53WuZdvbp6dXYWN3CAAAAANhnToHcB21t7fnxPb/ME08vS2OD1gEAAAD0BD0+xXn00Ufz0Y9+NEOHDk2/fv0ybty4g3a64sOLl2Tda6/n/PdOTalUOiiPAQAAAMCB1aNPgXzooYdy3nnnZeTIkbn55pszevToLF26tEtXbPziH39rvx/31tl37fd9AQAAANh/zy5buc/36dEB2O/+7u/msMMOywMPPJAjjjhi1/iVV15Zw6oAAAAAqCelcrlcrnUR++ONN97I4Ycfnt/+7d/On/7pnx7Ux2pra8+sv/l+DuvfL9f+l484/REAAACgRqZNm5YkaWlp6fJ9euwMsHXr1qW9vT0jRozYr/vvzymQ6157Pf/PTX+zX48HAAAAQPdt2N64z/fpsQHY4MGD09DQkBUrVtS6FAAAAACq5PwPf2Kf79NjT4FMkunTp+fxxx/PU089lUGDBh2Ux/jloifyg7vuyac/dmFOPmnUQXkMAAAAAA6ehloX0B2zZs3Khg0bcvbZZ+fWW2/N3Llz87//9//OZz/72QPy89va2vOz+xZkxLCjM2HMyAPyMwEAAACorh57CmSSTJ06Nffdd19uvPHGXHfdddm8eXNGjhyZT37ykwfk57+46uVs2PhGLvnAeyx8DwAAANBD9ehTIKthwxubclj/fgIwAAAAgB5KAAYAAABAofXoNcAAAAAAoDMCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0Oo6AGtvb8+sWbMybty49OvXL5MnT05ra2smTJiQq666qtblAQAAANAD9Kp1AR258sorM2fOnNx4442ZOnVq5s2bl8svvzxr1qzJ9ddfX+vyAAAAAOgB6jYAu+2223LrrbempaUlzc3NSZLp06fn4Ycfzpw5czJlypQaVwgAAABAT1C3p0DOnDkzF1544a7wa6exY8emd+/eaWpqSpI899xzaW5uzvjx43Paaafl3nvvrUW5AAAAANSpugzAli9fnsWLF+eyyy57x7Zly5Zl0qRJ6du3b5Lkc5/7XD7xiU9kyZIl+eY3v5lPfvKT2bp1a7VLBgAAAKBO1eUpkMuXL0+SDBs2bLfxTZs2pbW1NRdddFGS5OWXX87Pf/7z3HHHHUmSc889N8cff3zmzp2bD37wgx0+RqlUOgiVAwAAAFAN5XK5y/vW5QywoUOHJkmWLFmy2/hNN92UlStXZurUqUkqs8GOPfbYXbPBkuTEE0/M888/X71iAQAAAKhrdTkDbMyYMWlqasrMmTMzZMiQDB8+PLNnz86dd96ZJLsCsO7YubZYS0tLt38WAAAAANUxbdq0fb5PXc4Aa2hoyO23355Jkybl6quvzowZMzJ06NBce+21aWxs3LUA/qhRo7Jq1aps2bJl132XLl2a0aNH16p0AAAAAOpMXc4AS5Lx48dn7ty5u41dccUVmThxYvr375+kcqrke97znnz729/ONddck3nz5mXFihWZPn16LUoGAAAAoA7VbQC2J/Pnz8/ZZ5+929hf//Vf59Of/nS+8Y1vpE+fPrntttvSp0+fGlUIAAAAQL3pMQHYhg0bsmTJklxzzTW7jY8ZMyb33HNPjaoCAAAAoN71mABs4MCBaWtrq3UZAAAAAPQwdbkIPgAAAAAcKAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAABbZxy8HdHwAAoCcQgAEU1FOrkq/8a/Lwc13bf95TyR/ekSx75aCWBQAAUHUCMICCWro62bwt+d68zkOweU8l/+fB5I2tyfMvV6U8AACAqqnrAKy9vT2zZs3KuHHj0q9fv0yePDmtra2ZMGFCrrrqqlqXB1DXPnBqcsGpSXu54xBsZ/iVJB+ZkrxvQtVKBAAAqIpetS6gI1deeWXmzJmTG2+8MVOnTs28efNy+eWXZ82aNbn++utrXR5AXSuVkouaKl//x+JKCJYkU054c5+3h1/TTqlqiQAAAFVRtwHYbbfdlltvvTUtLS1pbm5OkkyfPj0PP/xw5syZkylTptS4QoD611EIJvwCAAAOFXV7CuTMmTNz4YUX7gq/dho7dmx69+6dpqbKEd3v//7vZ/z48WloaMjs2bNrUSpAXdsZgr31dMh/ul/4BQAAHDrqcgbY8uXLs3jx4lx33XXv2LZs2bJMmjQpffv2TZJceOGF+fSnP53PfOYz+/QYra2tSZJSqdT9ggF6iLM/+uW8+z//fu5/pvL9Pd+7Ln/6qW/UtCYAAICDrW4DsCQZNmzYbuObNm1Ka2trLrrool1j5557blVrA+jJNqxdvuvrcntbNqx7sYbVAAAAVEddBmBDhw5NkixZsiQXX3zxrvGbbropK1euzNSpU7v9GDtPrWxpaen2zwLoCd665leSlBoa86Hf+X4+de73d1sYHwAAoJ5NmzZtn+9TlwHYmDFj0tTUlJkzZ2bIkCEZPnx4Zs+enTvvvDNJDkgABnAoeXv4lVTWBNvb1SEBAACKpC4XwW9oaMjtt9+eSZMm5eqrr86MGTMydOjQXHvttWlsbNy1AD4AnXv71R53evvC+A8/V5PyAAAADrq6nAGWJOPHj8/cuXN3G7viiisyceLE9O/fv0ZVAfQsbw+/pp2S/MvDle93Xh0yMRMMAAAotrqcAbY38+fPf8fpjzfeeGNGjBiR++67L5/73OcyYsSIPPPMMzWqEKB+3Pf0O8Ovt9sZgr11JtiC56tbJwAAwMHWYwKwDRs2ZMmSJZkyZcpu41/5yleyfPnybNmyJa+88kqWL1+ek046qUZVAtSPvr2ShtLew6+d3hqClUqV+wEAABRJjznMGThwYNra2mpdBkCPMeWEZMSQ5JhBne+7MwQ788Su7Q8AANCT9JgZYADsu30Js0ol4RcAAFBMAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEKr6wCsvb09s2bNyrhx49KvX79Mnjw5ra2tmTBhQq666qpalwcAAABAD9Cr1gV05Morr8ycOXNy4403ZurUqZk3b14uv/zyrFmzJtdff32tywMAAACgB6jbAOy2227LrbfempaWljQ3NydJpk+fnocffjhz5szJlClTalwhAAAAAD1B3Z4COXPmzFx44YW7wq+dxo4dm969e6epqSnr1q3Lhz70oYwfPz6TJ0/OBRdckKeffrpGFQMAAABQj+oyAFu+fHkWL16cyy677B3bli1blkmTJqVv374plUr5/Oc/nyVLlmTRokX50Ic+lBkzZtSgYgAAAADqVV2eArl8+fIkybBhw3Yb37RpU1pbW3PRRRclSY488sicf/75u7afe+65uemmm7r0GK2trUmSUql0IEoG6DH++/fKSbz+AQAAh466nAE2dOjQJMmSJUt2G7/pppuycuXKTJ06dY/3+8Y3vpGPfOQjB7s8AAAAAHqQupwBNmbMmDQ1NWXmzJkZMmRIhg8fntmzZ+fOO+9Mkj0GYF/+8pfz9NNP52c/+1mXHmPn2mItLS0HrG6AnuDz/1D5t1wu17YQAACA/TBt2rR9vk9dzgBraGjI7bffnkmTJuXqq6/OjBkzMnTo0Fx77bVpbGxMU1PTbvt/9atfzQ9/+MPcddddGTBgQI2qBgAAAKAe1eUMsCQZP3585s6du9vYFVdckYkTJ6Z///67xr785S/nzjvvzN13350jjzyyylUCAAAAUO/qNgDbk/nz5+fss8/e9f1jjz2WP/iDP8hJJ5202/S3hQsXVr84AAAAAOpSjwnANmzYkCVLluSaa67ZNTZp0iRr2AAAAADQoR4TgA0cODBtbW21LgMAAACAHqYuF8EHAAAAgANFAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADKDAXn794O4PAADQEwjAAApq0bJk5r8l9zzZtf3vejT52g+TJ1Ye3LoAAACqrVetC2DfbX0j2bw+aeiVHHZUUirVuqLi2rKx0utefZIBQ/T6YNq8vtLv3v2TAUfWuppieH1z0l5O5syvfH/ehL3ve9ejyV2PVJ7jGzdXpz4AAIBqqesArL29PV//+tfzzW9+My+88EImTJiQP/uzP8tVV12V5ubmfOtb36p1iVX1xrrkmZ8nq59Kyu2VsX6DklFnJiPPEM4cSK+vrvT65WffHBswJDnx3clxk2pXVxG9ujx55hfJuhfeHDv82OTEc5JjxtauriJ47/ikXE5+ML/jEOyt4ddvnpNMPbG6dQIAABxsdR2AXXnllZkzZ05uvPHGTJ06NfPmzcvll1+eNWvW5Prrr691eVW18ZXkl7cl27ckKb85vnl9suRnle0nny8EOxBefTF5+P8k7W27j7+xNnnsR8mm15Ix59amtqJ5+Zlk0b9WQpq3en118si/JCd/IBkxuSalFcb7dgRebw3B3urt4deZwi8AAKCA6jYAu+2223LrrbempaUlzc3NSZLp06fn4Ycfzpw5czJlypQaV1hdj931zvDrrVYsSo4+KRk6pqplFU65nCz+4Y7way+9fnZeMvSkZNCxVS2tcNq2JYv//c3ZjLvZ0fsnflJ5Tvc7vKqlFc7eQjDhFwAAcKio20XwZ86cmQsvvHBX+LXT2LFj07t37zQ1NSVJPvKRj6SpqSlnnHFGzjrrrPzkJz+pRbkH1eurk/Urs9dAJklSSl5YWKWCCuyVpZVZdR32OpXAke556Ylk+9ZOdionKx6pSjmF974JyUfP3H1M+AUAABwqSuXy208+qr3ly5dn5MiR+fa3v53PfOYzu227/PLL88QTT2TBggVJkldffTVHHnlkkmTBggWZNm1a1q5dm8bGxg4fo9SDzhW86KzP5vrL/qbT/dZvfCUf/YOhVaiouD51/o35rQ/+z073e3blI/nc152b1x3//dK/ykXv/mwaG/Y+EbW9vT3zl/w4N3z74ipWVmxN51+T6Z++JUmlv//x11fkyXn/WOOqAAAA9t2+RFp1OQNs+fLlSZJhw4btNr5p06a0trbudvrjzvArSV577bWUSqV9akDP0LXfp7zHc8nYF+Uu9vodi1axzyq97iyILuv1AdZv4FG7vm5oaEi/w4bUsBoAAIDqqMs1wIYOrcxiWrJkSS6++M2ZHzfddFNWrlyZqVOn7rb/tddemx/96Ed57bXX8oMf/CC9enX+a+08tbKlpeXAFX6QbHwlue87nexUSsaecXQBw7/qWrussgB+Z5r/0+SUv67X3fHSryprgHWkoaExl191cf7fb+v1gfDWNb/OPCH55dJk2m/9ef7sz/98j1eHBAAAqEfTpk3b5/vUZQA2ZsyYNDU1ZebMmRkyZEiGDx+e2bNn584770ySdwRgt9xSOZ2ntbU11113Xe65554MHDiw6nUfLIcdlQwemaxbnr1PBisnI8+oZlXFNHhkMmBI8sa6dDjxbrizH7vtmHFJ7/7Jts3Za69LDcnwU6taVmHtacH7UUftvjC+EAwAACiqujwFsqGhIbfffnsmTZqUq6++OjNmzMjQoUNz7bXXprGxcdcC+G/X3NychoaG/OIXv6hyxQffxAuTvoftYcOOM8hOODsZMqqqJRVSqZQ0fTjp1SfvPDtvx/fj358MtNRatzX0Spp+PWlozJ57XUomXZz02dPznn2yt6s9vnVh/Dnzk3uerF2NAAAAB1NdzgBLkvHjx2fu3Lm7jV1xxRWZOHFi+vfvnyTZsGFDXnnllYwePTpJZRH8Z555JqecckrV6z3Y+h+RnPWp5LkHkhcXJ23bKuOHH5OMflcy7OTa1lckA49Ozrqi0uuXHk/a2yrjR45ITnhXMnRMbesrksEjk7N+M1n6QLJ6SbJzGbujTkxOOCsZPKK29RXB3sKvnd63Y9aXmWAAAECR1W0Atifz58/P2Wefvev7jRs35hOf+EQ2bNiQXr16pV+/fvne976XUaOKORWq78Bkwq8lY5uTud+ojL37ipqWVFgDjkwmfjCZMD2Z+2eVsTM/UdOSCmvg0clpH0q2b01advT6jEtrW1NR3L244/Brp7eHYA2l5L3jq1cnAADAwdZjArANGzZkyZIlueaaa3aNHXvssbn//vtrWFVtNPaY/2o9X2OfWldw6Oil1wfcqKOSPr2Sj5+19/Brp50h2L8vSka4MCQAAFAwPSZKGThwYNra2mpdBkCPMeG45PcvSQb269r+75uQnDG66/sDAAD0FHW5CD4AB8a+hlnCLwAAoIgEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAAwAAAKDQBGAAAAAAFJoADAAAAIBCE4ABAAAAUGgCMAAAAAAKTQAGAAAAQKEJwAAAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhdar1gV0pL29PV//+tfzzW9+My+88EImTJiQP/uzP8tVV12V5ubmfOtb36p1iQA9RntbsuaZ5KXHk22bkj6HJcdNSoaemJR8HHJAtW1PVj2ZrH4y2b4l6TcoOf60ZPDIpFSqdXXFsn1r5Tm95umkbVsyYHAyfHIyaJheH2jbNiUvPpa8srTyejJwaDJicjLw6FpXVjxbNiQrHk3WvZCU2yvP5xGTK89vDqxNryUrFiWvrax8f+TwymtIv8NrW1cRbXwlWb4oeX110tCQDBld+dvYZ0CtKyue9asqz+uNa5OGXsnQMcnxk5JefWtdWbGUy8lrK5IVj1ReSxr7JMeMT4adnDT2rnV17EldB2BXXnll5syZkxtvvDFTp07NvHnzcvnll2fNmjW5/vrra10eQI+xZUPy8Oxk48tJSknKlX9XL0kGHZeccWnSu3+NiyyIN9YlD9+ebF6fN3v9YvLSr5KjTkyaft2bogNl/UvJgh9UgpmdXn0xeXFxctzE5JQLKwdZdN/a55NF/1IJGXd6dXmyfGEy6sxkXLPA8UBZ9WSy+N8rwddOry5Pls1Pxp6XnHBW7WormhcWJE/+LJXX6R3WvZA890ByygeT40+tWWmFUi4nz85Llt63+/jaZcmz9yWnfTg5+qTa1FY05XLyxE8q4ddbrX0uefYXyemXVkJeuq99e7L4zsp76be+t35lafLMz5MpH/MBUT2q27eFt912W2699dbccccd+cIXvpDp06fnhhtuyDnnnJPt27dnypQptS4RoEcot1dCgo2v7BzY/d/1K5NF/1p500T3tG1NHv4/yebXdwy8rdevLE0e/3EtKiueLRsroe62zW/bsKPXKx9Pnrmn6mUV0sa1ycI5lZmNe7JsfrLsoerWVFSvvpg8+sPdw6+3evqeSphO9615Onnyp9kt/NqpXE4ev6sS/NJ9Kx55Z/i1U/v25JF/rcwKo/uW3vfO8Gun7VuTBbMrM5Xovifn7gi/kne839v6RuXD0He8R6Hm6jYAmzlzZi688MI0NzfvNj527Nj07t07TU1Nu41/61vfSqlUyuzZs6tZJkDde2VpsmFN9vgmf6dXl1eCMLrnpSd2hF8d9HrVE8kbr1arouJa8UiyfXM67PULC7z5PBBeeKhyymNHvX7ugR370C3PP9j5Ps/e5wOLA2Hp/anM2tibUrL0gWpVU1zl9h297mifcvL8/OrUU2RtW5Pnf9nBDuXKLN7lC6tVUXFt2VB5H7JX5UoItvKxqpVEF9VlALZ8+fIsXrw4l1122Tu2LVu2LJMmTUrfvm+ewPzUU0/lO9/5Ts4+++wuP0Zra2taW1tTKpV65G2nWtdxKNz0Wq97+m3Wl76btva9TN3Yob29Lf/v1X9a81p7+u0fbvlJ2ruQAnzm0i/WvNaefmv551+lfW/TZHY+r9uS//Te36p5rT399sT9r3b6nN62KTlr4gU1r7Un3/r3OSyrlrR1GDQmyRtrkzHHn1bzenvybdiQE7L+pXTc63Kyblly5MCja15vT75NGnNOtrzeQZ939PqFR7amsaGx5vX25Nu0qZfudpr6HltdLuehn6yoea09/fbxD17b6Wt1e3t7/u3vf1nzWot825np7Iu6DcCSZNiwYbuNb9q0Ka2trbud/rh9+/Z85jOfyV/91V/tFooBUDGw/+B0/DF35Q3RQKsrd9ugAUeloaGxw33ay+05vL9ed9fh/YekoQtXbxio1902sP+RXdxPr7ujf7/DO3392MlrSPfsy3O1q89/9qyrz9Xevfqkj8VIu6Urz+tSqeQ5fQB0pdcNDQ1eq+tQXS6CP3To0CTJkiVLcvHFF+8av+mmm7Jy5cpMnTp119hXvvKVXHTRRTn99NP36TF2nlrZ0tLS7Xpr4SezKv+WzYE/6PS6evT64PjVf1SuJtbRJ1WNjb3yf13zX/LHt/2XqtVVRAvnJC8vTYe9big15Mav/I/8zb//j6rVVUQP/H3X1oz5q7/9RuZM+MZBr6fI7vmrZOvGzvf7l3//fo4c/v2DX1BBtW9PWv68a6eS3v/wPRlw5EEvqbC2bEzu/asu7FhKnlv+lCvndcPrqyuv151p7JO8sXlDSi6msd9eXpos/EHn+w059jDvtbvpxUe7sKZrKZl4xli9PoimTZu2z/epywBszJgxaWpqysyZMzNkyJAMHz48s2fPzp133pkkuwKwBx54ID/72c96bIgFUA3Hn9rJOgU7HDfp4NdSdMeflrz8bMf7lBoql8eme44/bccC1h3o1TcZ6spi3Tb8tM7X8Ol/ZHLE8VUpp7AaeiXDJlauYrrXEL2UHHl8hF/d1Pew5KgTkleeT4e9PnZ8hF/dNPDoZODQZMMr6fDDoeNPcyXZ7hoyOulzWOcfWBx/WnXqKbJjxidP/LTywcVelZPhriRbd+ryFMiGhobcfvvtmTRpUq6++urMmDEjQ4cOzbXXXpvGxsZdC+DPnTs3zzzzTE466aSccMIJuf/++3PNNdfkT/7kT2r8GwDUj0HHdR4CHDcpOWxIdeopsqEnVfrdkdHvSvoMqE49RXbcpGRAJ2f3nvSepLEuP+rrWUacUTmo6qjXY9/n4PVAOOGspLF3On5ev7dq5RTamPfseM7uqdelpKExObHrywuzF6VSMva8dBg09uqXjJ66l+10WUND5bV4r0pJv8OT4U0d7EOX9OqbnHhOx/sMPDo5ZkJ16qHr6jIAS5Lx48dn7ty52bhxY5YtW5avfOUrefTRRzNx4sT07185P/yLX/xiXnzxxTz33HN57rnncvbZZ+cv//Iv87u/+7s1rh6gfpRKyWkfSo7dyx/h409LTrmgujUVVUNDcsZHK5/CvkMpGX2Wg9cDpVefZOonkkHHvnNbqTEZ15yMnPLObey7vodVer2nZQIbeycTL9z76wv7ZsDgZOrHk74D37mtV99k8keSwSOrXlYhHXFccvpHk9793rmtT/9kyscqB7B039AxlfchjX3eua3/oOTMTyT9BlW/riI6/tRkwq9VZpS+3cChydRP7vk5z7474axkzLmVmf1vd+SIymuID+HqT4/6TzJ//vx9utIjABWNvZPTPlz5xPu+v6uMjXlPctwplVOXOHB690umXLb7uidjz0uOm7jng1r2X9+Bybt+M3ltZTL/Hytj499feV5bS/nAOmxIcs6MZO2yZMHtlbGTP5AMO6USRnLgDBqWvOf/Sl55Nln0L5WxSRdVZhI4mDqwjhqdvO9zyeqnksX/Xhk77cPJ0WMrM8A4cI49uRKEvfRk8qsdayedfmly1Ilmjx5oI8+ovDa/9Ks3lwqY+olKKKPXB06pVAnARkxOVv4qeaqlMv6u36wE7NSnup0B9nYbNmzIkiVLdrsC5Nu1tLTkYx/7WBWrAuhZ3nqa45hzhF8H0+HHvPn1CWcJvw6W0o41kXYaNUX4dbCUSpXAYKcRk4VfB0tDQyWE2em4ScKvg6WhVyUs2OnYCcKvg6WxT2VNwZ2GjhHIHCy9+1WCsJ0Gj9Trg6XPYcnoM9/8XvhV33rMn9KBAwemra0Ll8UBAAAAgLfoMTPAAAAAAGB/CMAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUmgAMAAAAgEITgAEAAABQaAIwAAAAAApNAAYAAABAoQnAAAAAACg0ARgAAAAAhSYAK6CWlpaMHj0606ZNyyWXXJLNmzfvtn3WrFlZsGBBHnjggZx77rl573vfm+uuu67Dn7lixYp8/vOfz+LFi3Puuefmfe97X2bMmJFyuZxFixblpptuOpi/Ut3S6+rR6+rQ5+rR6+rR6+rR6+rR6+rR6+rR6+rR6+rR6/ohACuoK664Ii0tLTn33HMze/bsXePt7e35xS9+kTPOOCOjR4/Oz372s/z85z/P6tWr8+ijj+7159199935wAc+kAkTJmTevHm59957kyTz58/P5MmTc99996VcLh/036se6XX16HV16HP16HX16HX16HX16HX16HX16HX16HX16HV9EIAV3Omnn57ly5fv+n7RokUZO3ZskmTYsGHp169fkqR3795pbGxMS0tLBg8enGnTpmX06NG55JJLkiStra1pbm5O7969d/2svn37ZuTIkUmScePGZcGCBdX6teqSXlePXleHPlePXlePXlePXlePXlePXlePXlePXlePXteWAKzg7rnnnowfP37X90899VROOOGE3fZ55JFHsmbNmkycODHnnXdezjrrrLS0tKS5uTl/+Zd/mXK5nI0bN2bgwIFJkjvuuCOnnnpqVq1alaOOOipJMmbMmDzxxBNV+73qkV5Xj15Xhz5Xj15Xj15Xj15Xj15Xj15Xj15Xj15Xj17XlgCsoL773e9m+vTpefXVV3elxHuydu3a/PZv/3a+/e1vJ0meffbZjBkzJknywgsvZPjw4Vm0aFEmT5686z6//uu/nsWLF2fEiBH54Q9/eHB/kR5Ar6tHr6tDn6tHr6tHr6tHr6tHr6tHr6tHr6tHr6tHr+uDAKygrrjiisydOze33HJLGhsbd42PGzcuzz33XJJk+/bt+dSnPpVZs2Zl2LBhSZLHHnsskyZNSltbWxoaKk+PnecXJ8mWLVt2/axBgwalf//+SSr/Y5588snV+NXqjl5Xj15Xhz5Xj15Xj15Xj15Xj15Xj15Xj15Xj15Xj17XBwHYIWby5MlZsmRJkuT222/PL3/5y/ze7/1epk2blvvuu2/X/2BbtmzJ6tWrs3LlysyfPz9nnnlmkuSuu+5Kc3Nzmpubs2rVqlxwwQVJkiVLluT000+v1a9Vl/S6evS6OvS5evS6evS6evS6evS6evS6evS6evS6evS6ysqHqObm5nJzc3Oty9hvd99cue2Pm2++ufzwww93ef/vf//7HW5fuHBh+Wtf+9r+FdMD6HX16HV16HP16HX16HX16HX16HX16HX16HX16HX16HX17U+mUyqXD81rY06bNi1J0tLSUtM69tdPZlX+Pf8Lta3jUKDX1aPX1aHP1aPX1aPX1aPX1aPX1aPX1aPX1aPX1aPX1bc/mY5TIAEAAAAoNAEYAAAAAIUmAAMAAACg0ARgAAAAABSaAAwAAACAQhOAAQAAAFBoAjAAAAAACk0ABgAAAEChCcAAAAAAKDQBGAAAAACFJgADAAAAoNAEYAAAAAAUWl0HYO3t7Zk1a1bGjRuXfv36ZfLkyWltbc2ECRNy1VVX1bq8mtm49s2v27bVro5Dwetr3vy6va12dRRduZy8tvIt37fXrpaie2tvX1tZ6T0Hx1tfM15frdcHU9v2N7/e+Ert6jgUbN/65tdvvFqzMg4JWze9+fXm12tXx6Fgy4Y3v976Ru3qOBRseu3Nr7dtrl0dhwLHjNWzwTFjj1Eql+v3LfmMGTMyZ86c3HjjjZk6dWrmzZuXW265JWvWrMlf/MVf5HOf+9x+/+xp06YlSVpaWg5MsVWw/qVkSUvy6vI3xxr7JCPPSMacmzQ01qy0wlm7LHmqpXLQulPv/snoM5PRZyWlUs1KK5zVTyVP35u88ZY/0n0PT048OxkxuXZ1FdGKR5Ol83Y/kBowODnpvcmxE2pXV9GUy8myh5LnH9z9QGrg0cm45uSoE2pWWuG0t1ee0y8sSLZveXP8iOOT8dMq/3JgtG2rvFaveCRpf0vgOGR0Mn56MnBo7Wormm2bK+9BVv4qKb/lQOroscmE9yf9BtWstMLZsiF58meV9yLZcURUakiOPbnyGtJnQC2rK5Y31iVPzk1eefbNsYbG5LhTK38be/WpXW1Fs37VjmPGF94ca+yTjDg9Oek9jhkPpHUvVHr9+qo3x3r3S0admZzwbseMB9v+ZDp1G4Dddttt+Y3f+I20tLSkubl51/hHP/rRzJkzJw8++GDe9a537ffP72kB2Gsrk4f+qfJmP3v4L3b0uKTpw5U/2nTPy88mC/95xzd76PXwycnJ53tBOxBefCx5/Ed73z7m3MqN7nvuweTpe/a+/eQPCBwPlCfnJi88tIcNO14zmi5Jjhlb1ZIKqVxOFv8wWfXkHjaWKn8Pp16WHDmi6qUVTntbsuAHybple9hYShp7J+/6DSHYgbB9azL/tt1nE+xSqgQyZ/2mEOxA2LIx+eU/7PhQaA/v9wYMrjyve/evemmF88a6Sq+3bckeez3ouGTqxyuvJXTP+peS+f+0YxbSHno99KTK+5AGx4zd9spzycI5O2b476HXx5+WnHKBY8aDaX8ynbp96s+cOTMXXnjhbuFXkowdOza9e/dOU1NTksovfeKJJ+b000/P6aefni9+8Yu1KPegKpeTx3+89/ArSdY8tePTK7qlvS15/K5U+ryXXq9YlLz2YjWrKqbtW5In7u54n2fnVd400T2bXus4/Eoqn4C/9XQb9s9rK/cSfiW7Xld+ddfuM2jYPy8/u5fwK0nKldN9H/+xU08PhBcX7yX8SpJyZXbYkz+takmFtWz+XsKvJClXZpU+fW9VSyqsZ3+RbF6fvb7fe2Nd8twDVS2psJbM3Xv4lSTrVybLF1W1pML61X/sPfxKkpefSVbv7W8nXVZurxwz7i38SpIXH63MEKO+1GUAtnz58ixevDiXXXbZO7YtW7YskyZNSt++fXeN3XzzzVm4cGEWLlyYr33ta9UstSrWr0w2vpy9/s+VJCklyxdWqaACe/mZLqz9oNcHxMrHuxYCrPCGqNtWPNr5PuW2ZOVjB7+WoluxKLtmeu3Nts0+sDgQli9Ix70uVw5g37psAPunK71e98Lu682w78rtXXh/Ua4Ev9ap6p7tW7v2N2/Fo7uvMci+27y+8oFFh8cxqZzK7gOL7ln/0o7lWzo5ZnxhYZUKKrCXl+5YO9DxeY9TtwFYkgwbNmy38U2bNqW1tTVTpkzp9mO0tramtbU1pVKp7m+/cWkXFvwvJ8ueXFvzWnv67Qu//Qdd6vX9cx+rea09/fYnf/jNtHWSgLW3t+cH//Djmtfa02+3ffuOtHWyImdb2/bcMuvWmtfa028tdz3U6Zv8crk9N/zuH9W81p5+e+qRlZ32Okk+c/nv1LzWnn5bv7qtS72+ePplNa+1J9+GDDqmS8FWuT2ZMum9Na+3J98mnDC5SwtVb9+SjBx2Us3r7cm39511YeeNTrL5taR/3wE1r7cn3z7+4RldeAFJXnr29ZrX2tNv//2q/7dLvX74F0tqXmuRbzsznX1RlwHY0KGVRSSWLFmy2/hNN92UlStXZurUqbuN33DDDTnttNNyySWX5JFHHqlandXS1sXLdmx3eY9u60qvy+Vytrdt7XQ/OtbWti2lzqbKpOx5fQBsb9+WTo9eS15DDoTtbVvT+dKapS6/rrN3XX2+Vp7/dEdnH1bs5DWke/blueo1pHv25bnqed09+/Jc7eprDXvW1deQ7aY1dluX34M4Zqw7dbkIfnt7e84444ysXLkys2bNyvDhwzN79uzceeedWbZsWe6///68+93vTlI5JXLkyJEplUr5p3/6p1x33XV5+umnc9hhh3X4GNN60CL4m15LfvE3nexUSo47JZl0cVVKKqzXVlYW6ezMCWclY887+PUU2eqnk0f+pfP9xr8/GdX9SZ+HtOULkyd+0vl+p33Y1SC765lfJEvv63y/Mz9pcfbu+tV/VK5I2Jlzr6wsZs3+WzincrpHRzl6qSF539VJHwuG77dyOXnwu8nra9Jhr3v1S877r0lDr6qVVjjt7ckvvrXjFKYO9D+y8hpSsoj1ftu+Nbnnr5IOs5lScuTwyt9G9t/m15OffyudnpZ37ITktA9Vq6pien118sDfd77fqKmVKyVzcOxPplOXM8AaGhpy++23Z9KkSbn66qszY8aMDB06NNdee20aGxt3LYCfJKNGjUppx1+lT37yk+nTp0+efLJYK/v1P6Jy6esOlZMRZ1SlnEIbNKxy62hiUqkhGd609+10zdAxSb/Ds/de77iy2HETq1lVMQ2bmPTqmw573eewLrzO0KnhTZ1cjbdUuVLeEcOrVlJhjTi9832OOkH4dSCMnJJOJ5EeN1H41V2lUjJyajrt9YjThV/d1dCQjOzC++ZRU4Vf3dWrTzL8tE52Kvuw80Dod3hyzLhOdip37blPxw4/Jjni+HS8Pmapa+9VqK66DMCSZPz48Zk7d242btyYZcuW5Stf+UoeffTRTJw4Mf37V95hbd68OS+//PKu+/z0pz/N66+/nrFji3cUd8oFyWFH7WHDjv/pxr8/OeK4qpZUSKVSZRZM34F72li5Tbq48okg3dPQkEz+zzuCmb1sb7ok6d2vunUVUa8+yeSPJA2Ne97e2Ds5/T/vfTtd1+/wyqeqpYbs8U1RnwGV57UDqu47/Jjk5A/s+GYP/RwwOJl4UVVLKqyjTkjGvGfHN3vo9aBhlfchdN9xE5MRk3d8s4deH3VCMuacalZUXKPelRy9Myx4a693fD1sooPXA2Xs+yozvN5hR69Hv/W/Bd1yygeSw4buYcOOXo+btpf/Fuyz0z6U9OvomPEiH8LVo7o8BXJvTjnllJx99tn5zne+kyRZvXp1LrroomzdujUNDQ0ZNGhQ/uiP/ijvfe97O/1ZPekUyJ22b6lctWP5wmTL60lKlVk0o6YmQ0bVuLiC2bqxcjWa5YuSbZsqB7PHjE9Gn7ljhhgHzOb1ybKHKpcK3r618qn2sFMqz+uBe/oDzn7buLbS65WPVa7A2dgnOf7UyqeuQt0Da/2qSq9XPVFZsLp3v8rssJFTk74dn6HPPlq3vNLrl5+unELWd2AyfHLlE24B+oH18rPJCw8nrzxX+b7/EZXZ5yMmV4J0DoxyOVn9ZLJsQfLaisrYYUOTkacnx5/mw4oDqdyevPhY5Xm9YU1lbNCwyqzHYaf4sOJAat+eLH+kclXZN9ZVxgaPrPS601lL7JPtWyt9fmHhW44ZT9xxzDi61tUVy9Y3KseMKxZVvi41VJ7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" ] }, "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", "qft_dagger(qpe3, 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": 12, "id": "67bdfc38", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the results!\n", "qasm_sim = Aer.get_backend('qasm_simulator')\n", "shots = 4096\n", "t_qpe3 = transpile(qpe3, qasm_sim)\n", "qobj = assemble(t_qpe3, shots=shots)\n", "results = qasm_sim.run(qobj).result()\n", "answer = results.get_counts()\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "e45eb3b2", "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": "904c9bc2", "metadata": {}, "source": [ "## 4. Experiment with Real Devices \n", "### 4.1 Circuit from 2.1 \n", "\n", "We can run the circuit in section 2.1 on a real device, let's remind ourselves of the circuit:" ] }, { "cell_type": "code", "execution_count": 13, "id": "6589bab7", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qpe.draw()" ] }, { "cell_type": "code", "execution_count": 14, "id": "6ccdbc17", "metadata": { "scrolled": true, "tags": [ "uses-hardware" ] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":10: DeprecationWarning: Passing a Qobj to Backend.run is deprecated and will be removed in a future release. Please pass in circuits or pulse schedules instead.\n", " job = santiago.run(qobj)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Job Status: job has successfully run\n" ] } ], "source": [ "IBMQ.load_account()\n", "from qiskit.tools.monitor import job_monitor\n", "provider = IBMQ.get_provider(hub='ibm-q')\n", "santiago = provider.get_backend('ibmq_santiago')\n", "\n", "# Run with 2048 shots\n", "shots = 2048\n", "t_qpe = transpile(qpe, santiago, optimization_level=3)\n", "qobj = assemble(t_qpe, shots=shots)\n", "job = santiago.run(qobj)\n", "job_monitor(job)" ] }, { "cell_type": "code", "execution_count": 77, "id": "a27ca0fd", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_qpe.draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "86a92428", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 15, "id": "b45a224c", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# get the results from the computation\n", "results = job.result()\n", "answer = results.get_counts(qpe)\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "1e3f3a46", "metadata": {}, "source": [ "We can hopefully see that the most likely result is `001` which is the result we would expect from the simulator. Unlike the simulator, there is a probability of measuring something other than `001`, this is due to noise and gate errors in the quantum computer." ] }, { "cell_type": "markdown", "id": "dc2adc36", "metadata": {}, "source": [ "## 5. Exercises \n", "1. Try the experiments above with different gates ($\\text{CNOT}$, Controlled-$S$, Controlled-$T^\\dagger$), what results do you expect? What results do you get?\n", "\n", "2. Try the experiment with a Controlled-$Y$-gate, do you get the result you expected? (Hint: Remember to make sure $|\\psi\\rangle$ is an eigenstate of $Y$!)\n" ] }, { "cell_type": "markdown", "id": "8759613c", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "- What are the eigenstates for X operator? What are the corresponding eigenvalues?\n", "- Fill in the code below for initializing the target qubit to the eigestate of X gate, the one w/ the positive eigenvalue.\n", "- Run the circuit by running the following cells, calculate $\\theta$ and discuss your results." ] }, { "cell_type": "code", "execution_count": null, "id": "04872e86", "metadata": {}, "outputs": [], "source": [ "qpex = QuantumCircuit(4, 3)\n", "\n", "# Apply H-Gates to counting qubits:\n", "for qubit in range(3):\n", " qpex.h(qubit)\n", "\n", "# Prepare our eigenstate |psi>:\n", "\n", "\n", "# Do the controlled-U operations, CNOT:\n", "repetitions = 1\n", "for counting_qubit in range(3):\n", " for i in range(repetitions):\n", " qpex.cx(counting_qubit, 3);\n", " repetitions *= 2\n", "\n", "# Do the inverse QFT:\n", "qft_dagger(qpex, 3)\n", "\n", "# Measure of course!\n", "for n in range(3):\n", " qpex.measure(n,n)\n", "\n", "qpex.draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "646b62eb", "metadata": {}, "outputs": [], "source": [ "# Let's see the results!\n", "qasm_sim = Aer.get_backend('qasm_simulator')\n", "shots = 4096\n", "t_qpex = transpile(qpex, qasm_sim)\n", "qobj = assemble(t_qpex, shots=shots)\n", "results = qasm_sim.run(qobj).result()\n", "answer = results.get_counts()\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "4e0cf46e", "metadata": {}, "source": [ "### Answer\n", "\n", "Discuss your results." ] }, { "cell_type": "markdown", "id": "7d979034", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "- Fill in the code below for initializing the target qubit to the eigestate of X gate, the one w/ the negative eigenvalue.\n", "- Run the following cells, calculate $\\theta$ and discuss your results.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "366e0e8e", "metadata": {}, "outputs": [], "source": [ "qpex = QuantumCircuit(4, 3)\n", "\n", "# Apply H-Gates to counting qubits:\n", "for qubit in range(3):\n", " qpex.h(qubit)\n", "\n", "# Prepare our eigenstate |psi>:\n", "\n", "\n", "# Do the controlled-U operations, CNOT:\n", "repetitions = 1\n", "for counting_qubit in range(3):\n", " for i in range(repetitions):\n", " qpex.cx(counting_qubit, 3);\n", " repetitions *= 2\n", "\n", "# Do the inverse QFT:\n", "qft_dagger(qpex, 3)\n", "\n", "# Measure of course!\n", "for n in range(3):\n", " qpex.measure(n,n)\n", "\n", "qpex.draw()" ] }, { "cell_type": "code", "execution_count": null, "id": "5ca96071", "metadata": {}, "outputs": [], "source": [ "# Let's see the results!\n", "qasm_sim = Aer.get_backend('qasm_simulator')\n", "shots = 4096\n", "t_qpex = transpile(qpex, qasm_sim)\n", "qobj = assemble(t_qpex, shots=shots)\n", "results = qasm_sim.run(qobj).result()\n", "answer = results.get_counts()\n", "\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "1ed8963a", "metadata": {}, "source": [ "### Answer\n", "\n", "Discuss your results." ] }, { "cell_type": "markdown", "id": "85cc75bf", "metadata": {}, "source": [ "## 6. Looking Forward \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": "84de27e1", "metadata": {}, "source": [ "## 7. References \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. " ] }, { "cell_type": "markdown", "id": "96b5e20f", "metadata": {}, "source": [ "## 8. Contributors \n", "03/20/2020 — Hwajung Kang (@HwajungKang) — Fixed inconsistencies with qubit ordering" ] }, { "cell_type": "markdown", "id": "fa70ce0c", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "# Shor's Algorithm" ] }, { "cell_type": "markdown", "id": "98af3603", "metadata": {}, "source": [ "Shor’s algorithm is famous for factoring integers in polynomial time. Since the best-known classical algorithm requires superpolynomial time to factor the product of two primes, the widely used cryptosystem, RSA, relies on factoring being impossible for large enough integers.\n", "\n", "In this chapter we will focus on the quantum part of Shor’s algorithm, which actually solves the problem of _period finding_. Since a factoring problem can be turned into a period finding problem in polynomial time, an efficient period finding algorithm can be used to factor integers efficiently too. For now its enough to show that if we can compute the period of $a^x\\bmod N$ efficiently, then we can also efficiently factor. Since period finding is a worthy problem in its own right, we will first solve this, then discuss how this can be used to factor in section 5." ] }, { "cell_type": "code", "execution_count": 20, "id": "67d16199", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Imports Successful\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from qiskit import QuantumCircuit, Aer, transpile, assemble\n", "from qiskit.visualization import plot_histogram\n", "from math import gcd\n", "from numpy.random import randint\n", "import pandas as pd\n", "from fractions import Fraction\n", "print(\"Imports Successful\")" ] }, { "cell_type": "markdown", "id": "e51037f9", "metadata": {}, "source": [ "## 1. The Problem: Period Finding\n", "\n", "Let’s look at the periodic function:\n", "\n", "$$ f(x) = a^x \\bmod{N}$$\n", "\n", "
\n", " Reminder: Modulo & Modular Arithmetic (Click here to expand)\n", "\n", "The modulo operation (abbreviated to 'mod') simply means to find the remainder when dividing one number by another. For example:\n", "\n", "$$ 17 \\bmod 5 = 2 $$\n", "\n", "Since $17 \\div 5 = 3$ with remainder $2$. (i.e. $17 = (3\\times 5) + 2$). In Python, the modulo operation is denoted through the % symbol.\n", "\n", "This behaviour is used in modular arithmetic, where numbers 'wrap round' after reaching a certain value (the modulus). Using modular arithmetic, we could write:\n", "\n", "$$ 17 = 2 \\pmod 5$$\n", "\n", "Note that here the $\\pmod 5$ applies to the entire equation (since it is in parenthesis), unlike the equation above where it only applied to the left-hand side of the equation.\n", "
\n", "\n", "where $a$ and $N$ are positive integers, $a$ is less than $N$, and they have no common factors. The period, or order ($r$), is the smallest (non-zero) integer such that:\n", "\n", "$$a^r \\bmod N = 1 $$ \n", "\n", "We can see an example of this function plotted on the graph below. Note that the lines between points are to help see the periodicity and do not represent the intermediate values between the x-markers." ] }, { "cell_type": "code", "execution_count": 21, "id": "21030738", "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 35\n", "a = 3\n", "\n", "# Calculate the plotting data\n", "xvals = np.arange(35)\n", "yvals = [np.mod(a**x, N) for x in xvals]\n", "\n", "# Use matplotlib to display it nicely\n", "fig, ax = plt.subplots()\n", "ax.plot(xvals, yvals, linewidth=1, linestyle='dotted', marker='x')\n", "ax.set(xlabel='$x$', ylabel='$%i^x$ mod $%i$' % (a, N),\n", " title=\"Example of Periodic Function in Shor's Algorithm\")\n", "try: # plot r on the graph\n", " r = yvals[1:].index(1) +1 \n", " plt.annotate('', xy=(0,1), xytext=(r,1), arrowprops=dict(arrowstyle='<->'))\n", " plt.annotate('$r=%i$' % r, xy=(r/3,1.5))\n", "except ValueError:\n", " print('Could not find period, check a < N and have no common factors.')" ] }, { "cell_type": "markdown", "id": "63ddd38d", "metadata": {}, "source": [ "## 2. The Solution\n", "\n", "Shor’s solution was to use [quantum phase estimation](./quantum-phase-estimation.html) on the unitary operator:\n", "\n", "$$ U|y\\rangle \\equiv |ay \\bmod N \\rangle $$\n", "\n", "To see how this is helpful, let’s work out what an eigenstate of U might look like. If we started in the state $|1\\rangle$, we can see that each successive application of U will multiply the state of our register by $a \\pmod N$, and after $r$ applications we will arrive at the state $|1\\rangle$ again. For example with $a = 3$ and $N = 35$:\n", "\n", "$$\\begin{aligned}\n", "U|1\\rangle &= |3\\rangle & \\\\\n", "U^2|1\\rangle &= |9\\rangle \\\\\n", "U^3|1\\rangle &= |27\\rangle \\\\\n", "& \\vdots \\\\\n", "U^{(r-1)}|1\\rangle &= |12\\rangle \\\\\n", "U^r|1\\rangle &= |1\\rangle \n", "\\end{aligned}$$" ] }, { "cell_type": "code", "execution_count": 22, "id": "cbbb200d", "metadata": { "scrolled": true, "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax.set(xlabel='Number of applications of U', ylabel='End state of register',\n", " title=\"Effect of Successive Applications of U\")\n", "fig" ] }, { "cell_type": "markdown", "id": "3720592e", "metadata": {}, "source": [ "### Exercise 5\n", "\n", "Let's say the number we would like to factor is $N=21$ and we chose $a=11$. So we defined $O|y\\rangle = |11\\times y \\ mod \\ 21 \\rangle$. What are the results of:\n", "- $O|1\\rangle = ?$\n", "- $O^2|1\\rangle = ?$\n", "- $O^3|1\\rangle = ?$\n", "- $O^4|1\\rangle = ?$\n", "- $O^5|1\\rangle = ?$\n", "- $O^6|1\\rangle = ?$\n", "- $O^7|1\\rangle = ?$\n", "- According to your results, what is the period $r$ such that $a^r = 1 \\ mod \\ 21 $." ] }, { "cell_type": "markdown", "id": "760f106a", "metadata": {}, "source": [ "### Answer\n", "\n", "?" ] }, { "cell_type": "markdown", "id": "0ce7b370", "metadata": {}, "source": [ "So a superposition of the states in this cycle ($|u_0\\rangle$) would be an eigenstate of $U$:\n", "\n", "$$|u_0\\rangle = \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{|a^k \\bmod N\\rangle} $$\n", "\n", "\n", "
\n", " Click to Expand: Example with $a = 3$ and $N=35$\n", "\n", "$$\\begin{aligned}\n", "|u_0\\rangle &= \\tfrac{1}{\\sqrt{12}}(|1\\rangle + |3\\rangle + |9\\rangle \\dots + |4\\rangle + |12\\rangle) \\\\[10pt]\n", "U|u_0\\rangle &= \\tfrac{1}{\\sqrt{12}}(U|1\\rangle + U|3\\rangle + U|9\\rangle \\dots + U|4\\rangle + U|12\\rangle) \\\\[10pt]\n", " &= \\tfrac{1}{\\sqrt{12}}(|3\\rangle + |9\\rangle + |27\\rangle \\dots + |12\\rangle + |1\\rangle) \\\\[10pt]\n", " &= |u_0\\rangle\n", "\\end{aligned}$$\n", "
\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "4ba261d1", "metadata": {}, "source": [ "### Exercise 6\n", "\n", "According to your result from previous example, write down $|o_0 \\rangle$ explicitly for $a=11$ and $N=21$ where:\n", "$$|o_0\\rangle = \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{|a^k \\bmod N\\rangle} $$\n", "\n", "What is the eigenvalue of $O$ corresponding to $|o_0\\rangle$ ? That is, given $O|o_0\\rangle = \\lambda |o_0 \\rangle$, what is $\\lambda$?" ] }, { "cell_type": "markdown", "id": "36c448a6", "metadata": {}, "source": [ "### Answer\n", "?" ] }, { "cell_type": "markdown", "id": "74a3ca05", "metadata": {}, "source": [ "This eigenstate has an eigenvalue of 1, which isn’t very interesting. A more interesting eigenstate could be one in which the phase is different for each of these computational basis states. Specifically, let’s look at the case in which the phase of the $k$th state is proportional to $k$:\n", "\n", "$$\\begin{aligned}\n", "|u_1\\rangle &= \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{e^{-\\tfrac{2\\pi i k}{r}}|a^k \\bmod N\\rangle}\\\\[10pt]\n", "U|u_1\\rangle &= e^{\\tfrac{2\\pi i}{r}}|u_1\\rangle \n", "\\end{aligned}\n", "$$\n", "\n", "
\n", " Click to Expand: Example with $a = 3$ and $N=35$\n", "\n", "$$\\begin{aligned}\n", "|u_1\\rangle &= \\tfrac{1}{\\sqrt{12}}(|1\\rangle + e^{-\\tfrac{2\\pi i}{12}}|3\\rangle + e^{-\\tfrac{4\\pi i}{12}}|9\\rangle \\dots + e^{-\\tfrac{20\\pi i}{12}}|4\\rangle + e^{-\\tfrac{22\\pi i}{12}}|12\\rangle) \\\\[10pt]\n", "U|u_1\\rangle &= \\tfrac{1}{\\sqrt{12}}(|3\\rangle + e^{-\\tfrac{2\\pi i}{12}}|9\\rangle + e^{-\\tfrac{4\\pi i}{12}}|27\\rangle \\dots + e^{-\\tfrac{20\\pi i}{12}}|12\\rangle + e^{-\\tfrac{22\\pi i}{12}}|1\\rangle) \\\\[10pt]\n", "U|u_1\\rangle &= e^{\\tfrac{2\\pi i}{12}}\\cdot\\tfrac{1}{\\sqrt{12}}(e^{\\tfrac{-2\\pi i}{12}}|3\\rangle + e^{-\\tfrac{4\\pi i}{12}}|9\\rangle + e^{-\\tfrac{6\\pi i}{12}}|27\\rangle \\dots + e^{-\\tfrac{22\\pi i}{12}}|12\\rangle + e^{-\\tfrac{24\\pi i}{12}}|1\\rangle) \\\\[10pt]\n", "U|u_1\\rangle &= e^{\\tfrac{2\\pi i}{12}}|u_1\\rangle\n", "\\end{aligned}$$\n", "\n", "(We can see $r = 12$ appears in the denominator of the phase.)\n", "
\n", "\n" ] }, { "cell_type": "markdown", "id": "ac40561e", "metadata": {}, "source": [ "### Exercise 7\n", "\n", "According to your result from previous example, write down $|o_1 \\rangle$ explicitly for $a=11$ and $N=21$ where:\n", "$$|o_1\\rangle = \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{e^{-\\tfrac{2\\pi i k}{r}}|a^k \\bmod N\\rangle} $$\n", "\n", "What is the eigenvalue corresponding to $|o_1\\rangle$ ? That is, given $O|o_1\\rangle = \\lambda |o_1 \\rangle$, what is $\\lambda$?" ] }, { "cell_type": "markdown", "id": "4a86bf93", "metadata": {}, "source": [ "### Answer\n", "\n", "?" ] }, { "cell_type": "markdown", "id": "3f9e9fc4", "metadata": {}, "source": [ "This is a particularly interesting eigenvalue as it contains $r$. In fact, $r$ has to be included to make sure the phase differences between the $r$ computational basis states are equal. This is not the only eigenstate with this behaviour; to generalise this further, we can multiply an integer, $s$, to this phase difference, which will show up in our eigenvalue:\n", "\n", "$$\\begin{aligned}\n", "|u_s\\rangle &= \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{e^{-\\tfrac{2\\pi i s k}{r}}|a^k \\bmod N\\rangle}\\\\[10pt]\n", "U|u_s\\rangle &= e^{\\tfrac{2\\pi i s}{r}}|u_s\\rangle \n", "\\end{aligned}\n", "$$\n", "\n", "
\n", " Click to Expand: Example with $a = 3$ and $N=35$\n", "\n", "$$\\begin{aligned}\n", "|u_s\\rangle &= \\tfrac{1}{\\sqrt{12}}(|1\\rangle + e^{-\\tfrac{2\\pi i s}{12}}|3\\rangle + e^{-\\tfrac{4\\pi i s}{12}}|9\\rangle \\dots + e^{-\\tfrac{20\\pi i s}{12}}|4\\rangle + e^{-\\tfrac{22\\pi i s}{12}}|12\\rangle) \\\\[10pt]\n", "U|u_s\\rangle &= \\tfrac{1}{\\sqrt{12}}(|3\\rangle + e^{-\\tfrac{2\\pi i s}{12}}|9\\rangle + e^{-\\tfrac{4\\pi i s}{12}}|27\\rangle \\dots + e^{-\\tfrac{20\\pi i s}{12}}|12\\rangle + e^{-\\tfrac{22\\pi i s}{12}}|1\\rangle) \\\\[10pt]\n", "U|u_s\\rangle &= e^{\\tfrac{2\\pi i s}{12}}\\cdot\\tfrac{1}{\\sqrt{12}}(e^{-\\tfrac{2\\pi i s}{12}}|3\\rangle + e^{-\\tfrac{4\\pi i s}{12}}|9\\rangle + e^{-\\tfrac{6\\pi i s}{12}}|27\\rangle \\dots + e^{-\\tfrac{22\\pi i s}{12}}|12\\rangle + e^{-\\tfrac{24\\pi i s}{12}}|1\\rangle) \\\\[10pt]\n", "U|u_s\\rangle &= e^{\\tfrac{2\\pi i s}{12}}|u_s\\rangle\n", "\\end{aligned}$$\n", "\n", "
\n", "\n" ] }, { "cell_type": "markdown", "id": "dcb79120", "metadata": {}, "source": [ "### Exercise 8\n", "\n", "According to your result from previous example, write down $|o_s \\rangle$ explicitly for $a=11$ and $N=21$ where:\n", "$$|o_s\\rangle = \\tfrac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1}{e^{-\\tfrac{2\\pi i k}{r}}|a^k \\bmod N\\rangle} $$\n", "\n", "What is the eigenvalue corresponding to $|o_s\\rangle$ ? That is, given $O|o_s\\rangle = \\lambda |o_s \\rangle$, what is $\\lambda$? " ] }, { "cell_type": "markdown", "id": "f970e79f", "metadata": {}, "source": [ "### Answer\n", "?" ] }, { "attachments": { "image-2.png": { "image/png": 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" }, "image-3.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "5df2a08e", "metadata": {}, "source": [ "We now have a unique eigenstate for each integer value of $s$ where $$0 \\leq s \\leq r-1$$. Very conveniently, if we sum up all these eigenstates, the different phases cancel out all computational basis states except $|1\\rangle$:\n", "\n", "$$ \\tfrac{1}{\\sqrt{r}}\\sum_{s=0}^{r-1} |u_s\\rangle = |1\\rangle$$\n", "\n", "
\n", " Click to Expand: Example with $a = 7$ and $N=15$\n", "\n", "For this, we will look at a smaller example where $a = 7$ and $N=15$. In this case $r=4$:\n", "\n", "$$\\begin{aligned}\n", "\\tfrac{1}{2}(\\quad|u_0\\rangle &= \\tfrac{1}{2}(|1\\rangle \\hphantom{e^{-\\tfrac{2\\pi i}{12}}}+ |7\\rangle \\hphantom{e^{-\\tfrac{12\\pi i}{12}}} + |4\\rangle \\hphantom{e^{-\\tfrac{12\\pi i}{12}}} + |13\\rangle)\\dots \\\\[10pt]\n", "+ |u_1\\rangle &= \\tfrac{1}{2}(|1\\rangle + e^{-\\tfrac{2\\pi i}{4}}|7\\rangle + e^{-\\tfrac{\\hphantom{1}4\\pi i}{4}}|4\\rangle + e^{-\\tfrac{\\hphantom{1}6\\pi i}{4}}|13\\rangle)\\dots \\\\[10pt]\n", "+ |u_2\\rangle &= \\tfrac{1}{2}(|1\\rangle + e^{-\\tfrac{4\\pi i}{4}}|7\\rangle + e^{-\\tfrac{\\hphantom{1}8\\pi i}{4}}|4\\rangle + e^{-\\tfrac{12\\pi i}{4}}|13\\rangle)\\dots \\\\[10pt]\n", "+ |u_3\\rangle &= \\tfrac{1}{2}(|1\\rangle + e^{-\\tfrac{6\\pi i}{4}}|7\\rangle + e^{-\\tfrac{12\\pi i}{4}}|4\\rangle + e^{-\\tfrac{18\\pi i}{4}}|13\\rangle)\\quad) = |1\\rangle \\\\[10pt]\n", "\\end{aligned}$$\n", "\n", "
\n", "\n", "![image-2.png](attachment:image-2.png)\n", "\n", "Since the computational basis state $|1\\rangle$ is a superposition of these eigenstates, which means if we do QPE on $U$ using the state $|1\\rangle$, we will measure a phase:\n", "\n", "$$\\phi = \\frac{s}{r}$$\n", "\n", "!! Remember when we measure the state will collapse to one of the eigenstates $|u_s\\rangle$ and the corresponding eigenvalue is $e^{2\\pi s / r}$. The quantum phase estimation algortihm yields the value $\\theta$ in $e^{2\\pi \\theta}$. Therefore, we will get the value $\\frac{s}{r}$. \n", "\n", "Where $s$ is a random integer between $0$ and $r-1$. We finally use the [continued fractions](https://en.wikipedia.org/wiki/Continued_fraction) algorithm on $\\phi$ to find $r$. The circuit diagram looks like this (note that this diagram uses Qiskit's qubit ordering convention):\n", "\n", "![image-3.png](attachment:image-3.png)\n", "\n", "We will next demonstrate Shor’s algorithm using Qiskit’s simulators. For this demonstration we will provide the circuits for $U$ without explanation, but in section 4 we will discuss how circuits for $U^{2^j}$ can be constructed efficiently." ] }, { "cell_type": "markdown", "id": "c44353fa", "metadata": {}, "source": [ "### Exercise 9\n", "\n", "If you did the previous exercises, then you know the value of $r$. We also know $0 \\leq s \\leq r-1$. Than what are the possible values for $\\frac{s}{r}$ when $a=11$ and $N=21$?" ] }, { "cell_type": "markdown", "id": "7b955e36", "metadata": {}, "source": [ "### Answer\n", "?" ] }, { "cell_type": "markdown", "id": "0da77019", "metadata": {}, "source": [ "## 3. Qiskit Implementation\n", "\n", "In this example we will solve the period finding problem for $a=7$ and $N=15$. We provide the circuits for $U$ where:\n", "\n", "$$U|y\\rangle = |ay\\bmod 15\\rangle $$\n", "\n", "without explanation. To create $U^x$, we will simply repeat the circuit $x$ times. In the next section we will discuss a general method for creating these circuits efficiently. The function `c_amod15` returns the controlled-U gate for `a`, repeated `power` times." ] }, { "cell_type": "code", "execution_count": 23, "id": "8f0ce81d", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def c_amod15(a, power):\n", " \"\"\"Controlled multiplication by a mod 15\"\"\"\n", " if a not in [2,7,8,11,13]:\n", " raise ValueError(\"'a' must be 2,7,8,11 or 13\")\n", " U = QuantumCircuit(4) \n", " for iteration in range(power):\n", " if a in [2,13]:\n", " U.swap(0,1)\n", " U.swap(1,2)\n", " U.swap(2,3)\n", " if a in [7,8]:\n", " U.swap(2,3)\n", " U.swap(1,2)\n", " U.swap(0,1)\n", " if a == 11:\n", " U.swap(1,3)\n", " U.swap(0,2)\n", " if a in [7,11,13]:\n", " for q in range(4):\n", " U.x(q)\n", " U = U.to_gate()\n", " U.name = \"%i^%i mod 15\" % (a, power)\n", " c_U = U.control()\n", " return c_U" ] }, { "cell_type": "markdown", "id": "7d05ec6a", "metadata": {}, "source": [ "We will use 8 counting qubits:" ] }, { "cell_type": "code", "execution_count": 24, "id": "20198e1f", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "# Specify variables\n", "n_count = 8 # number of counting qubits\n", "a = 7" ] }, { "cell_type": "markdown", "id": "06c22c09", "metadata": {}, "source": [ "We also import the circuit for the QFT (you can read more about the QFT in the [quantum Fourier transform chapter](./quantum-fourier-transform.html#generalqft)):" ] }, { "cell_type": "code", "execution_count": 25, "id": "1989a22e", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def qft_dagger(n):\n", " \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n", " qc = QuantumCircuit(n)\n", " # Don't forget the Swaps!\n", " for qubit in range(n//2):\n", " qc.swap(qubit, n-qubit-1)\n", " for j in range(n):\n", " for m in range(j):\n", " qc.cp(-np.pi/float(2**(j-m)), m, j)\n", " qc.h(j)\n", " qc.name = \"QFT†\"\n", " return qc" ] }, { "cell_type": "markdown", "id": "39e3b393", "metadata": {}, "source": [ "With these building blocks we can easily construct the circuit for Shor's algorithm:" ] }, { "cell_type": "code", "execution_count": 26, "id": "715c189a", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create QuantumCircuit with n_count counting qubits\n", "# plus 4 qubits for U to act on\n", "qc = QuantumCircuit(n_count + 4, n_count)\n", "\n", "# Initialise counting qubits\n", "# in state |+>\n", "for q in range(n_count):\n", " qc.h(q)\n", " \n", "# And auxiliary register in state |1>\n", "qc.x(3+n_count)\n", "\n", "# Do controlled-U operations\n", "for q in range(n_count):\n", " qc.append(c_amod15(a, 2**q), \n", " [q] + [i+n_count for i in range(4)])\n", "\n", "# Do inverse-QFT\n", "qc.append(qft_dagger(n_count), range(n_count))\n", "\n", "# Measure circuit\n", "qc.measure(range(n_count), range(n_count))\n", "qc.draw(fold=-1) # -1 means 'do not fold' " ] }, { "cell_type": "markdown", "id": "3439c837", "metadata": {}, "source": [ "Let's see what results we measure:" ] }, { "cell_type": "code", "execution_count": 27, "id": "42d5bd63", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qasm_sim = Aer.get_backend('qasm_simulator')\n", "t_qc = transpile(qc, qasm_sim)\n", "qobj = assemble(t_qc)\n", "results = qasm_sim.run(qobj).result()\n", "counts = results.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "id": "28f8d5a9", "metadata": {}, "source": [ "Since we have 3 qubits, these results correspond to measured phases of:" ] }, { "cell_type": "code", "execution_count": 28, "id": "8f30a009", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Register Output Phase\n", "0 11000000(bin) = 192(dec) 192/256 = 0.75\n", "1 00000000(bin) = 0(dec) 0/256 = 0.00\n", "2 10000000(bin) = 128(dec) 128/256 = 0.50\n", "3 01000000(bin) = 64(dec) 64/256 = 0.25\n" ] } ], "source": [ "rows, measured_phases = [], []\n", "for output in counts:\n", " decimal = int(output, 2) # Convert (base 2) string to decimal\n", " phase = decimal/(2**n_count) # Find corresponding eigenvalue\n", " measured_phases.append(phase)\n", " # Add these values to the rows in our table:\n", " rows.append([f\"{output}(bin) = {decimal:>3}(dec)\", \n", " f\"{decimal}/{2**n_count} = {phase:.2f}\"])\n", "# Print the rows in a table\n", "headers=[\"Register Output\", \"Phase\"]\n", "df = pd.DataFrame(rows, columns=headers)\n", "print(df)" ] }, { "cell_type": "markdown", "id": "7a326c79", "metadata": {}, "source": [ "We can now use the continued fractions algorithm to attempt to find $s$ and $r$. Python has this functionality built in: We can use the `fractions` module to turn a float into a `Fraction` object, for example:" ] }, { "cell_type": "code", "execution_count": 29, "id": "f0bf7807", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Fraction(5998794703657501, 9007199254740992)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Fraction(0.666)" ] }, { "cell_type": "markdown", "id": "7a06d52a", "metadata": {}, "source": [ "Because this gives fractions that return the result exactly (in this case, `0.6660000...`), this can give gnarly results like the one above. We can use the `.limit_denominator()` method to get the fraction that most closely resembles our float, with denominator below a certain value:" ] }, { "cell_type": "code", "execution_count": 30, "id": "01f7bb6a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Fraction(2, 3)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get fraction that most closely resembles 0.666\n", "# with denominator < 15\n", "Fraction(0.666).limit_denominator(15)" ] }, { "cell_type": "markdown", "id": "8c56ae48", "metadata": {}, "source": [ "Much nicer! The order (r) must be less than N, so we will set the maximum denominator to be `15`:" ] }, { "cell_type": "code", "execution_count": 31, "id": "590770ba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Phase Fraction Guess for r\n", "0 0.75 3/4 4\n", "1 0.00 0/1 1\n", "2 0.50 1/2 2\n", "3 0.25 1/4 4\n" ] } ], "source": [ "rows = []\n", "for phase in measured_phases:\n", " frac = Fraction(phase).limit_denominator(15)\n", " rows.append([phase, f\"{frac.numerator}/{frac.denominator}\", frac.denominator])\n", "# Print as a table\n", "headers=[\"Phase\", \"Fraction\", \"Guess for r\"]\n", "df = pd.DataFrame(rows, columns=headers)\n", "print(df)" ] }, { "cell_type": "markdown", "id": "4d2758a8", "metadata": {}, "source": [ "We can see that two of the measured eigenvalues provided us with the correct result: $r=4$, and we can see that Shor’s algorithm has a chance of failing. These bad results are because $s = 0$, or because $s$ and $r$ are not coprime and instead of $r$ we are given a factor of $r$. The easiest solution to this is to simply repeat the experiment until we get a satisfying result for $r$.\n", "\n", "### Quick Exercise\n", "\n", "- Modify the circuit above for values of $a = 2, 8, 11$ and $13$. What results do you get and why?" ] }, { "cell_type": "code", "execution_count": null, "id": "b7e9e8ab", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3af808fd", "metadata": {}, "source": [ "## 4. Modular Exponentiation\n", "\n", "You may have noticed that the method of creating the $U^{2^j}$ gates by repeating $U$ grows exponentially with $j$ and will not result in a polynomial time algorithm. We want a way to create the operator:\n", "\n", "$$ U^{2^j}|y\\rangle = |a^{2^j}y \\bmod N \\rangle $$\n", "\n", "that grows polynomially with $j$. Fortunately, calculating:\n", "\n", "$$ a^{2^j} \\bmod N$$\n", "\n", "efficiently is possible. Classical computers can use an algorithm known as _repeated squaring_ to calculate an exponential. In our case, since we are only dealing with exponentials of the form $2^j$, the repeated squaring algorithm becomes very simple:" ] }, { "cell_type": "code", "execution_count": 32, "id": "309c873c", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def a2jmodN(a, j, N):\n", " \"\"\"Compute a^{2^j} (mod N) by repeated squaring\"\"\"\n", " for i in range(j):\n", " a = np.mod(a**2, N)\n", " return a" ] }, { "cell_type": "code", "execution_count": 33, "id": "7794b052", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "47" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a2jmodN(7, 2049, 53)" ] }, { "cell_type": "markdown", "id": "c497c5a3", "metadata": {}, "source": [ "If an efficient algorithm is possible in Python, then we can use the same algorithm on a quantum computer. Unfortunately, despite scaling polynomially with $j$, modular exponentiation circuits are not straightforward and are the bottleneck in Shor’s algorithm. A beginner-friendly implementation can be found in reference [1].\n", "\n", "## 5. Factoring from Period Finding\n", "\n", "Not all factoring problems are difficult; we can spot an even number instantly and know that one of its factors is 2. In fact, there are [specific criteria](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#%5B%7B%22num%22%3A127%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22XYZ%22%7D%2C70%2C223%2C0%5D) for choosing numbers that are difficult to factor, but the basic idea is to choose the product of two large prime numbers.\n", "\n", "A general factoring algorithm will first check to see if there is a shortcut to factoring the integer (is the number even? Is the number of the form $N = a^b$?), before using Shor’s period finding for the worst-case scenario. Since we aim to focus on the quantum part of the algorithm, we will jump straight to the case in which N is the product of two primes.\n", "\n", "### Example: Factoring 15\n", "\n", "To see an example of factoring on a small number of qubits, we will factor 15, which we all know is the product of the not-so-large prime numbers 3 and 5." ] }, { "cell_type": "code", "execution_count": 34, "id": "74e3ca13", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "N = 15" ] }, { "cell_type": "markdown", "id": "aa9c091d", "metadata": {}, "source": [ "The first step is to choose a random number, $x$, between $1$ and $N-1$:" ] }, { "cell_type": "code", "execution_count": 35, "id": "38c9a761", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7\n" ] } ], "source": [ "np.random.seed(1) # This is to make sure we get reproduceable results\n", "a = randint(2, 15)\n", "print(a)" ] }, { "cell_type": "markdown", "id": "d8ee4c9a", "metadata": {}, "source": [ "Next we quickly check it isn't already a non-trivial factor of $N$:" ] }, { "cell_type": "code", "execution_count": 36, "id": "275704a0", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from math import gcd # greatest common divisor\n", "gcd(a, N)" ] }, { "cell_type": "markdown", "id": "5fd0ad54", "metadata": {}, "source": [ "Great. Next, we do Shor's order finding algorithm for `a = 7` and `N = 15`. Remember that the phase we measure will be $s/r$ where:\n", "\n", "$$ a^r \\bmod N = 1 $$\n", "\n", "and $s$ is a random integer between 0 and $r-1$." ] }, { "cell_type": "code", "execution_count": 37, "id": "dd79319c", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def qpe_amod15(a):\n", " n_count = 8\n", " qc = QuantumCircuit(4+n_count, n_count)\n", " for q in range(n_count):\n", " qc.h(q) # Initialise counting qubits in state |+>\n", " qc.x(3+n_count) # And auxiliary register in state |1>\n", " for q in range(n_count): # Do controlled-U operations\n", " qc.append(c_amod15(a, 2**q), \n", " [q] + [i+n_count for i in range(4)])\n", " qc.append(qft_dagger(n_count), range(n_count)) # Do inverse-QFT\n", " qc.measure(range(n_count), range(n_count))\n", " # Simulate Results\n", " qasm_sim = Aer.get_backend('qasm_simulator')\n", " # Setting memory=True below allows us to see a list of each sequential reading\n", " t_qc = transpile(qc, qasm_sim)\n", " obj = assemble(t_qc, shots=1)\n", " result = qasm_sim.run(qobj, memory=True).result()\n", " readings = result.get_memory()\n", " print(\"Register Reading: \" + readings[0])\n", " phase = int(readings[0],2)/(2**n_count)\n", " print(\"Corresponding Phase: %f\" % phase)\n", " return phase" ] }, { "cell_type": "markdown", "id": "f865659b", "metadata": {}, "source": [ "From this phase, we can easily find a guess for $r$:" ] }, { "cell_type": "code", "execution_count": 38, "id": "4710d556", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Register Reading: 01000000\n", "Corresponding Phase: 0.250000\n" ] }, { "data": { "text/plain": [ "Fraction(1, 4)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phase = qpe_amod15(a) # Phase = s/r\n", "Fraction(phase).limit_denominator(15) # Denominator should (hopefully!) tell us r" ] }, { "cell_type": "code", "execution_count": 39, "id": "4c765cd1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4\n" ] } ], "source": [ "frac = Fraction(phase).limit_denominator(15)\n", "s, r = frac.numerator, frac.denominator\n", "print(r)" ] }, { "cell_type": "markdown", "id": "7a642db4", "metadata": {}, "source": [ "Now we have $r$, we might be able to use this to find a factor of $N$. Since:\n", "\n", "$$a^r \\bmod N = 1 $$\n", "\n", "then:\n", "\n", "$$(a^r - 1) \\bmod N = 0 $$\n", "\n", "which mean $N$ must divide $a^r-1$. And if $r$ is also even, then we can write:\n", "\n", "$$a^r -1 = (a^{r/2}-1)(a^{r/2}+1)$$\n", "\n", "(if $r$ is not even, we cannot go further and must try again with a different value for $a$). There is then a high probability that the greatest common divisor of $N$ and either $a^{r/2}-1$, or $a^{r/2}+1$ is a proper factor of $N$ [2]:" ] }, { "cell_type": "code", "execution_count": 79, "id": "f599a076", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#N = p x q\n", "a\n", "r" ] }, { "cell_type": "code", "execution_count": 40, "id": "07414b16", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3, 5]\n" ] } ], "source": [ "guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]\n", "print(guesses)" ] }, { "cell_type": "markdown", "id": "dec3a586", "metadata": {}, "source": [ "The cell below repeats the algorithm until at least one factor of 15 is found. You should try re-running the cell a few times to see how it behaves." ] }, { "cell_type": "code", "execution_count": 80, "id": "d5ea9ec1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Attempt 1:\n", "Register Reading: 1001\n", "Corresponding Phase: 0.035156\n", "Result: r = 15\n", "Guessed Factors: 5 and 3\n", "*** Non-trivial factor found: 5 ***\n", "*** Non-trivial factor found: 3 ***\n" ] } ], "source": [ "a = 11\n", "factor_found = False\n", "attempt = 0\n", "while not factor_found:\n", " attempt += 1\n", " print(\"\\nAttempt %i:\" % attempt)\n", " phase = qpe_amod15(a) # Phase = s/r\n", " frac = Fraction(phase).limit_denominator(N) # Denominator should (hopefully!) tell us r\n", " r = frac.denominator\n", " print(\"Result: r = %i\" % r)\n", " if phase != 0:\n", " # Guesses for factors are gcd(x^{r/2} ±1 , 15)\n", " guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]\n", " print(\"Guessed Factors: %i and %i\" % (guesses[0], guesses[1]))\n", " for guess in guesses:\n", " if guess not in [1,N] and (N % guess) == 0: # Check to see if guess is a factor\n", " print(\"*** Non-trivial factor found: %i ***\" % guess)\n", " factor_found = True" ] }, { "cell_type": "markdown", "id": "2c0880d2", "metadata": {}, "source": [ "## 6. References\n", "\n", "1. Stephane Beauregard, _Circuit for Shor's algorithm using 2n+3 qubits,_ [arXiv:quant-ph/0205095](https://arxiv.org/abs/quant-ph/0205095)\n", "\n", "2. M. Nielsen and I. Chuang, _Quantum Computation and Quantum Information,_ Cambridge Series on Information and the Natural Sciences (Cambridge University Press, Cambridge, 2000). (Page 633)" ] }, { "cell_type": "code", "execution_count": 42, "id": "a23d6d54", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'qiskit-terra': '0.17.4', 'qiskit-aer': '0.8.2', 'qiskit-ignis': '0.6.0', 'qiskit-ibmq-provider': '0.13.1', 'qiskit-aqua': '0.9.1', 'qiskit': '0.26.2', 'qiskit-nature': '0.1.3', 'qiskit-finance': None, 'qiskit-optimization': '0.1.0', 'qiskit-machine-learning': None}" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import qiskit\n", "qiskit.__qiskit_version__" ] }, { "cell_type": "markdown", "id": "81e51e07", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "# Grover's Algorithm" ] }, { "cell_type": "markdown", "id": "2d738f5e", "metadata": {}, "source": [ "In this section, we introduce Grover's algorithm and how it can be used to solve unstructured search problems. We then implement the quantum algorithm using Qiskit, and run on a simulator and device.\n", "\n", "\n", "## Contents\n", "\n", "1. [Introduction](#introduction)\n", "2. [Example: 2 Qubits](#2qubits) \n", " 2.1 [Simulation](#2qubits-simulation) \n", " 2.2 [Device](#2qubits-device) \n", "3. [Example: 3 Qubits](#3qubits) \n", " 3.1 [Simulation](#3qubits-simulation) \n", " 3.2 [Device](#3qubits-device) \n", "4. [Problems](#problems)\n", "5. [Solving Sudoku using Grover's Algorithm](#sudoku)\n", "5. [References](#references)\n" ] }, { "cell_type": "markdown", "id": "a609f9d4", "metadata": {}, "source": [ "## 1. Introduction \n", "\n", "You have likely heard that one of the many advantages a quantum computer has over a classical computer is its superior speed searching databases. Grover's algorithm demonstrates this capability. This algorithm can speed up an unstructured search problem quadratically, but its uses extend beyond that; it can serve as a general trick or subroutine to obtain quadratic run time improvements for a variety of other algorithms. This is called the amplitude amplification trick." ] }, { "attachments": { "image.png": { "image/png": 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6f+ESXeb/Fy/9qg48w/WvV67y82sqLP5fuHhJ3bvM9/EfZ4S9cOEiXcJ/vsY9lRaHNcPjGcJduXpNPbt06bLnbOaBbd1uKTNsWFCZfkBwjfEI6SGuGR953Lhxk9O/yM9+pXO8w8hF5MflUGXg8Mjz/PkLynIFPnKu8Xtev35DPUdYPEN4nM8wJucYE4TDs9Ps7+Xs2bMqLJ7v3buX2rRtSwMGDOTlgKfpJB+neMnaSfZ4febsOQ57TsVFfFzDEzYs7k6ePEUnTpxU4RD+DKeJ+9iK6vjxE5wG6uWMuof/R44cVfdxfZTrz4yLfI4dO05YJnf48BF1jeeYYNl/4ADt27ufy7hPlXP/gYN06PBhdf/AQb4+dJj2MWE1wuxV13h+8OAhJU/t3LlLnQ960tq1axcZx25uX9tp06bNtH3HDtrK17t24d42Dr9XhUG6u3fvJqSxY8dOPnao8+bNm2k9y8Tbtm9X5x07d6ryISyOLZu30vbtO9T1pk2bOI9N/N9Iv1ixYjRq1CiFP5b1YLnJJa4TnK9evaomk3ANnzzAGZicO3dOhTHD4TkslszD+zmsxlBPuIc6xmGGw31c49lhxgj44j/6DPkFNwJCsIO7fmyXrnHjxkozYjsBiegTApjZROfsz99Lgl8CGb8UxiNAIujL943I3veec9iX/j/n2Ve+9/w5z8yaZ1zjPp/Ryasj7vo5/ZPv4XjKQp55bfx/6pmJfeoRJnE2DwiaT5VQ+OSJITQ+fvzEIyQ+obM8uMBMC5psCI4PH7Lw9+gxPeDzAxby7j94cdy7/4BeOmLvs+B3Tx0xMbG8NjCWoljwi7uOiuZ9n6Ppd5yjY+ju79F8RKnjzt3fCcftO3fp1m934g48v3mLHa+xAHadhaobN2/Tdb6+ysLStes3WQA0zlf4fPkKC2NK6IMAaAiBFy7yYMsC5Dk+zpxjYcpznGJh8yQLnfgP4fP4CRZ0TrJAysLoidNnlXB65NgJFlaP04HDx2j/oSPqvO/gEb4+Snv3s5By5JgSHCHcmkIv1kOaAjGu4YRo5+59tHHLDlq/cSut42Pthi20Zt0mqlCpCk2bNl1hDWeJOLAvNjQm2HcVB+4hfZzN+/hvhsN95AOhFOHNZ7hGGNzHAWEVZcF91C3WFEJ4xRnPcDbDIh/zGmHw3LyHazMtpIcD6UH4gfCCw3yOe97PkBaeQxCC8GQKUKZgYwpT+I8Dz02Bx4zn/R/pIxyELAhbEJZgxon/OCCEITyE2iZNmtDEiRPVPdyHkGsIuseVMAWBCv+PHj0a9x/3oE3BxB6OvUqI3af6IVNYhDCK6wMs2EIgXb9uPf2yfiOtWb2ONqzfQhvX872fuc7XbKAd23fR1q1bleUCrBfWrl2rjjVr1qjz+vUclwXTdevWKRNrrEfEPTz/6aef1AQBzitWrFDatO+//54WL16s7sOEFde4hwNm2jgWLlyozvPnz1fnefPmqTM0zDjmzp1Ls2bNUtfffvstTZ8+XcXBefbs2er51KlTaerk6TRxwlSaNnkOTZownf/PoRlTv6UFc5bRsCGjacSwsTRy2HgaP2Y6VYysRvXq1qfJk6fQpEmT+DyZhg4dqvCH8IxrkHBYFYwYMUIJ1Lg/fPhwGjZsmNIWIgzKhXfAdf/+/WngwIE0aNAg6tWrF/Xo0YP69eun0sBE1eDBg2nMmDHUp08fFWbc2HEqHsIjPtJGnM6dOqswCI8DaSAOnnXt2lU9N9NGXKTdt29fFe6bb75RYUFqW7durY6ePXtSly5dqH379upo166dCo8JHdxr06YNmfeQnnkf74v8MZnZlskbwrRq1Yq+/vpr1f+iLLjG0bBhQ/UM4VEG5I/wFSpUoGzZslH16jWoZu06VKp0GYooX4GKlyxNJUqVociKlalcZCX1H9cFCxVRB56V4DCly5TlOGU5TkUqWy6SIitwmMJFqHiJUipuxUpVqWjxkpS/QCHKm68AFeP7RYqVUGE+yZufPv4kH3340cdkXOflcAVV+oiDex/l+Zgaft6ESpctp+LlyJlb3fsozyd8/kTFzZI1m7rOmTMX5c6dmwoVKkS1atWiihUrcjlK0Cef5KWs2bJTrtwfqTPSQNrVatSm8hUqUZ6P89L7GTJyWfKq69wffkS5P8yjrhE2e45clClzFvogU2Z1zpY9B2XOkpXSpktP6dK9z/eyUo5cuVV8vKcZP/37GSh9+vepcNHilCHjB/Qf//EX+utf/8p5fUDp389IqVOnVemlSZuO3n03FZl5IWzWbDlUGd9LnYZef+MNDpuG42Sgd1O9p854d+ST8YNM9Mabb9I/XnuN0qRJSxk4baT35ltvq2d4nprvo4xZGIO8+fKrfDJlyqLeC88/+CCzioN477yTgtKlz0DIF++dlu/hPREO53dSpKQUfOD5B540kOc7KVJwefMxnpWpQMHCCrs8H39CmblukB7wRD2bZS4TUV61BdQzwqNNmAfGtEKFi6o6QRyERftC+zPDVKlWg+uvFre5CtxOy8a1j+IlS9E//vEagWQf5MkBb/nI+9qQpl6Wscx73mfEkV/yQCDZE2yQBMzC4jBndL1nhHHfnL3FNWZrEc6ctTWvzWdmeMSBQGse5n+cERf3XxV+zbAQTHGYz3Hf+x7ygJBqCpEQECH04QzBEWcQvzkspJzgWc3jx0/SseMn1HGUZxyP8izjERbCDxxkQe3gITrIs4k472NhbM8ennHcd0Adu3lGcPsOngXcuUv937V7j/GfZwx37d7L93nmcPtO2rJtB23Zup02b9lOGzdtoU08E4jrdb9spPUbNqnzuvUb+Hqjer52/S+0Zi0LaGvX0cpVa2jZilW0es1aWrV6LS1fuVrdW62e/6KucQ8HwiHM0mUraOlyPvi8eMlP9NPylXy9Up0X/7Scvv/hR1r4/SJa8N0P6rx46TJ1veC7RTR33gL6duEPNO9bFuLmL6AZM+fQ9Bmzadbs+TRz1hyaOn0Wn+fSzNnz+HqmujeXw06ZNoMmTZmmzpOnslA3eRofU1mQyE7tOnSiceMn0YhRY2kC3xs3YQqNGTeBxo6bSKPHjqfhI0fTyNEs6PHzYSNGcbgxNGT4SBo9ZjzfH0dDho2kocNZsBk6gvoPGMzHEBo0ZDjHG0P9+g+iwcNGUL8Bg6hv/4EqnWEjRlPvvgOoa4/e1KVrD+rZuy//70/fdOlO3/D/zt90o06du1KXbj2pd78B1IOf4xrPvunWgzrx8zbtOnJ6g6hd+07UsVMX9bxdh870dZt2/D6dqX3Hb6jl123UuXXbDvTV123V/2bNW1Kr1u04XHtq3uJr+vKr1tTsy6+oSdNm9HnjL6hBw0ZUt0FDPn+u/uNZ4ybNCPGafvElfdaoKYdtTk34+tPPGitBB2EacfzPGjXhOE35XmOVTp36n1KNWnVV+NZt2xOEnYaffU71P/2M6tTjZzVrswBXl2rVqa/CI3/ErVGzDlXnZ7XqNlBH7Xo416eq1Wty+HpUuUp1qs6CEM61OR3kU7d+Q/UfgmCpMhFUqXI1FaZS5apUka+r8uALwQnPMQhH8jX+F2FBp0xEpLqPwTqyYhV1XbxkGTVAQzgowdcQIiEoQRiEIAnhDoM8hAEIhBDIcIYQgHC4xgEBEoIP7hcqXEwJVriG4AHBBmEgTOAoyUJpQRZEUSYItU2bNiVYWERGRlKlSpWoVKlSVLZsWcqfP7/KIycLcBAks2bPoYSyTCzgQeh77fXXWUDKRB99lIfDFlACJeJ8yMJXXs43H+eL+0WLFWfBszCXqzCV4XTxHOHwvCDfx/9CXJ5ixYtTRLnyqkwFChaMi1uqdGkOx5gwBkgrd+4P6eOPWTBmoRRxP8rDAhSfM2TIQKlYCMzBwlmOHDlZcHyXMrFgirQhPOdiAThXrlzqwHO8exZ+l1yc3vssQOJdMrCwi/dVwirfx3vg24WwmipVahXurbfeYmHwHcYgs4rzNl+/9trrlDLlu+o+hEEIh0gHwivSffvtd5QgmE49S6/SgZCL58g7VapUKn08R3gI0Sgb6htlT5kyJX2YsyBlzcikIHtR+iDtJ5Q9YxH6IE1eSvF6Jvqf/3qPUr2Ri95PUYCypy9FWdOWoAwpC1GKf+SgDCmKUvq3i9B7b35E//3v6emN/8pMb/81N6X8748p7WvFKf1rZdXx2r/nor/8f2npL/87Nf393z6gFP9Z2Dj+oyj9z//JSX/93xnpP9XzVBzmPfrH/8tK//Pvmej1v2Snv/3fNPTeGx9TjrQVKf1bRVXa7/w9F733el5K/UZeSvVaHkrzVh5K9fqHfO9jSvMm45q2FOXKGEHpU+Snd1/LTanf/JiypClBmdMU53fJrcqb7p28lCFVfsqSrijfL6bC5slckXJniKSsqctQhneKUZrXC1GmFBGUI1V1evs/P6F3/1qI3v5LPnrvr6Up4z9qUtbXG1Ga/6rIRyV677/KU8q/lKQU/1GCCqTsQ1lfa8L/S9H7f6/BzytQur9Vpf/+t2yU8f0c6jvB91yav3O0B9QDvnO0QXyPEMYjykfy91mOiWBF1c9UqlJNEbyixUqqeOhrqnM/gH4CJLBqtZqqPyhdNkL1FejnatWpx/1LA+7nGqk+Cn0QiF39Tz9XfR/6PRxftvyaqnHfhPv1Ghh92xfNWqi46CfrcX+H5+izvmjegr5q3Vb1/a1aow9upfq+5l+2Un0r8m3E/W2TL4w+Fv0z+m70wYjXmPtZ9OtNuT9GX9uSn6GvRzro+7v36kudeRzBNcJhLMDRpTvGj57Ug59j3MHRuQuPNXwM4nGrR+9+PA71U+MK3gP9HcYHjDXtOP32GGO696JefQdyHv2oC8au7r2pW88+6j/udezcjdryeNSBw/YfNIzHLh7zeCzE0YvHO/wfOHiEuu7DYxfC4Fm/gUOpT//B/Gwkl2WkJw7+j1DXQ0aMoQlTZqhjCI+dA4eMoEnTZvG4ymMuj7uIP5TDjB43iUaOmUBDedzFf8gEW3hyCpNPO3fuVJNHmNBaznLIpGkzaeKUmTzWsxww1bieOmMuzV3wA02fNZ+mzpjDz6bS5Omz1fXkabNpyvQ56hg/ieUHjjOJ7yHctJksa/B55pwFHH5OXBz8n//dYlrw/RL6/sfl6vzdop9o9rff07yFi2jM+CmqLWOsnfMtyzR8D/kv/GGpCo/zwkUvrhctXUk/LF6hnuMZ0vrux2V85ms+m8/NM8LievGy1Soe/v/40yp1LFq6in5audbr+Jmvf6blq9bRMj6W80Qezit4Am/Fml/4mmU7vodjJd9b+fNGWrV2E5+N5wiD/z//soVW8TPcR5jV6zbxxC8mgLep8+r1m1U4hMU1wuO5eca1eZhxvOObz9ZvYvmU04zvwDPvA3Hy8KQMJjrlJwhYQSDZE2yQWFMjANMLU2NgahIOsKkLtAWYucKB597aBFPbgHs44M4fZ2guzHtmGDxDfGgzjh8/rsKY4aG9wIFniGfGgcYDpiF4hjRx4P+SJUuU0JyHhVDMsObMmVPNsmKmFf8xqwnhDbOT772Xhmci06lZxyxZsxMEaTWzmCKFmtHLwcTFmJU0ZhbT8+wgZjwxA6tmQllIzJAxk5rlfJ/vY9YzHQumEBbTpE1Pqd5LzXmk9lyzQMjXEChxzswCO2YbEQ5pQIBHed5iwfTNN9/i420lpEK4hbCPWUxVZj5DsEW5MmXh+xwH+Wbma5wzZeF0WJB9L3Vqyop34pnPD5kQ4N7bPGOKciMtcwYVaWKmFEdqxkLl8+57PHP6rpr1RVkhaKflcuZkARwzvxCQIVSr2WZOHzPEyBszwSgHZm//7f/8Xxam31MkBXihvIiLWVWjrBkVjhn4PtJBGLwnnuHIxoQA4TETni17Tn6W3bjP15hpx8w2nmO2GPliRhxCIWZdIaQjTWPmOY+Ki2ukhTMOhDNn7iH0YDYWpAxED4JhgYK4V5oqV62uhEwQPxwggeV9xusAACAASURBVIgXwbO5OJdkYRREEmFxBrmE8GloIyqq8JhVB9FDupgBrsQEtlp1JqNMPCtXrcFCa0WVNggqyC7IKgRTCK/QSkDYgxAKgoznVTgOyC0mMJqxYAnyo4gzE2qkUZ3D1axtCK1fsMCoCD8Lq42ZwNdhwgyyDwG34edNlfDaoGFjJawiDwjIzb5sRZg8aNGqDTVmgbQpC7WfftZYCaoQfFvzJET7jl1Y6OOJBw6He1/wgXJCEGzDR2MWgJEv8lf3WRiFgNimXSeO30EJjd907aUmJb78qg215ecI14EnQCCUdu3RhzqyEIr0vm7TgQXWnipP5Iv0W7Vpr8qB9BAHQi6E0R58QLjF/45Iq09/FkAHsqA5iIXM4fTj4iXKhG7VqtVKkwhtI0yRv12wUE3eQKjs3pM1YAOH0IBBw6k7BOQ+AwiCLAgvJjsgwA4ePlqVEekinJEHa9mGscZv5FgaPmo8jRo7UR0QTidMma6E1GGjxtEwfj6SJ5HGTTSEUJzHeoTOaTyxNZmFXAiX02fNU0LlWJ6YGs8aSQi/EExxnjZzrgqHuLg3nYVeCMuTps5SQuWsuQtVONyDcDlrzgKaNfc7mj3/e/r2+8Uq7TkskM6e/x0LoD8qIXXugkXqGvcgxBrPFtEMThvC8ax5PPnmCQMBd/53P6pjAacHgXXhD0sM4ZQFVENgXcKC6Cr6fvFy9R9C6XcsEJvC6OJlq2jJ8tVxx9IVa1jI/IU2bN5GDRo0pvKZJ1HLfOfpq3wXqVX+X6lNwZt8vkKt8l1W91oXuE5tCtzi+7cJ11/nv06t89/ke7fV0Tr/Df5vHjc9z25R24K/GfEQ1xP+RTzjOcKYB9Jri8Nzr00BxDf+tyt4l4zjjnreruAdz3/P/UJ3qb06fufzy0eHwlGEo30hHMYz4/+LazMMzh2LRKujQ+FoTxwzrvUz0kCabQveoqJpB1CrFj2UAP7L5h2k49iyYw9t2rqL6xbpb9eSh45yu5Um3hvfYEvuU/HdWE13A1vUWI3jbnijzo4cP6WsoGCdZWocoYy5fed32r3vUIDLyFZHTAJBijEeYvLDXQwCXQfBlT9IOGRLyObyEwSsIJDsCTbAQieKztPb3MPsVF+9533fCtBuh4VGG7OpmzxrReAoB2Z8+A/zwBxMuJs0+1IJuMNZSwrhF8KtOXMKgRUzoJg5hbAKQRPPJkyeoQRZU5iFAAshF0IwrnGGUIzrGRwHs7Z4boRh4ZTvQ9BVwq5H0H0hpLKAysIpZlpfzLgawi6EYPMZZlSVkOo5L1m+Rgmu3/MMKmZTIbhiRhT3EQ7CLe4v4xlVPMM9XJv3INz++BNruVmwRRw1s7p6Pa3gA7OumIlFeBy4h1lXzJzivJz/Y7ZUzaryf5zxDPfwHBrGIUxCMINqzq7i/OLArKzxH2GMmVbMur56vJh5NWdZf+FBdPP2PWrwNGda12/a9tLs6ov7L2Zdcc97BtbKtTlQvxrHvB+I8/5Dx9gqYhsTvxKKxASiDHF5cp2gXtR/86xJWI/L08f0Idxu2rqbjp44y2b0f8QJhuh70G/BTP4km6Abwn/8QgzaDqwGQKTRzq2WwZfwG5mAoJxxOPr4fr6kHfxh0Hb4u962R5n0f9G0FVXJNo/J6h0mgiCDcniTbed4GOT+mzI3qVqBIdSpU19tBHvDlp1Gu0Z7DrK+Qf93YbTrjfxdT+fJs3oNGqqJK/35xt+POcl3++79dOXaTbW8yZTb0H9i2dHRE2cI9ewkfTfiYnzGxB2srzAp60aakkb8bQnyGCyeoPiSnyBgBQEh2FbQCpGwj9iEHWakfdncOLl3mhiIDELhIUUuCvMgI9AiQ+umA2cM5BDEdaQdKmmi7nbtPciTJiuUKecPS1YkazwSrTdu61t37uV13lfUGndMGuKHM9apnzp7wWhPiQj/ECawFq0na8QxiZRofna+Jc4bBFtp9xIph+v52imrljgGEdnE3/UGJtpVq9ShyEwzhWD/aWIBxNiNyYYo6lo6msZ9fYe+/oytMbr210OwuS2jv1ZjTTJu14pg8xIrmMXDCiTUvuNN23arfvLho0dxE5ToP++xj49TZ84r64RgmDyBXANlAkz/e/TuH3I4h1K7MAk2LFzlJwhYQUAIthW0QiRs7L0HimBjXVIodWQ6yoqBSEe6SBMEGybeMIt1NQ9PmTdCYAuC2XJX380CaVECK78/hDaY52LNMqwSAlWeYM8Xwv2+A0eVUzbTtBGO6UCuz1+8TNt3HzA0a4l8E2jTMKGHCTmsMFx9Z+SbSN6u5mWhnQUiX9QVJjCq16hHlbLOFoIdR6YNjbNb5LpTsSga2iCaFgyOohZ1x1CnjhoItrTrl/qJCTzhjLXk6LMD8W05yRPm33Bo6T05CQeaR46fDqqxGHINJp2xvAlrzZ28s8SNX3Nt4gKCDR8jWM4pP0HACgJCsBkteDuG4zCzU7UCYDCGjY6JVd4isb7S7CSS4xmDkE6CjY4X68qxdtRVfIWE/AlPrOcDwcaaV1exDnIiZuVdMSFx+NgpwvdvLm2Bw8Zfr15XVgAqrSTIAAg2zDsHDh4uBFtH24jDfzsT7I1Uu86nVDnbbF4jLCbi7pBqU+ttEHVor4c2iKGB9e5Q6ax9qeWXXdzXYMfVaeKCupVvOeTCxmGwXY2HtdnBJHwehMp7mJZSly5fZSe0j+O01+g/L12+Rlt27NUqS1jFCXIN/EHA2Sd8cliNL+F9/1Yh58FxJ/wmyU8QsIJAsifYINXwug0nYvDuHQ6/WN6WKDs7LkvuGmx/EGw4KoP3URmwfB+wfMIKApsXwQHBhlM0IdgJ44zlBGfPX1Jbl4FgP336lLcSu6O02soSIk4ITjgNEGx4pYVWRDTYCePk3TZ9vjbxV217u/KmW7VqHaqQZYYQ7DgNtkmQnZ7hLI3Nw8tEUxcm2W0L3aYiafpQyxZCsH1ur179b5JxzLbNyx7g6wU7O8APS5LxrOShMSz6TviniL13P25/YciGt27fiXNqpnOy3ipOKAssBOBoFF7arcaX8L737fCbk52dzQrBDgd25N93SHYEG52maT4JIRTX2O4KJBua7HD4Yb0QnG9hCwrpSH3vSK1ihY43fYaMQrB1CD6KhLyoOzjKw5ZXYiL+ApNX2+vOPQeVl9tn3MehL7tzN4r3yD6uTOxfDZvQfxDs5uwpfQj3He4SbI95+Cv1mlA5wvK+SUIUBgbBrlyFt3fKNE155nZXg+uUoIZyfEN7DfPwjkWNa3hGL5K2NxPszi5rsKVdq2/VbNtMsOGTBLs4wHFp8H/HmMjdzpOQR+i3u78r3xWQCyEnov+Eg001OaljjHOQJgg2ttnCThvYMi34cU543Ar2skPOwy492MFHfoKAFQSSHcE2PYZ7g4R7OMLlhzVD2FYAW+wEe+cVyuWDd/AUvJUYPKiH8nsEZdnjBDZjYMaWS3Dc9wNvfxSU5XUgLLn1PucuXFYC4j+fPlPrCA8dPWGJXKMcMIf7smUrGjF6vPJ470rZ4uryZasEV9IOAtx9fg8TB5y53NiFoFKlGlTug8lCsF3VYBukGhpswyM5a7CZYBd/fwB93aqbewTbrE8maD63gVBqr1bKGofFDrVtHvbitrNNl99x5HJja7XLV64rr+Hm0hrlMZy36sKWa8HoNwIEG3tZV+T924Vg6yXvINjYblYIdrgwJP+9R7Ij2P6DNnA5PeQ1RPBuLc4v9Ha80PC9n+EDtdWZ3wUDK8JPGITFej7svS0a7PjbNLzf3v09yuMx/JHaTsbOVlgg2PAAjD2wV693x4s4hEEc8o28XHcg2BUqVKOIjEKw3dXevyDWZrpY414sfT/6quU3rhFsadcvt2fz+4YGG07OQsVE/Aj7rcC2hviBYGPd9dnzF1/s4BGEfZdJsKHBFi/i8bdDsz06PYNgFyhQQFm5Bk6ql5xDEQEh2KFYa0mUGdt0gWAPGjZShFqN5BIEO336DGrfcKeduIrvISJCRv48YMJEPKJ8pBDsBNrzXvYe/tud39X6a3gMh+d1s01ZaZsg2F80+9JVDbYQkT+3Z9TJijW/ULnylahshgmiwdagwTbJNc7QYBdO251atOggBDuBPsRKP5FYWPgkqV6zTkhosLft2qdMwUGs8YPfistXrtF2vh+MmmsTd/SpWIMNDXb3Xn1FztPYpmGpmC5dOtFgJ8E75PGfERCC/WdMQv7Oo8dPqGy5SBo6Yox0vBo73pU/b6SUKVPRjNnfCs4acYZQARNxzNYvXfGzYP0K1vCAC1L94OEjgpk49lg2BTGrZxDspl80p+Ejx7pnIv5Kea2WKVzDr2QNdmSFqqzBnsIEULyIexNit69BsEt9MIDatO7uGsEO13bp9L3GjJ+iCHYoaLDPnLsYt+4amusr126oHReCfVIQ5YMJPpycdfymq+3+3mldJ4f4q9dtYjnvXeUIOeTJgbyAXxEQgu1XuP2TGQh2Xt5WYMBg2R9R5wCAbXbeeSeFexpsISIJCgowES9YuAj9+NOqBMPorOtgThv7pZ88c15pYvbsP+JI8wKCjW26DBNxl/fBlvb9UtuFBrta9bq8D/Yc3gf7Lq8XDmXHYsFddhDsoul7UcuWnWTiSPN3CIJdrXpNmjlnwUvtPdj6UDgwi4m5x/53DKeQt3+7q3ZcCLZyxlceEOx5CxdRqTIR1LZ956DGOb7yh9I908nZlStX/CPASy5hg4AQ7LCpyhcvgvVEOXN/SIOGiom4zo4cGuz32Yv41BlzZIDTLLTNXbBIOe6D51SddRqKae/ed4hu3LxNh4+eJGiznZg2gmDXrluft/gbRJi5D0U8QqXMK3/eQBUrVfdosH8Tgq1xggEWAiUy9KVWrToLwdbcV8NBYkT5ijQziC274J/i0q/XlPYauy5ERcdw/3nC6D814+NG/2RosBcrS8VvuvaUflpjnYFg58mTh27cuPFCyJYrQcAHBIRg+wBSqAUBwc6V+yMaMGi4dLwaO144KUqdOi3Nnv+d4KwRZwgkmK0vXrK07IPtjTNrMbbu3EcnTp8jOOqBJtsJuQbOINg1atWhvgOGuLxNV/zrkN0QNkM1DUzQRVaowmuwx1PbAreFYGsk2O2YYBdngv3VV6LB1v29jBo7kSpXqU6z5gbnuLiRPYMfYQ/hsPQDuf7jjz94ac0l9lsRnB7D46svbxPxbj37iPzhPS66fA2CnT17drp7926oUQEpb4AREIId4ArQkf0ffzylLFmzCcF2uaN9daBbvno9vc0m4nA28uoz+e8uocJ6vuIlStOipSsFa7NdM8GGmeMh1lzb8RgeXxsFwa5eoxb17scabJe8iMeXj9zbQSDYtWrXo4pZZiRjJ2emx2+c9ZmZq226MvRmgt1RNNhm/6HprAh21erBN/HM/SUsfLB9YWzsPeUx/J+8Peu16zcJzs5CqU8CwYZfkkqyTZf2elvDzmzh5Ew02DrYSninKQQ7DOvXINhZhWBrEiDMgXj56nX0Xuo0tHDRUu2dvJlncj1Dg124aHEh2F5tGqR6L6+53rydnZqxwOVG2zA12P0GigbbDTwTSwM+HBp+1pSq5ZyXjJ2c+Y9gl848gNq26SoE26sPSax92n02gbfpqv/p5zTn2x9c6ZPsluNP8biP3LJjr1pO85w1149Zg339xi3asWe/a/3nn/LUhLW5Bhum+J2+6R5cOGt6Z39h+2o+WCqVJk0aun37dhiyBXklnQgIwdaJboDSfvr0n5QzV24aIl7EtQ48y1atpRTsXXLB90u05vNqh58c/89d8D0VKlJUnJx5CS9bd+5lE/G93PbcIddoVyDY2Ad7MG/xh23okmNb89c7g2DXq/85Vck+Rwh2Yd0a7DtUJvNA9iIuBFt3+548fQ41bd4y6Lbp2sBLaLCUJvbeA+XYLJrXXe/j7Q3V5KRLE5S6sTXTNwl2mYhIatfhG+mnvcZFEyO3zqvY0ihlypR08+bNAEn0km2oIiAEO1RrLpFy//PpMypYqIjay9atTkbS+bPJ87KVa+m1198Qgq1xcDPb3ax53yknZ4uWrhBhwoM31lxv2IJ26S7BbsLbdA0aOkJMxDW3a5iI16gBL+Iz2Yt4ctymy1t77QeCnWUgtW3bTTTYmts1nH62aNWWvv9xeZD01Ub/CGeQt27fUXtdP3r8mE6fu0CbsaVhiJFrjInGGuzFapuuzl16BAnOf5aRzPE7lM+wVHzzzTeFYCfCOeRR/AgIwY4fl5C+i3VFOXLmYg32aOl4NQoTP638mf7xj9dEq6oRY3NghiO5Dz/6mL5fLAQ7TuMCwVAJh+4S7Np1G3icnIkXcbP96ThDM1K9Rh21Bjt5E2x9a6/Ndd3At0wWNhFv21X2wdbcX0+YMsNjIv59kMgfMA3fQxcu/qocmz19+pSu8n7Xbi6t0dE/JJamIti8dSU02OJFXC+xX7riZ3rttdfot99+C2leIIX3PwJCsP2PufYcnzHBzpwlKw2UfbC1DvA/sQb79dffpMXLVmvNJ7GBNrk8g0faPB/nlTXYEI5NYm2eXRSY127YorQiPfsOEBNxF3GN7ztdtXYT1axVjzXYM5KZBtt/mutXCXbr1t+IBltzux47YSrvRFCXZn8bBASb+0g4Njt28qxybAblQ0xsLO07xKbhwEFNUOolaPF9+07vgWAv/GEp1axdXxQpmtsznNmmTp2a90yP0S67SwbhhYAQ7PCqT/U2GERy5vqQhsoabK3EFzObb7zxJsGEyOmAKfETF3LgRbxUmQhasnyNYK0ECmit3dNcm+0Pa7Br1/uU+g8aJgRbs+AGgl2tem2KzDKF12Anp226/E+wsQ928Yy96csWbWV/d83tesz4KWyZUTs4nJwxEYWH8F+vXidsX3r/4UM6fOyksaWhZhzMPlXH2ViD/SNvh1aNevbpL2OixrqEr50PPviA7t+/H4ZsQV5JJwJCsHWiG6C0ocHO8/EnNGzkWOl4fe14MZNtcTb7hyUr6W9//zstWyUEW4cQ4Z3mbF6DnS9/IbEW8LU92wwHgl1NbdM1UIiITQy9221i14YGuy5VEIKtdYsuaLHbFbxLpTP3p1Zfd5KJI83tetzEaVSrbn2aOXdhUMgfe3inhVu/3aV79x/QsRNnQp5co09RBHvBIipbroKYiGtuz0uWr1ZexEWDHSBCE8LZCsEO4cpLqOgg2CVLl6VJU2cGxQCXmJAZ8GfexNr72odO+wdeD/y3v/1dNNg+YOW0nrHlC9r04mWrQrtNW2xjTnGzGh8m4pV5D9ve/Zhgyz7YWtsaCHblKjWp3AcTk4kG2/+aa8NEnPMtcodqFBxLXbv1EYKtub+ePH02fd74C8KyHqv9j6vhua/FtlwXL12l+w8eqvPWndjvWo/1j6tlT6KOQLCBb9HiJYVgJ4GV03qBzPHGG2+IiXhChEPuJ4iAEOwEoQndByDY+fIXoNHjJgV2gNPc8TntOF+KbxIfnH0s9w9LVvAa7DdYg73W5zi+pi3hXjYZnzVnoYdgh+h6d7Ndme3Mxzbm73bw8y9bqEKlKkywBwkR0VxHINi1eA1lhaxTkwHBfpVc479+52Yd1PZfUdS93F1qUnk89ew1QNZga27Xk6bNokZNmtE8dsLl7/4rLj/uZ7H2Gtrra9dv0vWbt9WWXNiqKy6MZhx05mOYiC+i8hUqUbeefcPinXTi5STtRUtXUqpUqeghLy+QnyBgBQEh2FbQCpGwWINdsHARGjV2onS8iQ2icWTHYx5ukqDE4ng9wzYkadOlJ2y346QDl7gvk+n48Jgxe77aeu7Hn0JUg222LfPs1Y7ie99A3QPBrla9Jg0YNJzWyD7YWr9reBGvVLk6lcs0iQn2b34inP4gtfHlETiC3aloFA37/C51aDaBujMZkf3dk+5vnfQ/49jJWc3a9QhbKzpJx2lcaK/PXbhMN5hcHzxynDZu3RXQ8jh9H+/4JsEuE1GeuvboEzbv5f2OwXL9w+LlimA/ePAgRBiAFDNYEBCCHSw14WI5QLALFSlK4yZMk443MSKjyI49co3OfwF78YQGe8WaDYJzYji78Gz6rPkeL+KhSbCVcBfk5BptGgS7arUavE3XYCEiLrTbxIREc5uuClmgwQ5ngh04cg0Ndq+K0TSuZRQ1KDeM4EV81VqZEE2sXTp9NpGXpjX8vAk7OQucF/FNW3fTidPnKCo6hk6dvUCbtu3mMdp36zSnGOiOb67BLlGqLHXp3lvkD419NTTYWbNmFQ22ixwluSQlBDsMaxoEu2ixkgRTLd0dfcilD5LjOWBChsPumixosN97L41osDUObmb7mjpjDu/tnjskt+nCur9QItiRFSszwR4iGmzN7Rqa1E8bNqEqOWaGMcE2yDW0yB2LeBPt+LTcbt7z5Fssinoywe5R4S6VytyPmjdvS5jYMPsVObuvzYYGG9t0zQqgk7Pd+w7R9Ru3lPfwnXsOeByYhhfBxs4a5SIrUT/uq6Udu9+OTUyhwc6VKxeJBjsMyZLmVxKCrRngQCSPNdjZc+QiePM0Owk5ezpgD7neyGuxMMutyLVNzeLCRUspTdp0ounTTETQdqfPmkcf5fmECXYIabC5XW3etofNE0+QWvtns53589uFBrsSb/0yYPBwWauquV2DYDdu0oJq5J4X1gS7M5PcTnyY66GNs5tkOr60jPy+KRlNHTnvdtimK0MfataMCTavfffnN5Xc8ho/aZra6m/2/MCYiG/ZuZdOnjlP5y9epp17Dhp1HQJ9r5V2Ag22QbArKn8ZVuJKWGtkHDhnyJCBHj16FAhxXvIMYQSEYIdw5SVU9GfPnlPuDz9iJ2eTRZB4VUjmgQlaa6zPUgQbA6/NwRcCxFtvvS0a7Fcx1vB/2sy5lDdfAQqZNdiednXg8HHCESpCDQh2/U8/p6EjxgjB1tCOvdsBCHa9+p9T5ezhqME2CG5H1lyD5EKD7R9ibZJtIz+T2INgl8o0iFq06CAabM3t2jARbxyAfbANDTW015euXKNDvN+19/cWTtcg2ObOGt17iZMznXWLpQ7Zs2enP/74IyGRW+4LAvEiIAQ7XlhC+yZMxHPl/pCdnIkX8Zc6Xg+R3r57P2EQVubhNsk10sW64HffTSUaEc0CG7CeNnOe8iK+ZPma0BCauF1hEgfOdXB+qR36AS+7+RlOzmpRn/7iRdwuhr7GA8Guyaa0kZnDbQ32C3LdPSKaupYG6fUnwTbzMs/GPthlMg+lFl92kglRzf3PhCkzqN6nnwVgmy70uXvo0NGTvN/1WTK25LKmrfT12w10OBDs2Uz8ipUoST169QuZ8SXQuNnJf+acBZQlSxZ68uRJaBMDKb3fERCC7XfI9WcIE/FMmbPQyDHjpeN9RZjYyGbhO3hN1lY2I7O79trspLHGDDiLt2X9QgzWYBcuUoz3wQ7ybbowYcMHrCMwibNt137POn/9GJnt0skZBBtbv8AzrZjS6q0zYx/s6lQ243hqU+B2GHkRN4gtNNcg2J2LvyC6+rfmMvMyz4ZGu11BXoOdcTB90bQ9rRSnlFrlAhBsWMHMnu9HJ2eefvfw8VPs1Ow8wUzcST8Y7HEVwWZ84UW8d7+BYf2uga6LeQsXUZ48eejx48f6hXfJIawQEIIdVtVpvAw02Nlz5KQx46dIx/sSwd7OhGefR6MIczLDpMxuB461OVmyZRdT2pcw1kNKpnnWYP+wZGVwt2kW9GAZAbPww0dPeLzX6sHEbrtNLB4miypWqir7YPuhTYNgV69Rh8pnnkxtw4ZgG8QWptndQK5LmEQXZ9N8W9c5itoXMo5XNeYg2KUzDqPmX3QWDbbmtj15+mz6vPEX/tVgc7+LSfOX1l1rfs/E+lHdz0yCXbxkaerZZ0Bwj4khXg8wEc+fP7+YiIchV9L9SkKwdSMcgPSfPv0nb2n0CY2fPEM6Xq/OHeZj+w4dJTg4c0quMYDCRPxNXoMNU0/dA2pyTx9YFyhYmHSYiENYwWF3Lf6rdQMLiZOnz9O+A0cdL0N4NW3d/0Gwq/A2XUNGjKa1G7ZKu/bqP9zGHv1Gw4ZNqWK2qazBvuWAgPqTxCZFjo0118MaRlOvCghrli2peG489ybYL6enNNgZhtMXTdhEXDTYWr/rqTPm0pctW9P87xZrzSfue/T03UeOn1bOzdTSL43fbVy+AcwD4xUs6AqxVVfXHrJNl846mTH7WypZsiRBrpafIGAFASHYVtAKkbBPnz6l3LwGe8qM2f4Z4AI40PjascJk99iJM66uy4Izl9Rp0ooG2w/1D4Kdv0AhLQTb3LbN17aUWDiYhP969bpysqPWALpI3BPL161nIH0ly0RQj979ZOJIc7s2TMRrsIn4OAcm4v7QDL9MVhPTRGMrrl6VomlQHXZsFuc53Pf4iaXt27P4CT0IdpHUA6h+nZa0fNU6GRc1tm1sD/pZo6ZqjbBb/VJS6WA5zrGTZ3m3BrYWQp+r8f2CIW0Q7JlM/PLmy0/fdO0V9u8bSMyxg0nNmjWFYIcI/wmmYgrBDqbacKks8HZYpFhx2QcbgywPRCDXp89epP2svY7TVrowAM+YPZ9ee+01ISIuYJnUADp+ynTKkDGTy/tge5YJuESCoTlRHmwvX2Vh7wzvfY1t4ELHPBxlBcGuXLUG9Rs4VNq15rpbvX4TVa1Wiwn2WFsa7JfNof1JYuPLyyC2WHc9sHa08hzuX6/h8ZXpxT0Q7IKp+lDdWs1pmRBsrf3S6HGTqFqNWuzl2g9rsLnvxlaIe9laaNO20Otv7Y4PkGNmzPmWPsmbn7qLkzOt7XnC5OlUqFAhMRF3iZ8kp2SEYIdhbUODnb9AQRo3abrWjsfu4ODveIfZq+it23fU+ms3Z7dHjZ1Ir7/+hmiwNRMRtBc4zilRqqx7GmyTVJtnR+9gaEx2sHf6S0yur1y7Qbv2HgrJb+/nXzZToybNeAeCfn5B5wAAIABJREFUiWIi7qhNJD2xsnodE+yqtah0htHUusBNGybiprY2GLTYUQTtdd9q0TT0UxBbO2Uy3+cFMfZNa510eBDsYqmHU4PabYVga27X4yZMoxo16xBMa7WO9ei7+V1gNYRlOW6O7VrL7QL+SoPN3q2LFivBk6FD9OLsQnmDHc/EyoexMFeuXATnwfITBKwgIATbClohElZpsIsW562N5ibfjtcz+MJM98bN23Th4mXXscBM/RtvviUE2w8D8IQpMylb9pzu7YNtEmvz7PAd4LX23IVLFB0dQ6fPXVBalVAU+OBFvMkXX9LgYaNEg+2wTSQmtOEZrAWqVqvNBHsMa7CtEmyTjNohskkTUmvE1ihLbzYNB8G25zVc7/uAYBd6dwA1qPM1rVi93vWxIKm6Tk7P4Vy1ClvBwMJL63tz3w3tNSYzcdaal+a+wGrZlQab8S1ctJh4EddcN9Bgw8nZ8+fPQ4QBSDGDBQEh2MFSEy6WAwQ7S9bsNG7itGQ16Lw0SPHgC9IDsoM1sZjlfum5C50ytkF78823RdPnApZJ1c0Edtj38Sd5aekKl/bBNok1zg7Lv4Gd5h06doKioqPp96hotfe1StOFtJ2WzWp8aFXLV6hM3Xr2lW26HLaLpLDHZEaNmnWpTMYxFjXY3mQ00ATb0FwPrhdNwxrGeHkNt0rivd/Jatykw4NgF041iOrVaiUabM3t2iTYWLua1Ddg+7mnb4Xj0k1bd+nLRzNWdt8fBHv67HlUqHBR6tN/cLJ7f7u42YkHgl2qVCnRYLvIUZJLUkKww7Cmnzx5orR947ljsNOhhEMcODs5yk7Nrt24RQd5uyQd7wQNdurUaWndxm1a0tdR5lBNEybi8Iy/ZLnDfbAhmL16OBGiNu1Q277BNDw29h5dvHTV2AbOIwCGGt5YFxxRroLsg+2kTfgYF17aa9aqTxEZJ1pYg+1NRANPrmEK3r1cNP007j71rgyia6VMr76LlbhJk2pvLXy7Qr9TkVSDeQ32V0KwfWyfdvuusROm8vZztWkmmzDbTcOXeNBab97u0VyHaH/ry3vGF8bUYOfLX5C6s0PK+MLIvaSX6fiCEQh2sWLFxMlZGHIl3a8kBFs3wgFI/9Hjx5SVNdjw5ulLBxKOYTDwXrj4qzLb1WU+BkEiU+asxhZPmoWWcKwjK+8EE/GP8rhDsCGcmIdTM25or4+fOsfa6xi6zpM5e/YfMb65EBX4YLaMfbB79ukvGmzN3zQ02FWq1qZS7/u6Btt/hNSbnCZ8HUVdSkXTiEYxNPbLGLUGO+Gw8RFi/72PaSJejwn28tXiRdxK32s1LCznatdtQLPna3Jyxn0r+t3N2/caW26GaF9rFVfv8IYGez57ES8g+2Br7qfHT5pKRYoUEYIdAC4T6lkKwQ71Goyn/A8fPaI0adMqx1DenXKyuPYMvkeOn6Jbv92lw8dOGnsRa+iER4weTxk/yCwEWwO2r7bViazBzp4jFy1etsrZpBG3D5Nc4/xqPpb+c/wdew5SDGuuHzx8pIi2Ya7oMF0/4JnQe4Jgl69QiXr1HSBrsDXXA7CuVLkmlX4fa7B92Qfbf4Q0aaIcpczBh38Och1r02u4/95HmYi/O4jq1/6aCbaswU7o+3fj/jieeK5Zu67ap9mN9OJLYyMTbJDsOGskzd9qfGUI5D1FsNkEH1tXYseHQJYl3POeMHkaRUREiIl4PFxDbiWOgBDsxPEJyacPWdhPnSaN8gQc7p3fq++HrZL2Hz5G19mx2Vl2OrWV12E71VK+mof5f9iosUqDbf6XszsmWfHhOJE12Lk/zOOMYINQexFsp+0CbQ17r/7z6TO6/+AhHedrCH6/bA59gt2n/yAh2JqFdjWZEVmZiqUdQq3z30jCi7j/yKgv5Bqm4H2qRNOY5jE2TMNNbfar72Ted/9smojXqdGSflq5VgiJxrY9auwkZQWjcw02+t74xonkcs8g2PPVNl29+w1M1ljorvOJvEVo6dKlxclZSLKhwBZaCHZg8deSO0zEM3yQiWDCrLvzCbb04TX84qUrimDvPXDE0F471VQmMJhDg50pc5Zkh7GlOveQWqdkFssdChYq4mybLq+yONZeM4netmsf3f09mme2nyvnZgcOH/e0hdAl2IbZcnVDg80OzyzVdQLfSdim4bBfURrsSjWoZPoRSRDsV4ko/rtPQn1L0ygL9rue0CqG97yOoU5FzfJZK1NHjofD2rpta3mY7wSCXSbdFPqiYU9asWaDtOvEvlWH7XrshClUo1ZdC/tgo7/0rc9Ev+287w59cg4MsEsMtmPtO0C26dI5xozj9lyiRAkh2FrYSngnKgQ7DOsXJuKZs2SlyaG0BhuDusOBHSZjcGyGbblw3rRtt1YTsmGjxlG69zOIsJaYsObSM3imzZotuzMNtlkWF9oaBMKjx08TvjV47T934bLyWu+0DesUFHxJeyfvJ1u/wafUf9Aw0WCb7SWhs8P+CpMZ9es1pYpZZrCJ+O1ESDOTUN5j2iCi5tke0TQJp72zkTfWXY9uFqMIdrcIlMNqmaIUKbcX1957t2eCHfH+TPry8760Ugh24mOWw3YNE/HqNWtb2KbLBsF2pQ8PXaJtEuyixUvR0JFjE6/PhPovue8TbqPHThAv4mHIk/zxSkKw/YGyn/OAiXjadOkJXq59EaqDIowLA+auvQfp9p27dOfu77R73yHt7z5g0HC1Ljgo8AvGwdKhoOaN66Sps6hY8ZLumHc6bWscH5YSaGf3HjygS79eVdpsRa5dfGfv9/fH9Q4m15cuX6E6deqwF/He4uQssW/KaRvitE0nZ8XTDaWv819PgGB7yOtLBNseybRHqr3zilJrreHQbHaPe8pE3Dq5Ngg5yHWnYlaJuXdZrF2DYEOD3eTTHrIGW3O7htxRuUo1CwTbB6Jrfm+vnhN7lzB+BoI9fRb2wS5OAweP0C7r+GP8CdY8BgwcIvtg+5nDhEt2QrDDpSa93uM+C/1p0qRNPmuwebDZvHU3nT57ge7df0Cn+GyshfVh4HYwCGP7hk/y5pfBLSkMTaEoqXCJPJ88fTZjnc/WPtgQRnC4M4BvV23r8pXr9OjxE7U11xF2pKfSdi0Pve02Phxg/XHwyAm6fOUq1ahRg3r27i8a7ETaoxv1jS3RIiOrUZHUA5lgX4uHYJsE1PtsjVi+INVmGnbjI14UYb/rb/vfo6ENoj1ew5GulTQNz+MwMTfIuZW49sOCYJfPMIeaNugr23RpbtewNqpWvWbS23RZGBfi+vAQ7mPj63ft3gMeM2bPFydnSbVlF54PHT5SrcF+9uyZl5Qtl4JA0ggIwU4ao5ALcZ9JJrxbj580zSVSoVngtzDQJjQg7Tt0jNfDRtGVa9dpx+79js3NE8rH+35/9t6ZK/dHoYGxCwON97snfe0WoTXanjmZsWT5Gmt4x7UtzxIEJwKaJ+62XftZex2lTMNv3/mdNvLkTqibhm/ZsVdNTMECpOFnnymCvWqtrMH+UzvnNuDWZM1qXuNevnwVKp52GLUucPMVomoSYu+zfYJpT9Ns5meUoUf5aFrA5PqHofepZySeWSfX0Frbi2uWxd4ZBLtk2nH0ef3OosGObyzwtGs32vaosROVkzMQwD99P2be6EtVf+rjOGGGV3E0yyNmGYP4jHqaPf87KspWXX36D04Y5yB+hwTbRpCVeczY8VSrVi3ZpivkmFDgCywEO/B14HoJ4NEY61XDnmB7BluYtmIP4pu37rwwDffDQIy9gjNkzCSDW7wDoilAuSMMjRwzQTmUW7J8tTW80Q7MtuB9HW+Zkygrx8e6/stXr6ttuW7dvqPW+oeKoJBgOfm9sFf8idPn+Du6SXXr1qXuvfqKiXh8bYSxcoOEoC5gIl61Sl0qlT6+fbANUvvCCZhVMutNRI20rGmazfhGXDgyG9E4hhaPus+OzfDMaprs0IzN3EHSu5Q245t56D/DyVnhVIOoVvUv2QrmZ2t9SHztINzuedq1G23bGsFOos8NN5xdeh/U08y5C6lYiVKyTZdLmCY0Po4eM56qVauuJtRdF9YlwbBGQAh2GFbvvfv36f0MGQmelxPqNILq/iYeZHFY7Sh5kNmwZQedPHNemeqePX9JEQXL6VjN1xO+e8++lCmTeBH3B94wO8yWPad1L+LcRuLK531tsc4h0MCMGubg9x8+VINtdHQMHeAt4eLSt5hm0MTz4LKFt7TbsWc/NW7SlIYMH8UEcHPov5ubdQKczMOFdEGwK1eqSyXTMcHOH48G27V111bJsDfhNYhx/5qGafjUjuw13PLaacOpWZ/K0dSnKpuW+8lzuPeEAjTYRd4bQjWqNOM+xOIknQt1HTTfenzvYrZp8xxfGAv3DBPxWkmYiKNf9uqbLaQf1Fj66T0wHs2Y/a0yEe/VV7bp0tkmRowaTVWrVhWCHYZcSfcrCcHWjXAA0sc65Ow5ctKkqTP1CMgYiF0bSBwIrVyO7WwOfuPWb2pbLn84NvN+7x6s5cueM5eLWNiYZHCtHlzM29X2YZQLe6vCHN+SiTjK4X04wAoCDdraNdbwPnnyRA228Fa/nc3F4zTkDtL3blcBufbUGSasmjRtxp5pxygNa0DKEqw4utSWTEyVk7PKDZhgj3plmy6TEJtnb8Lr7+sotc/1omH3acmY+8rJmRXT8PaFjHfoXTGaRjSKoW5lUX7/vxcIdvHUo6hO9VbW+pBgbYtulsu7XXv6AbON2jmPmziNatVtwCbM38czNvJEpZtlT6ZpGQR7PpUuW46GjBgTD84ujufJFGOz7ffrP5AqVaokJuIB4DKhnqUQ7FCvwXjKHxMTS1mysok4O+EyOwlXz04H4Zfie5Egix35Jl77evzUOYqKilHmrf4euHv07keFChfVg7FFLFytX6d5v1S/7gz04yZMYydnBayZd3I5VJtwoTzQXh86elK1NWzLFRt7j/Yf8ux77UL6Aa8/vAMfazdspdp16qm9VbFPc8DL5bQtuhXfg0/chI0L6QLf8uVqUFHWrL7sRdwkoDj7m1B752c4JJvf9x6tmvqARjaNsbjuOopAsLuXM8h1zwqBIdfAEAS7WOrhVLtaS1uOEsP2O9DQrqHBrqqcnC2Mp/8Qgu1GWwLBnsUm4hHlKyYfZ7Yu9Ll2sO/dpx9FRESQODmLh2zIrUQREIKdKDyh+TA6JkZp+yZOnRHPAOeA8GAwRidnnu12eGZ8nM1ri2mBOMHrsdJe8/prf2uvgQO2MipesrS7GFvEwc6AkWgcm/WRaJouvBOEto/yfGJZOFbe5F14J2zLdfHy1bh9r6G93sLrlu22X9142UqfcYLjrbLlIgmTR7i2lY4L9e1qvqh/p23ATMM8u/COINjlIkCwvbfp8ibXgSfYWG+9bs4Dte+1HdNw7Jk9ktduY/02rq1ov92cXFAm4qkGU/XKTWjxsjAyEQ/Cdo012JUqV2MT8fgINuQPjxzhwjfkaj8RQuUBwZ45ZwEVK1mKNdijw6OfDlL8e/buowj206f/DE1CIKUOGAJCsAMGvb6Mo6KjqVTZCJq38Af3Ol4XBUtoA+FUyYl2EY7N4DX896hoOnj0BEGb7e/Btkv3Xor0+Ttfrfm5UM+oX7fLiL1VP/4kryWCjXKoNuZw4IaH7XMXLqkt4J4+fUpRau31cVfSdhsnp+mpdcFVqlM/9pAfNmuwXWjTTnGNLz6wjixXV2lWX2iwvQm2tzbZ39dR1L9GNC0bf59mdrlHnYtbLZcRHgR9SvtYtfY6EKbhJkkHwcZERs2qzcPLRBxt22H/5nZ8OKSMrFjlTwR7kznmC8F2XGcg2NgHO1/+AkKwNbf/QUOGUoUKFWQNtj7KErYpC8EOw6q9c/d3qly1evxkxO6AbAqpduOjE/SksWnrLkeEePP2Pbwd1w21FvZX9ugcCHINoaRth87hR7AdDlY6yDWwhlYEe4775AHY0842cjsz25xdIRLvc5hNw+HX4Pnz5+qA1QQ02o61og6xtvtOicWDVhXCcd8Bg2Uf7JfqB0TGXTJjEOw6VIQ1q8Y+2IZJdSCJqEFIo6hbRDRtXPiAdix7SL0rmZpnKxp1I43JbWNoQqvAaq8NE/EoKp5mFNWq2lKcnGlu18rJWY1ayoTZ7Guw+8K+A0fDclLSfEd/ns012HnzFSBMaPgz7+SWV99+/alKlSqyBjsMuZLuVxKCrRvhAKQPgo3tG77/cfnLHa9Jkl8aYC2ajDsh2Cygbtu1j3btPWiUy2ZaR4+fppiYe3zE0r6DRwNGdFq37SD7YHu1JV3kGgP6iNHjKc/H+einlT5sscPtSpmGo2wO27wyDb90lWevnypyHXvvAXsSP6U8ioejoLHy541UrHgp6sYe8mUNtmnOapJrDQQ7oo7aPqpV/ivKfNp0CmZqXq2fTU2zXY23ER9a5+1LHzI5jrXh9dtIY1CdaJrW6Z5ykhboSQPgWjrdJKpbo60QbNVne7dpd9v1hCkzqG79hi95EYfF2fbdB16WR7zGjnDsS3W+Ewj21JlzeYL/Y3ZIOVZw1diW2nfoSJGRkbIGOwBcJtSzFIId6jUYT/lhOp05SzbCQPdSJ2+SDZytdkhmXKvxvMJD07xn/xHayYOtXeKzkdO4dOUaYa/vi5eu2Dczd+F9vm7TgXJ/mMc6ll6YWK6HYI9rp2358E6Ypc+WPYcP5p3YTmuH2q/a0DjaaOte5dl/6Chhwgrrr0Cu1VZwbEHhRtrBWPer1m6icpGVqFffAeFBsJ20R7OPMM9e7cKNuoMGu1JkQ8NEvMBVz/pkK1pibxJtEmvvs/dzX6+jaECtaNq25KEy7e4UZxrue3yQadOxWZ8qvC2Xa9uN+VqGP4cDwY7MMJca1uoeHgQ7iNs1nKvWrtdAbSOFcX4HE2tor5WlmZNyu/z9ufENByoNEOzJ02fThx99TIOHjRIZRGPbaNuuA9WoUUNMxOPhGnIrcQSEYCeOT0g+BcFOmz79nwm2k04IA6PtwREkZzvBtBvaaydrr6E9jGbN9a/XrittuF2ibjueF4bNvmzFA5wQbAgZILU6Ndhjx0+lvPkKsgZ7bRLChJf2Wpn02ifYmMw5cfqcmsyBefgD3v8ae67jvhvtJ1DCWWL5QoNdsnQE9ejTP/QJtqM+y8v6wWk6Xn2GN/Yg2OXK1lIa7K/zBwPBjlJrpbHuev28BzY1z+x5vLSx7npi61ivbb3sThz8mSxb1+obXsQjM86jz5hgh7yTM6ft0YxvnhNon95t1co1iB/GRljQYWvD0+cuOLZas5J/cggLgj2NNdiYdO7Tf3ASY6JFK0WX20Oo10fb9gbBxvac8hMErCAgBNsKWiES9rc7d+n9DB/QRKf7YLs4AMOp2SH2+r1n32GbRH270kpizfXDh4/oApvtBrrjbtWmPZUqExHwcjjGwYV61kmu8X7DR42nHDlzJ7kGG5M3TtfkQ3jBgeUMWOsP7TW25rp6/aYhKLqAl+M60yQEgWAXLV6SurCHfGizg7WcSZYrBOoIBLu8ItjmGmy7ZNKp1hr5GltyfTfkPh345TFNbBNLnYrZKQ+co8Wobb2G1GftddHAEmuTjEODXS3LT/Rlw2E+TNIFMSEx2zXOmvoAp+lOYA12w88b0y8bN9Gt3+7QmXMXacuOMNtxIcDYY3yawV7EsQZ7+OhxQdsWnLalYIgPDXajRo1Egx0i/CeYiikEO5hqw6Wy3Lx5i9KmTUfjJkx1oeM1tM9OHPyAfO1lEzFspaW01zYGJ5AmDNT3HjygaPbibKznMsvmq0BkNXzi6TZu2pwqscflYBgEnJTBiUWBk3ytxIWTM/gVWL5qXaJ4o53Erb+20c7MMkFLDW31kyd/8Nqr53SfJ3VOnb1Am03ttYO0zTyC8bzy5w1UvkIl6jtgCK0J5X2wHRMQLwLjOK34+xFFsCOgwR5Ixhpse4T2xfpmu2Q2ShHhqR1i6fDmxzS/3z2bW2pFUdcy0TS7xz2a1f2el/baznu5GwcEu0y6KdSwTmff/DgE6/eNtuioPepv19jx4bPPGtHhI0eUn5TDx04afbKjcsf/DQVjH+qPMpka7Hz5C4qTM83fatduPbg9f6ac6rokoksyyQQBIdhhWNHXrt+g91KnYYI9zSAjjgY256QUmkCQFZztCAcggHBmduu3uxQbe5+OnTyrTJItD2SmcGKeHXbMX7b8mooULZ4o4bNcRodlCkR+urXXeCeswS5YuAgtS4JgYxmCG3tfb9u1n67fuK0cm0B7fe26sdd6KExGOGkD0FpX4R0IBg4ewdt0bUmWbdu0YIhbBuCo/0yYGADfsmWqUaF3+zPBvsZaZDuk0qn22oiPtdKrpz2gLYseUr/qKIdVss4knddaj2keS7N7xlKvimYaVtOxg0HScbBNV4k0Y6hOtVbhsQbbxjjhr3atCPbnjejYsWN089YdgoOzuG/JRrmd9GfhGhd1OXXGHCpYqAhNfNXXjmDs6rjVslVratq0qWiww5Ar6X4lIdi6EQ5A+leuXqW330nhEsFOWED0ZfAC2TnIpuFYOx23dtXiAIB1XJfZsdnDR4/YZNez9tpiGqqsJrE2z3bS8IrTgjveQoWLutqZ+4JpcgwzZMQYypnrw/hNxFGfXC/YCiaujXnu2cEKbfYwt1c40nv27JmauT5/8TKbOe4N+7qG1roeewDuN3AIrV4XwibiXt+p1TbwJyLiIK3E8sY+4xFlq/M2XUN4m67rLhBsq2TWINdwSPbDsPu09+fHNKubfe11n6rRyjR8UF2TXCdNfO1NKlhPFwS7ZNpxVLtqq9Bfg22zPfqrXY9ly7kvmjWng4cOKx8WblgUJfYdJcdnqEusdYeTVXFy5kxGTar9fN6oCTVu3FgIdgC4TKhnKQQ71GswnvJfuXqN3n33PXednNkc1OGF+cbN28o8PKmOLL7nIExHj5+iqKhoRXSOm9prOwQKcczD5vt4l7FR42ZUolTZkCVd0DwrjawLWHjjouMa23QlaCLOdYp3gfYaztac1vHWnXvVemuQa2ivYTmRLPZwZRxBqgsVKUpduvcOfSdndtq12T+YZztp+BgHGuyIstWoYMp+Nk3EDYJsz0TciNujfDTN6XWP9q97TD+Ne6CcnL1Iz1ciy6bhZaNp4aB7NLf3Peps2fO4r/nYDwcT8VJpJ7AGu3WyJdhx/SLato9t1E44LE1r1LgJrftlo2zNpQnn9Zu2KYL98Sf5aMjw0Vrr004bCKc4Tb9oLibi8fAMuZU0AkKwk8Yo5EJcvnKVCXYqmjRtli1TapAUN2adtzBRucaOobCd1satu2yZh2OLj2s3brGjqacE7+jQZscJCpoGL18HB6zBrlipasgObv4w7fYVy6TCDRs1lnLkyp2ggyJor3EY6TgTIGFxce/+A7XvNdb8Y+3/i7T1zpYnhYPW5yx4Yw12kWLFqUevfkKwNRMRg2BXpwIp+1CrfL9a1GC/Sq6tks8odmIWRRO+jqWDGx7Thm8f0uB6plMyM21f0jTCTmoby+blj9QWX9YJui/5OAsDgl067cTkvQ+2OWmkuV2PHjeZ6tSrTz8uXe7Y4aTW/i7A8oOTd1u3cZtyYpv7w49omOyDrVUGa9a8BbVs2VI5Ow05MiAFDigCQrADCr+ezC9e+pVSpEhJk6fNttbx8MALjaZjR1GeARza5utMjuPWYFkc0EDQQW4esIMpeA7H2mtHxN9lweLzxl8oh1BOBspAxVWaXov18WpZ/UnQsSY4a7Yc8RJslAPm23Yncbzfy1h7fUs5NsPWXLfZI//eA0esfUcOcfUuj7+v4UUclgLdevYJTRNxfONOv3MzDafpJNEO1m7YSlUqNKGi7w1jgn3FAcG2Sj4NUtyzgmHSfWjjY5raIcbLKRme+5omew2vGU07lj2k2ezYzPAabiW+r/k4CxfyBNtsk0m0qUT7CzMNze0aJuI1a9el+Qt+UJZFiZbJyfsk47gg2FCgYNkUrLsEY30T39Bgt2jRQgi2HroS1qkKwQ7D6r1w8ZIi2Ha26QJZcURiMejxAA7TcGieoQ3EeiGrQi/KAe+j2PManpyvXrtpaK9tD6rWy5DUoFXv08+ocpVqyXJwQ/3gSAojt54PGjqSsvKen/Htgw1ijW3gVF4OhEdMLp09f0ktRfjXv/6lzMPxP1lorz3fFQg2/Ap807Vn6G3TZfYzDtpAXBtymoYP/RQIds3Krdh0eTyvwfbVyZlBjl9oie2Q2Shlxj2uRSyBXK+cYn/P629KRtOKSfdVGt14LbfvxNy/YbEGGybidWu0CT0nZyHWrsdOmELVatSimbO/5XHfReJj4uDDt+XWuBOs6UCmmjZrniLY2MIyWMsZDuX6otmX1KZNG1mDHYZcSfcrCcHWjXAA0r/ADpngRdxngu01cCktIAYw3LM5kG1isnOV9w++cPFXpVlUBNtiWtAkgqBjDSw8hx89ccZwYLXZYrni3s1iPB/KW//Tz3mbrtAj2G4RY7fS8aWdYZ0Z9sF+lWCjDLB0UHtfx9W1PaEOXu7hLwD7XkN7jckd7N3uz/f0BQudYVas2UCF2TN+l+69kh/BNtuPefahD3BSFyDYFcs3oMLvDrKgwXZOsGEaDnPwncse0e6Vj2hE4xgbmmejHONaxNCGBYZ5uUH6/UucfSX0hhfx0VSzSgteg73K9tjmpL5txzXbI8522qQZz0zHThoW4kCDDYKNfZqFYNsbi5KqZ8hUU2fOoU/y5id4bU8qvDy3Xw+fNWpKrVu3VhPvARDnJcsQRkAIdghXXkJFP3f+AqVOk9Z3J2eegRcOxUCObXfGaiDfToeOnqA7vF76wOHjttICoTlw5DjFxN5TZAdEW5mZWxjk495Bo1BRh70tV+YtjeLyslO+UIuj6tj+YGUXqwGDhqvZ+mUr176EN9rs1p37DGdtDst2EO32bpSa1Hn0+LEi22o0t3RYAAAgAElEQVTNf6jVkYPyQoNdvkJl6t1vYOitwTa/dbvtwGl8i7iDYJfnfbALpOxrYQ32qwTbKqGNop6R0bzm+gFdOv6H8hoOLfQLjbiv6RmOzRax9/H5fYNrz+v4SDcIdul0hgZ78bLVL/Uhdvskv8Vz2i6dxrfYrkeNnciWXdVp1tzvQgtni+/pt/qPp1wwEZ/A23PlzVeAxo6fKjjHg5Fb9dOgYSNq166dEOyECIfcTxABIdgJQhO6D06fOUtvvPEmjZs43beOlwdgw8x2ty2naHEdGaezk/e8xLprkGK177XVjo/T2MzOqi6wYzSQnCdPntCpsxc82msbxM4ULqyWw4fwn37WmOoyyY57fx/iBDpsqGpjBw0bSQUKFnppH2y8y669B9l7+F5jGYJd/LmNYA33zVu/0ePHT5T2Gu3u7PmLIeNl3a12BQ122XIVqE//QYQtu9xKV1s6bn3fZjo4221HFuPByVmFcvV4m67BPu6D7ZRcG0R6wlexdPbAE1ox+T51j7BHrkHIZ3S5R7tWPKQxzWLVHtjxEdtguYc12GXTT6f6NTuFhom42R4ttqk/tV0zHT+2a6wJRh8ybeY8F78lfJf++zb/hKPTenA5vnJyNmUm5fk4L02aOtNFnG3IWC6/W7BhX6f+p4pgP+JtYuUnCFhBQAi2FbRCJOyp02cpFZuIY59EnzorHnz37D/q2EkUCM+J0+eYqNxRW2vZJXO79x2m33lbLpiHw8kUSJRP7/FqR69ZuIDpEJy52Crbq2X1w3/lvI41vqEoqAxlT6kFCxWh5avXx+GNtdG79x1S7dbOMoS4euN2Agd6INUwDcf59p3flR+BuDB+qJ9gyAsEu0ixEiG1BtvoZxwK4GZf4cd6hga7UmRDj4l4Ul7EXyXX+O+rttkMx1rnMtG0ceFDRbCntI+hDkXMdM0wSZ2N8NjrevuSRzSzWyx1KYU4dsqTVF7uPYcGOzLDXPq0RpeQMRFHuza2UXRALAPQrqHBrlS5mosabH7/ALxHMPTHCZXB1GDny1+QgHdC4eS+8wmDcpEVqX379jz5/jhEGIAUM1gQEIIdLDXhYjlOnz1Pb7+Twrc12Dxw7WdT7v2Hjzlad42OHET4NyYml65cY42gdVNzkCSQQDiWgvY6OiZGOTqzPbiagzLOGgTnmrXrKXNaHWnrSFMJbCy0OU17w2bnaVgtAzTYhYuWoBUmweY6hXm4csjnsH63sYn5bd7rGuT6+fN/qbZ3+twFbov2tpaz+m7BFB74Fi9Vmnr1HRAaGmzzu3bYBpz4nLBbf4YGuy5rsIckocH2kOA4MmyHzEZRN9ZWT+0QS1fP/KG0111KWyXGRjmg9Z7d4x7N73eP4Incunm5e8TZ10kGEOziaUZR5cgm9P3i5Y77QLt1biWeItdutGunaZjfmI9nODmrUrUGa7DnuoSzw8kzH8ttpW4CHRb7YMOL+Ed5PpE12Jrrt3yFStS7d28h2C5ylOSSlBDsMKzpk6zBfuvtd3xag72VHUT9evX6Cy/MVjsrDN58wMT85BnWXrOTqD37sa2RtUER5BrHvgNH6f6Dh7xN0jO6zmlh7bVl7aSnTHHEHP+tvpcP4StUqkI4dKTtdpomuTa0ffZndZ3Gt/teWIONfbCXr1qn2hvKgbarthuzW7+eeGivmBgyCDY7N4uNZe218wknu+8ayHiGiXikItirg9lE3FN3TrebM/udQBHsiLJJ7YPtIddKQ2xeWyWoUcqEezybhmPP6+1LH1KvSnaIseF9fEr7WFo754FyjtapqN0yWX0HZ+FBsIulHk6RZT+l7xYtDd4+W7Vr3i5zi/0+Gv3HS+3abv/owxgYX18FjSrGxens5Tq+55buefAIRasrS+9pEWsQbDixzZ4jF2uwxcmZTqxBsDt27CgEOwy5ku5XEoKtG+EApH/i1BlKnTotr8GeluQAd+L0eSa1Dvb5xQDIB9ZeXzE9h9twlAaBACa/V5jsw4tzLDs4O3z0pL01sJzWSwKGxcHLl84a6UdWrEJVqtVIEmNf0tMZBpoQYOt4+zVOJ1AEu9/AIcqLuEmwsb5/5x5eOsD1YJsccVy8z7ETZ+khr6/C1lxoe2jHcV7JNbQdnXXtNG1osIsVL0Xde/cLbidnqDu0a7XkwT4Z0d1PJFYfMBEvF1GD8qfsRV/lu5yAybdJYM2zVaLJ5JpJ8OB6MXT+yB90/cJTGtM8hjqXsJqeEX5QHex5/UgR7N5xJN1qmfwf3tBgj6TypT+lhT8EOcHmtu10a8CX2jX6SD/2Y2PGT1FOzhwRbJTZPPxYdn/i5CQvtQabCTZ21hAv4vb7f1/qoGy58tStWzch2AHgMqGepRDsUK/BeMp/5OgxSpkyFU2ZPifRgRUkBeRiiw1CHNcx8SAIB1FYe33p8lXWXh9ONM+4ePEMmvA+fu/+A7UGFlp1mO5aJk+eQTlOwIgnn8TK4OszpI+ZTXhL9TVOoMLBuiBu+zVNeOh+t4GDR1DuD/OwBtvwIg7v3o5NKLkOYTGB9dbPnj1XX9LDh48M7/doRyGKlZNyr/x5AxUrUYq69ugd9Nt0qfp3UkeeviJQgjwIdmS5OlQwQS/iJgn2Plsjpx3ZrHxIfWNLrof3ninv4fbWTEeptdZze7Njs+Xs2IxJOoh7sK+9Nk3IQbBLpBlNkWU+C26Cze0Z7dpR2w5wuwbhq1i5qjMNtup/jQlQJ/1ZuMYFwR4/eTply55T1mA7GQN8iBtRvoJyciZrsOMhG3IrUQSEYCcKT2g+PHDwsPIiPmP2/ARJArbjOnzspH0HYp6OCRpA7FENjfOVa0yKmbTbGdRA8q9ev8mzhE/YRPzBC+21VaLjJ+ECBBtmcDVr17f1vnYwshMH9QPNdaA0z3bKHF+cgUNGxjk5g3bHDQ0z0sFEDpzpQXsN52ZXr91Ua7stT+z4MFDH917Bdg8abDiT6/RN96Am2C9IiIOJED/1FQnV8doNWyiSt+kq+G6/ePbB9pBXp+uuy0bTt/3v0a+n/lAHiLH1NdOGifnA2tG0dOx9AsnuxumGCrkGyYYX8RJpxlKFso2CmmCrds39tSOT6AC3a5Ng216DjfJzfxrqk8IJffdu3DdNxLNkySYabM1jLywVu3fvruSD0GQEUupAISAEO1DIa8wXBPu1115XTjDi68wxcB1nr8nQOtve99oziMOx2Q1eK33/4UPWhp+xZYYM8nfwyAnVgUGTiPRsEShvwUJzp2tqsGvVbRDUBFs5AnNoRos25Eij4kJdDBrKBLuw4UUckziqPB5BLL427su9vbw0At7qsd4fR1R0DGuvPWuvHabtS/7BGAYm+Hnz5af2HbvQKt4TOxjLiDKhzzDWqTog2Ga7NPsN87+fziDY5SNqUv4UPeMxETcI9gstMf5b1F6zhnlS61jas+oRXT7xB83pZWe/aqMc2Dt70fD7tPmHRzSsYXTQb8v1KlbQYJdMO44qlm1CC4N4DbbRrh0SbLP9Bqhdj50wlarXrM1exBfa6z+43Ojf3VjSFKz9l9NyQf7ALjHQYIuJuF4T8XKRhpMzTMDLTxCwgoAQbCtohUhYk2CPnxT/GmysXb185brhyMkcjK2euYPHAHjyzHl6wGa1IMW2HJJxvthqCftmm1skQSNueQbfI0xg4MHhdABLKj7ywF6fNWrW0Z5XUmVJ6Dnqx7W111bbh8vhYSKeN18BXhe86cXki9165nib2WLizLmLymM42h3WXsOCYvN29n5vN12X3zmhetV5f8WaX6hQ4aK8TVevoNVgvyAhTgQr7iNQzwGs63UbDRPx/Cl7x0uwQa5h4m1PUxylPHz/8u0Dirr1T0Wye5Q3tc5WyHoUdSoeRdM736ODGx/T4pH3Q2JbrvgIdrkMs6h6hdbs5OynoOyz0a6dk8rAt+sJU2ZQvU8/o9nzv7OOM3+PmDhzjoOTviH445prsD/86GPChIbOMSG5p12iZBnq06ePrMEOEf4TTMUUgh1MteFSWQ4eOkJvvvV2vF7EMXiBwGIrLLWVlgMBE4T6+s1bdOdulGHSzQKCVXILDetFXrtt7kGMfa+xvtYqwTaJtXnWPSggn1JlIthEvF7QDm6uaa+5XnXjmVT6cHKGNdhxhMhBu0UapuUFNNcg2Fj778ZWdUm9R7A/B8H+/9s7DygriqyP735p9+zqrmtOq2LGvKLoIooYyBlBJOcsWSQNQ5SccwbJOUsOAhKUJGBEBUFFAQnymdfvfvd/e2p4MzsD8968ZrqHf59Tp7qrq6vr/apfd91b91ZhHewOicGd5AzPdeY5Zr0gAh/sooUrpDGC7QnW0U9E5ka4VSjOf0KGNTkl+3f/LF98/LNMaP+deDN+uzwZjU9Ip1In5c3Z38u2N34UrH8dvYl5Ru/lXz6MYJe4e5q8VLq1zJwTzGW6sstz7SY5i8lEXN/NsFDK7OSFmX8/RMzEHkDFKQRsKDLwTRwyLO2BlHgwYBlvyaO5H5eOiYnyg06Eyo0EoiFAATsaWiHJu3XbO3L9DTeaCVGKF6R+vLAk0WcHDsk7u/bEbmKp5aAzABNzmNViFBsjginulcGPEoRpCNUQcuALu0tNxaHJj7asZMFa6xbttbHkx/1KliorVavXuiD3i7aOaJ+Yzf8j2i6Wtoi2rhnJ/1rPvvLPPHllpZrVWv5Y21mvg/nhe+/vF0xohufu11/+ZRYdNnNvrOVGMMvI7wlqnuQR7PaJ8sbKdcF6trVt4iOEJI1Qoa2zsL0hYBcvWkme+nsPXQf7UIQJuC6HpbN8xzZ67V3Xr9YpeXuZWhZ99ossn/C/EuuM36jDwHqn5K0FP8j0Ht8lzT7unyCceuQ5XscQsMveu0Aql04I3gi2Pddb4vdfy+LnGst0wawWJszRvufe1KUX0UeJ6/88xndzcp8ixuuj/e3R5IeAjVVi7rv/QY5g+9w+T+R9Sn2wEyhgh0T+CVI1KWAHqTXiVJftSZOcjRgz4ewHTj+6mEjswMEvzDQ2VoEYHwEIKDt275MT6r966tR38q5OlhbNxyEy774P9sspXXf4Vx1J/EJNdGPSXLsOhYt9fuGi/vj4Yhbx2nUbxPzbIznEe9/M7OIw0hcUAbv/oGFStFgJNVvOvF8wOnDHjnvrXmME+/i3Jzzfa6zdjmfoAjw/Qb0HBGx0KF5t2zF4JuLaNtbxzlQboX2D0cY2i7iOYD9xY2ed5OzzJAFbBeTk2bljMQ/XEWddPmvVZM80fIeuez2g7ikb0Y7e1PyErZe9eOQZmTvwTMTa2eEUsMvdt0SqlukkM+YsDNZ/3J5rFbCzyXMNk2UsXxmVgK2/Hd+at3VVB1jGZfn7EW3hQgC/B2YiriPY9+gkZ7AYyHJeAWQULyYP/uNh6datG03E4ySfXEzFUMDOhq29Zes7cvMtOWTUuJQaZIwOH9RZk2EKm5lJoiCow+f6p59+tlmXY505HNdh9Prnn39R7eCPOtHZvpg+FMma5kx1UKLzu8I9n1HfnOYtX42pzvF6+adVDoRr+BLHbxbWrBdI+vQfrLyfFwiAaf3mDKVpm61LmuAP8wZ4M4f/LJ989rktNWeC1wV8hjJU5wvcccEs4vDBbqvLdMHfPTB11HbB82zPdCbaKOW7Igufa/0Ny1Zs1FnEq9gs4t462CekzXMnI4Th6HylIUBjdu+p3b+TL/b/Igff/znVjN/RlKcTmamgP6XLd/Lxjp9kcINYZh8PjiCOWcRL55wtdat0l/mLlwXruVbBMjs918N1feZKVapLVCbi+n+A0n/rO7u9eTCyUAmW4h2RiXeNn+9OZyKOdbDB2897Xexl3//gQ9K9+2sUsLOhrOT3T6KA7TfhLCgfJuK35LhVhuk6ie7luGnrDhUkDppZN9atdumxxNvVvPykmoafOnVahWIV1lWgi64cbyKTT7U+EK5hpnvk62NJH9Zoy8qa/PgIP/X0M/Jys5ZR/nb/64tRvsy2MdozKKPXqEevvgMkV67csnDJikzx3qBrq2P+ge+//9FMwzF/AKwxMqNwiu7Z97/9M1OfRSpg53niKWnbAQL2+kyxzkw90ro22eUh051eCNZZKFwnKU1WrNosRQq+KHluTNRJzjCC7a01Hf1IsyfIts5/UgbU0Xfy6h91YrN/yYpJahqu/tOxlXdCOhQ5KVuX/CAze52xic7iZa6dFeXARLzg7aOkbLGGgfPBxnNt79ps8lxjVutiJUplfARbfzcmNYPbmo1eg0OmWcT2nk0hXF9g5WZa77z00iBgY+T6IR1dHTrqbD8vvfxMj+15ADcshZbQsSMF7CyQZcJ+SwrYYW/BNOq/afNWyZHjNvHWwfZMr3bteU/Xqf4qczOHJwld3qjzz+q3+sXZD2KUH6Nt23fLtydPehNM6brXmHQq6o+q+xBnwccYH2L4BDduGiwBGx21d3T5KfMnjrJNUn+ETejMZBmpy4zlGKPxAwYPk8cef0IWvbEyZqEPbPA/wJrtWA4Oo9gfYP4AN3N4FjxHsfDw8xrwxQh2oCY503Z5a9t2m/wo6neEe37RtpHBpWdJ7M0DsGb9ZileBAK2m0XcmYRHN9LsCdAqEOss4VO7fief7vlZPt75k0zs8F2MM357ftyvdzotH73zk3R9IVYhPVgj2AVvGyVlijYIjg+2Po+w4tq4BZN6xigARD7T2I+1nLhc590fq5dgdY3xGVmmS+uM7wzcdvbs+0CgAM2y35DEMlnIjguTGNv1PPd2PtgP53pERka6Ap7nuixjG+J63XV3TmnXvr0q5b9Po7fNJBJInwAF7PTZhPYMBOzbbr8j2UQLy2Ad+vIrm9wsUx9zfUnCRwqm4Zj1+7MDh70PYjQfds0LbTXW4YaAg7KwXFJMGvykD2JWfDTwEYavap16jbKuQ5DGRwtmdpu0wxa9VUFERyCa9kyjDvFsDzwX6HR16d5TtfW5BOs0x1r+Bp1A51M1B4fVhBOw8ezZfAQB+s2x/r54XAcBu3jJ0vJaz/6yfHXShHI+t3FG6g0LnEyZ0bp3hYuz9Dd5rgoQLIoULiePXd9GXs77WYyTmnnCb7sCJ2WOLqF18ui/5NgXv8riEWekc2knGEcvsGNJL4yAn107OzjCciwj4DARL3zHOClRsL5MnTk35ndIRp7VaPIkz5gd6/vHPc8uzuLneq1as0HgK1e+YpKCP+K7kk7dwODjTz6TvdoniGkOlnTKjaYdkt2DlGNYBOyhaqGY855701wtJrrffv42upjLu1cnkoOA/eOPP4ZWJmDFs4YABeys4e7rXTe+tUWX6bpWP3QTTXiAKTaWIcKs35n5gG1S325MCPXb//2fCSn7Pz2YZFobxQtaP2DeEklfm3CNyaZs9BofSXQSovlYRps/mrLPkxcaZIz0NW7aIro6n6fcqH5/GmVBiDRBJI1zGS0bHX+EjOb3Mx+e141JAjbWwYYJcyz3g6D+ro6QnNLRazy/mNwMlhhQPiV3rgLym2P5ffG6ZqEqMPI+mS8462DrfxwuD5mZlNFjE6QRbJ0jYeNWUzSWLFZV8t7USVrkPxCzgI2ZvgfVOy3ffK5zWZz5Td7f+pMMqh/7xGbwvR7Z4rSMb/ud+YTHZmIeLIEcAnah28dIqcL1ZfqseTG9Q+L1H7Ny9LnGOynZ7SHmd0+wnmu8ryFglylbPlnBnyY3fLs1IP9eXTb04KEvzf866j5AzNxSf9/Q94hgGbdyU98nPsfof2AyuZz33EcB2+e2uu+Bh6RP3342qORrx52FZzsCF5WAjUmNTuuM1QinTp2y+MyZM8kxTED+V82VXcCxS0MMDRZirIeXOh1puM6dc+eRhv3IgDwun9tH2RgVjjxGGgLS3D7yuOCucccuXrNuvVx55VX2gdusM3JCkIA5NzTFmLkWI1Pwr3Rh+er1lob0yLBCl0Ryx7hut5rXnlFBHfeB/zVmD0d66oBrcG1kOj4IK9dusI8qTMFwPSY2+/DjT02Y884jz7nDqnUpz0Pb7K5xmucLEeOeTz/znHTs3D1Z453R+6bZ4YjDRwJm4YGYgTUOvwWMvA6oLjemnTCsg/1o7sdiNhGHgHboiy/NJQHvgTP/+71ZUSSPiqLDF6d6h7kcWAjkeeLJQPlgYyk/WL1kjmtSBzoAvtdQXmGyPbwvShSrJPlydJGmTx5M8pWOfrQZvtJLRum3R4VrTGyGGb87FnOj19EKuiekW3kdvZ7wvQrpp2OsU7T39D8/fLAhYBcvUCcwI9hQhmbelSc4zzX+n3iuBw8bZUtYjp0wOf3/rL1vvWVDMQ8GrOHsP54V72Hc0wV7PwT/W4D+BwTsXI/kpoDt83cbs4gPGTqMAna2E3/9/0EXlYCNUauPP/7Ywocffij79++XTz75RD766CNLO3jwoCAgDeew//nnn9vxgc8OyKFDh5LTcOzyfPHFF5YP5Xz66aeWjnMI7n6uTMTIE5kP+7gPysc+8qD8yLwuDfkQXD337t0r27Ztk7feUj8mjbdu3Sqjx4yTK664Ujp16S4LFi2RjRs3yYxZc2zSEczsiYCJMYaOHGMTZQzT/THjJ1vA0l6YlXL46HGCD+T4iVMt/+Rps+Sd7TsF3Pbs2aP3elsWLVkmk6fPkYlTZsqE12fIpKkz5XXNh/0J6n/lHc+2Ds3k6bNlyoy5MnfhEsEkbB9pO3zw4UfyxvLVmj5Hps2cJ7PnL5Fps+ZrmKfHcy3/VE3HOQSY9k2fPd9ilBV5jPw4N12vR3DXIG2GhQU2uc2MOYssH+5h53TJFrtO8+CaGbMXyKy5i60urjykubxY4mWmloH42ecLSvuOXSyvS5s5d5HMmrfYysC+Bc3vypy36A2Zs2CpcnhD5i1aZjGO8dtdmDVvSXIenHP53TXzFy/XmXC9gDIW6MRfGNnFGtFvrFhjs+S6shEjL/IsWILYC+68S3flYRIx7GMk0zvnHeM6nEN65DmXB6bFmIEaAhrqgnTLr7GlaxpizAKOsGTZmuR0XLt0+Vo7XrJ8jS3FheW4MIs1lDU4l9jlNTMRB0fk8fKt03itnUeMgLWbPcWRF9v1K3Q2bO1AHTh4KFlJhrXgN2zeZnmX6nlcs0yDUyiljp2yKHV65LFTKrk0d41LxzE6Ri4dCienHHJpLo9Lz0jsFDvI6/Zjjb1Jzp5MHsGOtZzI6zIjGGNdXFgZmEVFZjrfKTrQ8RlFivV3QZCACwfaq3jRCvLkzbpMVx4nYEcnbLbOf0KGNDwthz/6Wb478ausmfq9dFGf6VjX0G5f8JTMG3RGpnU/YzOSZ4fRa5iUeybiY6XQM9XtGxVr28XrOsz7AMstKA8zNWobsOcazzbWwS5WorSMHjcpfQFbhSLMq/DZwcO2Isk76noWL7bRlhMUa61o6o13B9bBhoCdYjlWn4XNaOqYXfLee/8DHMH2XxbNlne4qATstEaw3Wi2G9HG8UmdfAsBaRjhjjxGGgLSTpw4kTz6jbTjx4+nCN9++22K42PHjqU4Rn6kISAvAva/+eYby3f06FFBQJqL3T1wDEG3Z8+eUqpUKSlYsKCUKFHCwj//mUd+97vfy4MP/UOeL1DAzuV5Iq/AxBajUwiPPJrbAibJeDT34+ZPDJPnp/M/q5NJ5ZGHcz1q+ZGWV01G8+mM2VWqVpVq1apJuXLlpFixYlKocBEpomsTFy5aXJ55toAuo1TAhM7nCxa2GOeKFCtp5wsU8vKWKl1WqlarLvXq1pOGjRpLhZcqmc9nyVJlpGy5F6Wkni/7wotS7sWKtl+6bHkpoedKlX7BAvLBRxSTqCAf1tss80J5O36xYmWpUKmqvFS5mrxYsYq8oHlQTpVqNSzdi6tIRT2P9Iq6lEjV6jXlJb0G5ZXRsl4oV8HSq9esIxW0jPIVKll51WrU1ry1bPmRKtVqSu069SXHrbfZTOI4h/WwK1WtLtVq1pbqGmrWriu1NE/tuvWlbv1GUkvP12vQ2EKDRk2lfsMm0qhJc5uFvHmrV83UvEnzVtKilfpjqtl5q1fbyStt2kujl708zVq0lqYtXrHlk9q0S5RWrdvZKGPbDokm5Cd06ibde/TR/c5JoYu0S+ik6xknqLDU0dI6dX1N4Muc0Kmrjrx3s7WOO+h+5249dIS4t+A8RuQ7qTDbuVtPb79rD8vbs+8A6TdwqPTuP0h69RskPfoMkB69+0vPvgM1bbAXa3qfAYMFS2p16d7L8rzWs5+lYZIyrGWNMnC+/6Ch1hFDGmadHTF6gil74Fc2TNf3HDV2oip2JlmM4waNmwomG+nTf4h2KMZbpwLrrI5WZdHIsZNMKYR8UB5BMWTxxCmm7Bk/aZrMmrNAlU/bZN++ffLevvdk9dr1MlUVO1AE4fykqbNUWTTblCyIke4pjWZph3y2nUM69hGgjIFy6Wyad71Lg3IJ59wx9k2RpIodpCUrgKBM0gBlEfKgHjBhhVLIu967N651iigokKD0wTVWjuVfYAopp1zCOe+8l8crX++reV0elOf2oSDCuYlTZuj7Ia89a6inpWtZqJNTRJkSSpVAUHaY8knrg3IQcGxBFVD4Dbje5XPKJqd4gkIJyiOcR5g931MmeWmL9HixKk9Wq9Jmhe17CqY3TBGFfeRHGdifu/DstdhHulMiLdTrse8pm7zYHSOGMghKJSi/3DGUSFjOyVM8LTNlkVMmufzuGIokKCYQTAEF5VKSosnSIs5DAbRClUZQMKHsQgXLqA/2K1Iv93vSJM+XSeGLiP2vbL9pnq/EwhNHks/huHeNr2XdnONy+uQZ+eyD72RcwjFpme+INHviawvJ1yVd76V/o+cQvDwubp73a3mt4nGZP/SUdKtwTJo/edTyNde8ySHvUWmeHDRP3mPSQoOX5u3j2AvHNXbBpbnYpUfEOsp8Nn9SOtI0YAQ67XDChGcI0OcO35oPduH81U3xG6kAyux+VIJEkpII82QkT+gVF8VR1sAHKosAACAASURBVCqNYG0ESxMojvBOR5/gXOtgw+1jj5qGH1OXM1jXYTQ/U4qGTAqWUHTgN2RlHaJ5jpyAjdHVc1oKZJJLNHXKbnnxjOKZuPOunNKzVy9TzmdLKZA/yjcCF5WA7RvFLCoYAvmiRYukd+/e0q1bNxO2e+mLoHnz5nLJJZdIo0aNpGvXrtKpUyfp3LmzdOnSRRITE6VDhw7Spk0baddOhbS2bS1ur5M4dEhI0DxdBfstWrSw0LJlS3nllVcsoKyOHTvaNbgH8rjrkQ9lvtr6VUtro+Xinh31frge55G/ZctW0qrVK5YX9UlI6Cht2rbT47aajnOtbEKJtlaHlvpbWkiDho2kabNmFurVqy916tSx9Pr1G9j+y02aSJOmel7Dq21UMH1FhVHNDwG+Zs2a0vjlJlKnbl2p36Ch1FXBHuVVr15DateuI/Xq15datWpL5SpVVdh/SV56SQXyqtXsmho1akjFSpVMsYC8NWvW0jwV5cUKFaRGjZpyzTXXSO7cuS2tmpb3UsVKVk7FSiroWznVLR/yWlrFiirYV7Dyy5UvL+V1H/lwDqGm1qN2nbq6X8ViKCLKln1BhX9VOGgoWaq0lV9NFQa4F+pZqTLqXUmVDeXsuvIVoCjANRVUWfCiFClaVIoVV8VLyVJ6TWWprEoAKCmQr1DholJAlSFFixVXJUZpKV2mrJ0rUrRYUnoJKahKFChdoJyAAqK4llOsREnL96wqVLCP9OcKFLRrkL9AocI6w/oTkv+ZZ02Zk0+vf65AITufX83q8z6VT/I/+7wpbaC4wfrWOMZ9oIjJl/8ZVdCoYkj3ny9YyOr5wIMPyZ//9Ge99mmbvd3LU9AUOM9q2VAeYdK55woU1jKKWlm4L8p9RkMJrWeVKlWkgrZd9epgUMoUQoWKFNP9snqfwnrfZ1XJU8GWmIFiCcuwwUrhOQ1W36T6FVRuzxcs4pWta6GjDHQoUfdCRYrbPtKgYILCCOcwogMGUAhBaQPlDRRCVVTBU0HbG8dQFEGhVLlqDVMmQZEExRLSoHxCPiiGoLzB8nBQ7HhKolqaVs/yQFGE6ytWqWYxFEhQCOGeKKNu/caqAKpj98W1UAwhVK9Z1/JXq1FL7rjzLnN/gKKobv2GUq16LWnYWP9jzVpIM1Xy1FOFUcOXm6oy6FU7bqDnmqpyCIohhOYtW2velpbWvOUrltZYlUnIg3Nt2iWowqeTJCR2kTbtO0rLV9qosgiKos4Wu/3Ezl2lmyqEuqgCKFEVQnAT6NxNlUR63EHzJiR2tf1uqhzq0bufKYqQD6FPv4EaBplCCTFCX1UOIR8CjvsNGCI9+/S3JeAQv9azrx4PMOUPzFyRr9/AITJETTFHqEUPlj3E6Jw7hgXQSFX2wOd0uFoB4TwUO4iHjfQsgKAoQpj4+nQ7N10tiSZNmW7XDB46Rp56orDcf1UtKX//Yqn+yFtS7eGNFqrn2qyxHmtcPdcWqfHINqn1yHapk/tdqZlru9TItU1qPrZZpgzcI7t3fCA7t++VJdPek1dK7NTz70iNhzXPw29LdQ01Hn5Hqv/jban2j2163Q49j4B8CMi3XeN3pH7e7dK3yV7pXnufNMy7V++3S9N3SK1cuzTstFD7kd1S+5F37RzO47iWpSH2jnG+7qPvSYPHPtGwXxo+/okdu/O4L/LUeWSfpu+z/dqP7NF4j9RJOnb184732PUo07u/Vwcc18/9cVL571s5SEOZXvyelYf9erk/lGdy9JNC+aso/2myfNVaWblaLWQ0Rli99k1Zo+5Hb27cIm9u2iqr1ugSdaqE8+I3Na8er9ugeTZoGo6hKMH1Xlil1+P8arhBaUBZyOfKd3lRDs6t36BWDMij18HyCOetXD1eoXlQLtKwj3il1gcB6au0fKTjumUrUX9Y+njnlulveWPFWjvv0hCv1nvhHPLiPK6z+6B81BPlJZWL/WWaDxY97hyOcR3OIc2lLwcDTdvw1lbZoiPSqBP+M3jXQXGabNUUoXCC0gn1+Xj/p3Lg80O6TOJeux8skBar4smUVcgfcY1n/XTW6gn5YNmEAGsmHCOGNZJZNSXFbh8WUdi3Y1yn553lEiyOYDmE3wGrqbNWUGfd6GDh5CyTIuNIyyOvDK8sL91zsUudB8JxWmkuHfH5Aq4H35z33mfvktT5M6s0ysj12U2gjvw9ULhg+U64lmEgpW+//hSws0jOCfNtKWCHufWS6o6ReawljRgBpuk333yz7Nq1y9JhGo/wyy+/WoAPtfPfdr7dqWPnh+5i+JDjOuc7jnSM7ruAkX/nZ459nEdexG7UHyP+zhrAsxDwfOG9fc8qAEoD5LPRfB3hx0g9RvSPHvVG9r/88ktBQBpM8w8fVhOzr75KDkeTLACQ5/DhL8yU3pn2O5N/mNjDFP/AZwcsOLN8mPM7036Xx7kPwET/44/3ywcffCDvv/++xfny5ZNhw4YlH+PcBx98aAEjpcgHk3qkw5QfFgcIOPfuu+/K7t27LaCdsI905MM+8iF9586dFnbs2GHm/9u3b0+Rvn37DjPXh2uA5yKwTTZv3mx5EW/cuFE2qfsAwpYtXp5NmzZZng0bNsratWstrFu3TjZt0nx6Dvtr1qyR9eu106nxypUrNf+W5PTVq9foNdqxWr7cziP/ihUrZIXms1j3ly5dquENWbxYTbqXLLHj5ctX2L6XtlQWLlwoCxYsNCXR/PkLBAHn5s2bJ3M1zF+gaRoWLlxkyplHH31UXp88RaZOnSbTp0+XmbNmyxzNN326uiRMmCCTXp8sU6dNlxkzZsjESa/LuHHjZfz4CRaQB+lTpkyRyZMny8hRo2TwkGEyZuw4FX4my/ARI6X/gIEyVq8ZPXqsfVAxsQnS+vUfoBrs3tL9tZ7SQ+M+fVUY69FLEjt1ttC1W3dL66rCX2KnLmoB0FXz6vnOXSzGcUKiTmSlyqW27RP0fDfp3FUtBVSA7KLXtFPhMiFRLQ8SVPmlgiNC4ybNTHhtogJrIxVmG+kxhNOmzVuaZQKESAivEGQh+CLUrddAatSqY6P99Rs2NcHWCdANGjXRc3Wldr2GZmlRR2OzxFDhGukVK6syRy1CYPmBFQhgnfKyKqag4IKiDsorKMpat1bhuWlTgaKriSq2WrRoaYorKLSQFwoyKLZwbaPGL+u1jS001v0GDRtKA1VyNWrcWJo1a26Krlq1apmiCIovKLqc4gvKrWqqCMF57OM8FFUNVTkGpRkUVFA6QSkGRVWlypUtP6x5SpcubQooKMVwvqQplyqZMg2KKZwvXtyz9imqyqRnn3tOChcpavFT+Z62c2VU2fTkU/k07Xl5QZVXlSpXsTKLFSuuFjjV7J6lVCkFJRiUY1Dg4ByUYFAsPfPsc6bEgXKrnioCC6rSqVjx4lZG6dJlBPd5Kl9+uebqG+Qvf/y73HpNXrnv5sLyQI6i8tg95eSevxeSe29S4fuWYpLn/ory+L0vSa47yssDN5eRh28rr3lLaCgkL5RWRY3+/qJFSki5YvUk120vyS1/yy83a7jj6sJy9zUl5e6rS8ktlz0vd1xVRHJeW1ruv7685LisoOS8uozccUUJufPKkhbfe0NJyX1/cXni7rqS+5b6csflpeSmSwvKPVdWknuvrig5r3hJ7ruqusaVLNx7ZQ25+4qKkuNSvcflFeWhaxqasiDn5ZX1uJLcf2UduefyavLg1Q00va7ccVk5uf2vL0jOy6vKvVfUlAeuqi//uKaJnff2Gyft15OHr20mj173ijxybUsr56GrG8uTf+8uz9wyUP55Q4KO+reTvDd2k8ev7yC5r3tV0zrK4zd0kEevbSX5buqpo9Xjpeidk/R8O8lzQyd56u897P7/uC+vKXuhLO6h1l+d9D88Vt8B/bQDjf97L1VW99L/OEassD948GB9H6gr1aBBMlTf9WPGjLFjvC8GDhyo54fYuUGDBsuIkSM1jDJ/zeEjRuh7ZooMHz5C+uv7A+eGDR8uA/R9gnKmTMU7DO+kmfaefF3fSZP0nTVJY7zD8H6bO08tQGbOsrxIW6DvS7zzJk+ZKrPnzJWFi9TyQxU2KAvvuxmad87ceZY2b/58WaLv3/n6fl2yZKkF7M/Td+wCfZ8uX7HS0hYtXiJvLFsuy/TdvFjzIc+Klatkjb7f39yoE7FpjGOEpW/o+z4pfau6iG3E9+KtzVbWWvtmrNVvxgb9/cNNwQm3HriewVQc8fhJ03Vm8almQbBw8VJ1Odtu95ipli4TJ8OtbEZyHiiqvOs8iyQsOYprx06YomGyjDOrI89KaKJaC+H8BC3DuanBVQ3WOK5cnEOAOxvq4fLBYmjmHHUTmzXP0nANLJSQjmuR33OBm27prkyXx8VIR5moCyyDzFVOr8dSZbAEgksbzlseLRPl41orD9ehrhrAwFklwYLJ6qtlmNud1hu/AdZIuB5WZrfedrtZi6Esy69lIQ/u71lAeVZW2EceXIv6udisqfS3m4VSkgUS8sLKyOVB/kiXPFgymSufWnHBSgnWQnDRc/VGDBc6WDR5ZXjuftPVugnub7BqQrpzu8P1ngUTzukzrveGFRMsiGCdlGwZpdeZRZSWAesluOI5KybnVgcLJJTl3Oqwj/JwD3cfXIfzOEZ+5/LmWTHBammZKYA+/Gi/xTfc+Hf7/qNfir4s+rcI2Hf9X9evRRr6wUh3fWTkjTx2fWjECOh7I6/rk7vzrk/u8iF293d9bfTruQWXAAXs4LZNzDWDMAhzcQiZ3PwhAEVGZe3Uz9eODLfYCIBhZPjtt5THOOcURxDSMfKMj5WnMPotKf6X/PoLlEe/6Mz2P1sMRRL2EaAUQuwUTC7tB3zU9EOIGJPtuQ/W9/oR+16Xj8Nkft+dhgJJY/1Yug8qPqRu/1tTBJ1QhRDcSTzXkuOqIELAuWOqIMKs+8d1pnwofo4c+Vq+/loVRqo0MkUQlEa6j/Rvvjlq53Aex1AOQXF0GPM7HDosh/T4sE7ShuMvdck97H+OOSF0BMgLn8uBAwdVcfSZhgPy2WcHdEmyAzrXwX758CNVHH3yqcX73vtAlTf7ZN97H8rud1WZo2HHzt2y7e0dsnnr27L+zY0C4RKKCCigoGhyiigoqFzAO8bNC+Filx9KKqe0cvlwjHSnxEI69p0CysVQRkGpBeVUZMB5HLtzUEBBSYXYKaSgoHLKKpxDfpyHkgrHKBvHyAOFlQtQTEFxhXjLli22j2uwD8UV9p0yDPlcmdhHuSgP+2+//Y4FzIcROScG6uWUWu4+GzZsMAUWLFSqVq2qiqYFycouKL5WrVptSqy1a1XxtfEt2bBBZ1NfoyOZK1T4Wa2jmCtXq4JrhabraOmaNabsWoeRSJ3fYM6c+SpkzZa56hYxTzuYCDO0cz1bO9LYnz9XO8TayZ8zS+elmDZXZk7XzvGUWRYmvz5NZs9YJHNnLZXJk1QYGfu6TJ6oQt4k7eyPmy5TJs6T8WOmyehhKjgNmyKjNB7Yf6QMHTheJo6eL2OGz9T9idK/1yjp11OVVr1Gy6C+4zVMlNe6DJKuif2kW+JA6dlluIYR0rvrWOnReaR0TRgs3RKGSqe2A6V9q97Spd1wea3DOOn06lBp16KvtGnaWzq3HiPdX50iCS1GSrtmwySh2Whp3XCgtKzfT1rWHSCtG4yU5rUHSMvaIyWx0XzpUHeBNKgwUGqX7Se1Sw+QJx+qJHn/+bwkJiaqEN1Lhep+tj9xoloZqMINAjOstyB849yAAQMsrU+fPnYMiyu4ZA1RoRpKOliCIQ0WYrDkgsUWrMKaqgLKrLc6drTzSEPZzVQJBdeoBg0amCIqQS3GoKBduvQNywdFFqyzkA9lOAuzZKswtRCDUgtuWohxHlZjeC/iGAEKLliXwWKsdu3aZrWDukEpBUXVS6pwaqiKrpdfhvKrkdRXCy4EnMP3rEiRIlJRLa1Qz8aqCENeWP7AJaxkyZJ2b1yHspEH9cS5woULm6sa6oLjHLfeahZKGMmGpdOTqlAqX6GiKh27qZVPUVNYQQEGxRYslWAtBCshs3QyS6BielxAihYvaaFYiVJm2QRLI8xQDuseXAO3NFyX98l8tv9S5WpmDQRLJtwHlkawHkI5sCpCOq4rXBTuayXMXQyWWygflkYoF5ZEL6gFGKyNoHREGqyisI/0ChXhfuadhxsaLItgDQSrofIVKpubGZSWsBSCW1cdVXy2bN1WoOSsqtZAsAwCC+fSBrcyXAtlKNzI4FKGa6EMhaVSs5at5ZVX26sSFRZAr1oeuJjBIunKq65SRaO2aZIrGSyIWqhFEALKatSkhbmJtVZ3M6x4AiuiJqqkxXnUqV2CPrMa4GKW2KW7KnrV4rErXMR6WAw3NVgZdevRR5XCajmkiuBefT2rH7ikDRo6Ui19VOHcq6/6hI+WgYOHWRrWQoc7mLMM6tGnv/RWdzJYCCF/1+7qQqYWQs5qqN8AdR1Ti6JeannUVy0gevZRCyR1N/Pc0tTtTM9hxB7uB0hHDGsiWAthzqChI8Zq2nC1Fppkk78h7/BR49XaaIz5qmNFHbiQwW8dMfKhjkiHwgbHI8bAEmm8WrjMUKXTStmp7/W1696U66673iwt3bcJ3yB8vzBwgz42BoG8AZ3DFjuXziNHjtggEAaCEJAHAefxbccgEfJEHqMs++7rwBHyYj8ydvd231cI5tyCS4ACdnDbJuaa4c+Pjhy1WzEjPO+FEP7QuUInnJv/BCDw5cqVy4Rb/+8W3jvoY2kbnk9siBGcosL29fhf/4KCQsNvv8mvqgXHuwIxlAHoaMOKAMoIbv4RQJtAGILAh7k1XFudK07Rjnq9a1ukIzhFEpRMkQFtmdYx0p3SCcooF1yaG1VButtHnKyQUiUVOnkInqIKVkvfm3IKCqrIcOoUlFCwVNJ5TE7qCFBEOHnilJz4Vuc10fDtcbVgOq7zoJw4bfHxY6qsOqpKq+M6z8kxhJN6jHBKjn5zwsI3XyM+JYi/OaL5vz4jR498J0e++Fa+PHxcvvj8uAwfOlZeadXalCLo1II5OrgYmULAsev4urlOkA8dYcTI6/ahaENepCGgE4wYHWl0vFN3jNFxdpZUUFphH3mRDoUd8kN55ZRULg8stJDXxciD7ztipCOgs438SEPsAvJBqYU8iBHQQcc9XHAddZyDwsspsbCP6xGg3IJlFRRF2Mc5lIN9XAclE5ROCMgzbdo0c7Wao6PsO3dCmbXTlFc7d+2WT1QBCMHFy7/XLKM2bdLZx9e/KetUmFm7br3tQ9G3es1a3VcFkiqZVq5W8+6ly1TwWSHLVbm0VCfGnDt/oVowqZJIR/Enq9vF1GkzZN7CxTJ3wWKZrPsTJ0+V8RNe14lap1gYp/vDRo5RwWq0Td46UgWzBZp/iubFnCC9dJ4RhL4qzEGA66UCYe9+g0xITOzcXec46asCoVo5JAmKcFlBgFAIQRBl9OzTz1xRxo2fKEOHjzTrqEVqGYDfMWv2PLWAGGsWCLCaGDduvFpPjFULBB2Z13iMhgkTJpiVBPKNV+srWCsgwJoBVgwTJ002C4lBquRpqlZAN910k7nEwRqrd5++ZmEF64qhajnRu3dfs8oYOHCwWmSpa4wqh2BNMWToULWiGK7n+qqVRh/PekvTndUGrp84aZJZanTu3EWVR+3sXNeu3Wy/o76vUE7//v2tXBxDKQVrjt6qjEK53j2G2XVw2Wum77kEVTjBPRD7cNtrDCWPWjY1VIUNrJ6Qhryt1c0QCqEGDXXOGnVRgpVQNXV1guscFBOYx6dUmRd07pwq5iYFN6hKZoFVXufIgWtUdbWKUvenOvX0uKq5z8GFD7zqquVVdc3f+OWmSS52cMerY3lgpeQslWBlBSUV3A///OdLJI+6vDnFFyy54JYJpSnehe6d696xOI5Mc+m//OK9k9259I6RjmvcdZGxewe79zTe+dyCS4ACdnDbJuaa4QOIjgA3/wj8nwophQoV0o/kOP9uwpKTCYxQk8ucOXOaiVRyInfiTgCmbBjNwtwO+NBz848A3iEYScRIKFxiuPlLAC4tGI2GAMotJQE8i+fbIvO4/bRiCB4YpYfVB86nFXCvtNI9RdFZpaBTHP2m5STvQ5GkAcdOmEEcqSjEPoITYty+E1x+/tmzeMJ1SDOlkVovQTkEy6bv1HLJs1TyLJNOnDjpWSOZdRImwYWp8He63KMuw6rXQeBBOT/95AQjZ1H1q9URdYWllROWXL28Yy8v9lMHJ2w5ocydR33XqVl+/vz5TVmBdCd0uTzuOHWc+nzkte53uPviOFKow37kcerzkfdy5SK/M4WONHeO3IfCLvWxU+I5BR5iZ5L9b3HSuci8lj8p3ZXvynBxpOk29p11mme95k1wDNe00aNHmzLM3RflgRE3EjgXAQrY56IT0nPQZLPD5m/j4YO3XrXueFFz85/AqlWrpEePHvZx9/9uF+8d0IHAaBU6Gtz8JYBONwVsfxlHlg4rGJg0QwHNzT8CsOqCuToEbG7+EMC7A+4hjz32mFkr+nMXlgrOl112mVkVQFHAjQSiIUABOxpaIckLsy+YsHHzjwBevBBEIGhz858ATBphgulGTPy/48V5B2jm8f5AzM1/AvADx3sEoz3c/CWACRRH6mRjMMvm5h8BzFkAH3SYkXPzhwC+g1BgwIwZ7gnc/CGAUepLL73U5lzgN9Efxtm5VArY2bB14TfFToS/DQvBGv5mFLD95exKh4ANtwcK2I6IPzFM/KDIQMzNfwLwrUUHme8R/1nDzxmB7xB/WUMQgRk+rGG4+UMAzzB86/E8c/OPADhj4j5MQklrRf84Z9eSKWBnw5bdv3+/TdiSDX9aYH4SOsSY5IUd4wvTJBhVpdLIf9boHMPFBP5w3PwnAOGaArb/nHEHKDMwsRgFbH95u3cI3Uz844xnGM8zlKHc/CUA1lgVgiPY/nLOjqVTwM6GrYrlBDArKjf/CECwxkyoFLD9YxxZMoQ+CtiRRPzZRycC1gLsTPjDN3WpGIVC4IQ5qcnE/9ixpoAdf7aRJbp3CAXsSCrx3cczDCsBTmYbX65plQbWmFeASue06DDtXAQoYJ+LTkjPYWSVk5z523joENNE3F/GkaXD7YGdiUgi/uzDDA6+kzSH84dv6lKd0EcBOzWZ+B+DNUb9KGDHn21kiRBEwJkm4pFU4ruPZ9jNSxLfkllaagJgjZnx+U1MTYbH5yNAAft8hEJ4HgI2Jznzt+EwKREsBTiC7S9nVzpMxDnJmaPhX4xRJ8yyzBFs/xhHlnzggK59fOAAR7Ajofi0D/Nw+mD7BDeiWAjYUGZwBDsCSpx3IfThm8gJzuIMNo3iwHrjxo38JqbBhknnJkAB+9x8QnkWgt+pU6dCWfewVBqTQHEE+8K1Fic5uzCsKWBfGM7uLp9/fkhNPWki7nj4GXME20+6Z8t2JuLsg5xlEu89CH1wm6IPdrzJ/nt5TsCmifi/s2HKuQlQwD43n1CehYkntcf+Nh3WRKQPtr+MI0vHxH0cwY4k4s8+zDphjs8RbH/4pi4Vo6owp6WJeGoy8T12I35Q1GGJRW7+EaCJuH9sXcl4numD7Wj4G4M1Jznzl3F2LZ0CdjZsWYxgU8D2t2GdiTg7a/5ydqXD7YE+2I6GfzEEbCgzKGD7xziyZJh4UsCOJOLfPiZJPHbsGH2w/UNsJUP5DGUoR/z8Aw2hjz7Y/vFNXTLM8fFccyOBaAhQwI6GVkjyvv/++xSwfW4rmIhD6KOA7TPopOI5gn1hOMOsE881J3S5MLwhXGMkiiPY/vOGUILAzV8CUM5xHWx/GeM5BmOaiPvL2ZW+a9cufhMdDMYZJkABO8OowpMRvsGcwdPf9oI2E6b4FLD95exKh7Yeo0/c/CVAAdtfvqlLRycZvpQUsFOT4XFYCTgBm1Z0/rUgBOyLZWUNfJOmTZsmy5YtSwaKtHHjxtmkhcmJPu5gFnE+zz4CzqZFU8DOhg27e/duvgx8bleYv0GRQQHbZ9BJxWNUletg+88aijku0+U/Z3cHCNhQHsHlhBsJZAcC+DbiuYYQxM0fAhCwsVLMxeDKg/dj3rx55aGHHpLNmzcbUCglH374YXn77Xf8ARxRKlivX/8m+9QRTLibMQIUsDPGKVS5YM7CEWx/mwydCJqI+8s4snS4PWBCKHzsuPlHAJ1izOFAE3H/GEeWjGcagcv9RVLhfpgJ4N0BoYgjfmFuxeDUHc9SoUKF5KabbpKXX37Zvk0XUsAGiS1btlwUyozgtHr2qAkF7OzRjil+xY4dO0IjYKNjiQ8yFAJhEp4gYEMQCdsINjTe8NvCerBh6gBBmYEJocL0jLg/JdwJMEEb6o9RhyA/M/gfch1s13L+x/gfYvmoMJiIo47nGzEL0zvF/9a9OO+AbyPXwQ5H2+PbhP5XWt9VfKfwf/fTugbvlOPHj1t/5MSJE2kqGiFgV6hQQSpXrizlypWThQsXmnn8hRrBRkviPR3k73Y4nraLr5YUsLNhm2/fvj0UAjZe3nhZJiYmSps2bULlYxs2H2woMnbu3CmvvfaalC37ghQvXlxatmxppk9+fkDj9feC0IePXFodgXjdI97loK5wIxgwYICUL19eChcuLE2aNJH58+fLt99+G+/bxaU8KAA4gh0XlBkqBEqXMAjY6ARPnjxZhg8fnu6zC8spvMeh4A3T/zRDDcVMGSaAbyPe1bSCyTCyLMs4e/Zs6dChg+zdu/ffBEi8m0aMGCHr1q2Le/3wfoCi//XXX5caNWpYf6R+/foyY8aMf3u/OAG7f//+0rVrV0G+tWvXXjAT8bj/eBZ40RCggJ0NmxqCVNA/bhgpmzhxouTMmVNuvPFG+f3vf2/CSFiaA50I+JmFpSOJZ+L555+Xe+65xwQ9CNh33XWX3HnnnbJmzZrAY9+vS0eFbZkuCNelSpUyxkWKFLF9+JFdc801BoEkxAAAEcpJREFUMmTwkEA+OxhFQGeLLiYX5i8BJWN6I0gXpgbnvwtGJPv16yeXX3655MmTRzDHR1pbnz595He/+5089dRTJmSnlYdp2Z8AlLl4rsNglZH9W+Pcv7B06dL2n61ataqNJEfm3rp1q9x7770mgEemx2MfCrtOnTrJrbfeau+LEiVKyIMPPijXXnutKfEinx0nYI8ZM0agxHvxxRelY8eO1pe5ED7Y8fi9LOPiJEABOxu2OzpA6BQFdcMo2dixY+Xuu+82k5/27dvLf/7nf4ZKwAZfrI0YBrMhLCnWrl07eeCBB2TKlClmGo5R61WrVskVV1whJUuWDOqjklwvTLwVtknOVq9ebdYCUCRBiMKzgslSoOR45JFHzFw8+QcGZAeKIygywmDVEBBk2boaUCBCOXfdddfJDTfcICNHjkx38ir8R4sVK2Yd9kqVKgVeyZutG44/jgQyQAAC9p/+9Ce59NJLZebMmSlMtP0SsPFO2bBhg9x///1Sr249W0UB3xvcDwpoCPWRCt5IARuCN0ayYQ2GOlPAzkAjM0uWEaCAnWXo/bsxXjroKAd1gwIAHTGYBqFTBjOhsAnY0NBjVDUsAvbixYvNNDn1zK5PPvmk3HbbbSk+rEF8brAkybGQLdMFxQaekcj/IkzDYS4Oy42wjcgH8blgnfwlgGe4bdu29n5u1qxZimc5rTvDPPyqq64yqyQsbcONBEgguAQgYD/++OPyxBNPmMk1rPLc5qeAje8iRqThjhS5NWjQQP7whz8ILKncFilgIw2TQlasWNEUeRSwHSXGQSRAATuIrZLJOgVdwIagtGTJkuR1pDGqGjYBGyOSUA6EQcDG44R6pjVT8aOPPmpa46CbuuODHHaBFMIK/K8hXMOPjKPEmXzR8XLfCWAkKVeuXHL11VfLggULku+HZxf+kOjoRnbKoUDCHA8YFRs6dGhyfu6QAAkEjwAE7GeffVamT58uV155pbRq1Sq5khkRsHFdemHp0jfOqRRHnyR1/6latWryt7/9LYV1F4TtqVOnphithl84rPIOHz6cXF/ukEDQCFDADlqLxKE+27ZtO+9IQxxuk6ki8GJ1Qh0F7EyhjPlifED/8pe/pPioxlyYzxdC0x22Sc4ckgkTJpj/O3xTodBAxwAKA24kEHQCsHj561//Kjly5Ejhew0LHqxNC59rmJC7DQI5nm+kY8IzbiRAAsEl4ARsuLs1bdrU/utuVDgjAjbmdUkvwEJxz549Gf7x7777rpmHw7oR7xe3oa+I90qkJRgUfFDmpTVo4K5jTAJZTYACdla3gA/3D4OAHfmzwyhg4wMQphHsSN7Yx7rS6DRjYhHMFhr0DQI26umUMkGvb2T95syZI5hEBkuM3HzzzfLYY4+Zv1lkHu6TQBAJYL6M//iP/5Dbb789hVIoPQEblj1dunSR//qv/5LGjRsH8SexTiRAAkkEnICNkWBYiOF/DrexX3751b5R55vkDMtnphcgtGd0LiCYfWNCUEx4i7lhwvid50NFAqkJUMBOTSQbHMMPDuaoYdnCKGDjwwG/4NQmTmFgjmXcIFzD7BNa4zBs+FjDtSCMGzTvMHODxh3zDzz99NOSP3/+FH5mYfxdrHP2JwABG+476HhjqTy3OQEbgjS+N26DgA3TcaRjSTpuJEACwSUQKWCjlnADwYouWJ4rIyPY8fhlBw8eNAU0+iPjxo1LMXodj/JZBglkFQEK2FlF3sf7QoAKk39nGAVsdCTR4QybgI2ZrbEUBmYUD5NPc5hNxCP/6hC20XlBZ2L58uWRp7hPAoEjABNxTFp2yy23pDAFh8IIlhjojG/ZsiW53jDlxKRoGPVOTExMTucOCZBA8AikFrBRQyyZhT4C5sk53wg2Zv1OL2B1kkj3kbR+PQYpsIQlvodz584NVb81rd/DNBKIJEABO5JGNtmHDw0FbH8bEyM7YTIRh8kXJiO56aabpEyZMukuteMvtdhLh0l7mEzEYeIGn3EIKJHmbrB8GDhwoHUoli1bFjuQi+BK+NdBIXE+JRbOw2IHz/j5NuTBuzGyTc53zcV8HiPVBQoUsDWwJ0+enIwC35j77rvPBOlhw4Yls4fSDkvowG87Mn/yhRfpTkafZTyXeOYz8izjmQ+TpdpF2vSB/tlpCdgYOIBSDYIvlpTs0KFDur8B59IL+M5FToAYWQje2W41GUz6uXDhwvO+5yOv5z4JhIEABewwtFKUdYTJXkY+0FEWG7fs6ERAQIXAhDBk8BAzQ1y7dq0dQzDBCHGQN4zUwLQpDB11fMwwC+f1118vmKUTE4849oiPHDkSeN5YquP48eNBfiRS1A0jfNDgv/jii6bFh3k4wq5du2zkD77vhw4dSnEND84SwPtrxowZ0rx5cxshPddkNhD2MLEWlvvDeyW9De+V4cOHS6dOncxvML18TD9LAO2Ata8xaRkE7b179wr+i2gXuDrkyZPHJu6Dqwn8KKdNm2ZCN4RvjE5xExOYMTqHZc7wjTvXBkUiTOtHjRp1TuEZirr27dtzJuVzweS58xJIS8CGArJbt272n7/iiivOKWCf9wbpZNi3b59g0k9YxkDxH9kfwf7p06fTuZLJJBAeAhSww9NWGa4pfGfO1SHNcEE+ZUQnGFpPZ1oEf2D4+UFbirR8+fIJZl4O8gYBGwJSGARsCKaVK1eWSy+91JaIctxdDH9gCOBB3s43ihnEusP1AYL0XXfdZeu+Fy9e3HxZYXY3adKkIFY5MHXCyAeWj4EJcsOGDc9pcdGxY0d7f4ArRkXS21asWGEdOvgHB/39kt5vyIr0o0ePSqFCheSPf/yjXHLJJXLNNddYgKvD+vVvmoB92WWXmXUM2gudZoxqc/MIQIGJ1QNgNg8F57m2hIQEe+YxqgcLqfQ2uIGhvP/5n/8xv9X08jGdBM5FAP0CmIRDqI3c8MxifWwI2BC247nhWz5z5kz57//+b1P6u35IZDxgwIB43pJlkUCWEKCAnSXY/b0pRnSCLJDA7BDCB5aFSCtgNAq+wkHeYPoblhHs8/HGSMiGDRuCjDu0ddu8ebMtg+aWMmnRogVZZ6A1YcHSp08fKVq0qMybN++co3lYb7V8+fI2Mo1R6vQ2mD5inddKlSpxFvf0IKWRDiXi/v37bbQU5t+Y7ReWAM6iZOPGjSY4QlGHDjs6z0FW8KbxE31NgjIWzzIUbPjunWvDCDcYw4/9XKN4YI/1xitUqBCaiSrP9bt5LmsI4HnExGLoz0RusFxZs2aN/ecxq3c8N7xPoAhNq+/n0hYtWhTPW7IsEsgSAhSwswS7fzfFyyvoArZ/v/7ClQwTYJhKgjc3EiABEiABEiABEiABEiABEgABCtjZ7DmAwAfzMQp+/jYsBOywjGD7S4KlkwAJkAAJkAAJkAAJkAAJOAIUsB2JbBJDsD7f0gjZ5Kdm6c+ggJ2l+HlzEiABEiABEiABEiABEggkAQrYgWyW2CsF3+tt27ZxBDt2hBm6EhO1cQQ7Q6iYiQRIgARIgARIgARIgAQuGgIUsLNZU2NyGUw6E+RJzrIDckwyQwE7O7QkfwMJkAAJkAAJkAAJkAAJxI8ABez4sQxESZj9EUun0Afb3+bAmsZYSoic/eXM0kmABEiABEiABEiABEggTAQoYIeptTJQ159++okCdgY4ZTbLsWPHhLOIZ5YirycBEiABEiABEiABEiCB7EWAAnb2ak9bL3bTpk0cWfW5XY8cOSKffPIJTfF95sziSYAESIAESIAESIAESCBMBChgh6m1MlBXjGBv2bIlAzmZJTMEIGDTBzszBHktCZAACZAACZAACZAACWQ/AhSws1mbnjlzRjZs2MARbJ/b9auvvpJPP/2UnH3mzOJJgARIgARIgARIgARIIEwEKGCHqbUyUNcffvhBdu/enYGczJIZAhjBpg92ZgjyWhIgARIgARIgARIgARLIfgQoYGe/NqVf8AVo09OnTwtmEucs4hcANm9BAiRAAiRAAiRAAiRAAiEhQAE7JA3FapIACZAACZAACZAACZAACZAACQSbAAXsYLcPa0cCJEACJEACJEACJEACJEACJBASAhSwQ9JQrCYJkAAJkAAJkAAJkAAJkAAJkECwCVDADnb7sHYkQAIkQAIkQAIkQAIkQAIkQAIhIUABOyQNxWqSAAmQAAmQAAmQAAmQAAmQAAkEmwAF7GC3D2tHAiRAAiRAAiRAAiRAAiRAAiQQEgIUsEPSUKwmCZAACZAACZAACZAACZAACZBAsAlQwA52+7B2JEACJEACJEACJEACJEACJEACISFAATskDcVqkgAJkAAJkAAJkAAJkAAJkAAJBJsABexgtw9rRwIkQAIkQAIkQAIkQAIkQAIkEBICFLBD0lCsJgmQAAmQAAmQAAmQAAmQAAmQQLAJUMAOdvuwdiRAAiRAAiRAAiRAAiRAAiRAAiEhQAE7JA3FapIACZAACZAACZAACZAACZAACQSbAAXsYLcPa0cCJEACJEACJEACJEACJEACJBASAhSwQ9JQrCYJkAAJkAAJkAAJkAAJkAAJkECwCVDADnb7sHYkQAIkQAIkQAIkQAIkQAIkQAIhIUABOyQNxWqSAAmQAAmQAAmQAAmQAAmQAAkEmwAF7GC3D2tHAiRAAiRAAiRAAiRAAiRAAiQQEgIUsEPSUKwmCZAACZAACZAACZAACZAACZBAsAlQwA52+7B2JEACJEACJEACJEACJEACJEACISFAATskDcVqkgAJkAAJkAAJkAAJkAAJkAAJBJsABexgtw9rRwIkQAIkQAIkQAIkQAIkQAIkEBICFLBD0lCsJgmQAAmQAAmQAAmQAAmQAAmQQLAJUMAOdvuwdiRAAiRAAiRAAiRAAiRAAiRAAiEhQAE7JA3FapIACZAACZAACZAACZAACZAACQSbAAXsYLcPa0cCJEACJEACJEACJEACJEACJBASAhSwQ9JQrCYJkAAJkAAJkAAJkAAJkAAJkECwCVDADnb7sHYkQAIkQAIkQAIkQAIkQAIkQAIhIUABOyQNxWqSAAmQAAmQAAmQAAmQAAmQAAkEmwAF7GC3D2tHAiRAAiRAAiRAAiRAAiRAAiQQEgIUsEPSUKwmCZAACZAACZAACZAACZAACZBAsAlQwA52+7B2JEACJEACJEACJEACJEACJEACISFAATskDcVqkgAJkAAJkAAJkAAJkAAJkAAJBJsABexgtw9rRwIkQAIkQAIkQAIkQAIkQAIkEBICFLBD0lCsJgmQAAmQAAmQAAmQAAmQAAmQQLAJUMAOdvuwdiRAAiRAAiRAAiRAAiRAAiRAAiEhQAE7JA3FapIACZAACZAACZAACZAACZAACQSbAAXsYLcPa0cCJEACJEACJEACJEACJEACJBASAhSwQ9JQrCYJkAAJkAAJkAAJkAAJkAAJkECwCVDADnb7sHYkQAIkQAIkQAIkQAIkQAIkQAIhIUABOyQNxWqSAAmQAAmQAAmQAAmQAAmQAAkEmwAF7GC3D2tHAiRAAiRAAiRAAiRAAiRAAiQQEgIUsEPSUKwmCZAACZAACZAACZAACZAACZBAsAlQwA52+7B2JEACJEACJEACJEACJEACJEACISFAATskDcVqkgAJkAAJkAAJkAAJkAAJkAAJBJsABexgtw9rRwIkQAIkQAIkQAIkQAIkQAIkEBICFLBD0lCsJgmQAAmQAAmQAAmQAAmQAAmQQLAJUMAOdvuwdiRAAiRAAiRAAiRAAiRAAiRAAiEhQAE7JA3FapIACZAACZAACZAACZAACZAACQSbAAXsYLcPa0cCJEACJEACJEACJEACJEACJBASAhSwQ9JQrCYJkAAJkAAJkAAJkAAJkAAJkECwCVDADnb7sHYkQAIkQAIkQAIkQAIkQAIkQAIhIUABOyQNxWqSAAmQAAmQAAmQAAmQAAmQAAkEmwAF7GC3D2tHAiRAAiRAAiRAAiRAAiRAAiQQEgIUsEPSUKwmCZAACZAACZAACZAACZAACZBAsAlQwA52+7B2JEACJEACJEACJEACJEACJEACISFAATskDcVqkgAJkAAJkAAJkAAJkAAJkAAJBJvA/wMC7k8fNQRy8QAAAABJRU5ErkJggg==" } }, "cell_type": "markdown", "id": "041858a8", "metadata": {}, "source": [ "### Unstructured Search\n", "\n", "Suppose you are given a large list of $N$ items. Among these items there is one item with a unique property that we wish to locate; we will call this one the winner $w$. Think of each item in the list as a box of a particular color. Say all items in the list are gray except the winner $w$, which is purple.\n", "\n", "![image.png](attachment:image.png)\n", "\n", "To find the purple box -- the *marked item* -- using classical computation, one would have to check on average $N/2$ of these boxes, and in the worst case, all $N$ of them. On a quantum computer, however, we can find the marked item in roughly $\\sqrt{N}$ steps with Grover's amplitude amplification trick. A quadratic speedup is indeed a substantial time-saver for finding marked items in long lists. Additionally, the algorithm does not use the list's internal structure, which makes it *generic;* this is why it immediately provides a quadratic quantum speed-up for many classical problems." ] }, { "attachments": { "image-2.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "ce15f25f", "metadata": {}, "source": [ "### Creating an Oracle\n", "\n", "For the examples in this textbook, our 'database' is comprised of all the possible computational basis states our qubits can be in. For example, if we have 3 qubits, our list is the states $|000\\rangle, |001\\rangle, \\dots |111\\rangle$ (i.e the states $|0\\rangle \\rightarrow |7\\rangle$).\n", "\n", "Grover’s algorithm solves oracles that add a negative phase to the solution states. I.e. for any state $|x\\rangle$ in the computational basis:\n", "\n", "$$\n", "U_\\omega|x\\rangle = \\bigg\\{\n", "\\begin{aligned}\n", "\\phantom{-}|x\\rangle \\quad \\text{if} \\; x \\neq \\omega \\\\\n", "-|x\\rangle \\quad \\text{if} \\; x = \\omega \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "This oracle will be a diagonal matrix, where the entry that correspond to the marked item will have a negative phase. For example, if we have three qubits and $\\omega = \\text{101}$, our oracle will have the matrix:\n", "\n", "$$\n", "U_\\omega = \n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "\\end{bmatrix}\n", "\\begin{aligned}\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\leftarrow \\omega = \\text{101}\\\\\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "What makes Grover’s algorithm so powerful is how easy it is to convert a problem to an oracle of this form. There are many computational problems in which it’s difficult to _find_ a solution, but relatively easy to _verify_ a solution. For example, we can easily verify a solution to a [sudoku](https://en.wikipedia.org/wiki/Sudoku) by checking all the rules are satisfied. For these problems, we can create a function $f$ that takes a proposed solution $x$, and returns $f(x) = 0$ if $x$ is not a solution ($x \\neq \\omega$) and $f(x) = 1$ for a valid solution ($x = \\omega$). Our oracle can then be described as:\n", "\n", "$$\n", "U_\\omega|x\\rangle = (-1)^{f(x)}|x\\rangle\n", "$$\n", "\n", "and the oracle's matrix will be a diagonal matrix of the form:\n", "\n", "$$\n", "U_\\omega = \n", "\\begin{bmatrix}\n", "(-1)^{f(0)} & 0 & \\cdots & 0 \\\\\n", "0 & (-1)^{f(1)} & \\cdots & 0 \\\\\n", "\\vdots & 0 & \\ddots & \\vdots \\\\\n", "0 & 0 & \\cdots & (-1)^{f(2^n-1)} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "If we have our classical function $f(x)$, we can convert it to a reversible circuit of the form:\n", "![image.png](attachment:image.png)\n", "If we initialise the 'output' qubit in the state $|{-}\\rangle$, the phase kickback effect turns this into a Grover oracle (similar to the workings of the Deutsch-Jozsa oracle):\n", "![image-2.png](attachment:image-2.png)\n", "We then ignore the auxiliary ($|{-}\\rangle$) qubit.\n", "\n", "For the next part of this chapter, we aim to teach the core concepts of the algorithm. We will create example oracles where we know $\\omega$ beforehand, and not worry ourselves with whether these oracles are useful or not. At the end of the chapter, we will cover a short example where we create an oracle to solve a problem (sudoku)." ] }, { "attachments": { "image-2.png": { "image/png": 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" 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" 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" }, "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "e60453dc", "metadata": {}, "source": [ "### Amplitude Amplification\n", "\n", "So how does the algorithm work? Before looking at the list of items, we have no idea where the marked item is. Therefore, any guess of its location is as good as any other, which can be expressed in terms of a\n", "uniform superposition: $|s \\rangle = \\frac{1}{\\sqrt{N}} \\sum_{x = 0}^{N -1} | x\n", "\\rangle.$\n", "\n", "If at this point we were to measure in the standard basis $\\{ | x \\rangle \\}$, this superposition would collapse, according to the fifth quantum law, to any one of the basis states with the same probability of $\\frac{1}{N} = \\frac{1}{2^n}$. Our chances of guessing the right value $w$ is therefore $1$ in $2^n$, as could be expected. Hence, on average we would need to try about $N/2 = 2^{n-1}$ times to guess the correct item.\n", "\n", "Enter the procedure called amplitude amplification, which is how a quantum computer significantly enhances this probability. This procedure stretches out (amplifies) the amplitude of the marked item, which shrinks the other items' amplitude, so that measuring the final state will return the right item with near-certainty. \n", "\n", "This algorithm has a nice geometrical interpretation in terms of two reflections, which generate a rotation in a two-dimensional plane. The only two special states we need to consider are the winner $| w \\rangle$ and the uniform superposition $| s \\rangle$. These two vectors span a two-dimensional plane in the vector space $\\mathbb{C}^N.$ They are not quite perpendicular because $| w \\rangle$ occurs in the superposition with amplitude $N^{-1/2}$ as well.\n", "We can, however, introduce an additional state $|s'\\rangle$ that is in the span of these two vectors, which is perpendicular to $| w \\rangle$ and is obtained from $|s \\rangle$ by removing $| w \\rangle$ and\n", "rescaling. \n", "\n", "**Step 1**: The amplitude amplification procedure starts out in the uniform superposition $| s \\rangle$, which is easily constructed from $| s \\rangle = H^{\\otimes n} | 0 \\rangle^n$.\n", "\n", "![image.png](attachment:image.png)\n", "\n", "The left graphic corresponds to the two-dimensional plane spanned by perpendicular vectors $|w\\rangle$ and $|s'\\rangle$ which allows to express the initial state as $|s\\rangle = \\sin \\theta | w \\rangle + \\cos \\theta | s' \\rangle,$ where $\\theta = \\arcsin \\langle s | w \\rangle = \\arcsin \\frac{1}{\\sqrt{N}}$. The right graphic is a bar graph of the amplitudes of the state $| s \\rangle$.\n", "\n", "**Step 2**: We apply the oracle reflection $U_f$ to the state $|s\\rangle$.\n", "\n", "![image-2.png](attachment:image-2.png)\n", "\n", "Geometrically this corresponds to a reflection of the state $|s\\rangle$ about $|s'\\rangle$. This transformation means that the amplitude in front of the $|w\\rangle$ state becomes negative, which in turn means that the average amplitude (indicated by a dashed line) has been lowered.\n", "\n", "**Step 3**: We now apply an additional reflection ($U_s$) about the state $|s\\rangle$: $U_s = 2|s\\rangle\\langle s| - \\mathbb{1}$. This transformation maps the state to $U_s U_f| s \\rangle$ and completes the transformation. \n", "\n", "![image-3.png](attachment:image-3.png)\n", "\n", "Two reflections always correspond to a rotation. The transformation $U_s U_f$ rotates the initial state $|s\\rangle$ closer towards the winner $|w\\rangle$. The action of the reflection $U_s$ in the amplitude bar diagram can be understood as a reflection about the average amplitude. Since the average amplitude has been lowered by the first reflection, this transformation boosts the negative amplitude of $|w\\rangle$ to roughly three times its original value, while it decreases the other amplitudes. We then go to **step 2** to repeat the application. This procedure will be repeated several times to zero in on the winner. \n", "\n", "After $t$ steps we will be in the state $|\\psi_t\\rangle$ where: $| \\psi_t \\rangle = (U_s U_f)^t | s \\rangle.$\n", "\n", "How many times do we need to apply the rotation? It turns out that roughly $\\sqrt{N}$ rotations suffice. This becomes clear when looking at the amplitudes of the state $| \\psi \\rangle$. We can see that the amplitude of $| w \\rangle$ grows linearly with the number of applications $\\sim t N^{-1/2}$. However, since we are dealing with amplitudes and not probabilities, the vector space's dimension enters as a square root. Therefore it is the amplitude, and not just the probability, that is being amplified in this procedure.\n", "\n", "In the case that there are multiple solutions, $M$, it can be shown that roughly $\\sqrt{(N/M)}$ rotations will suffice.\n", "\n", "![image-4.png](attachment:image-4.png)" ] }, { "attachments": { "image-2.png": { "image/png": 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" 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" 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" }, "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "6d9882b9", "metadata": {}, "source": [ "## 2. Example: 2 Qubits \n", "\n", "Let's first have a look at the case of Grover's algorithm for $N=4$ which is realized with 2 qubits. In this particular case, only one rotation is required to rotate the initial state $|s\\rangle$ to the winner $|w\\rangle$[3]:\n", "
    \n", "
  1. \n", " Following the above introduction, in the case $N=4$ we have \n", "\n", "$$\\theta = \\arcsin \\frac{1}{2} = \\frac{\\pi}{6}.$$\n", "\n", "
  2. \n", "
  3. \n", " After $t$ steps, we have $$(U_s U_\\omega)^t | s \\rangle = \\sin \\theta_t | \\omega \\rangle + \\cos \\theta_t | s' \\rangle ,$$where $$\\theta_t = (2t+1)\\theta.$$\n", "\n", "
  4. \n", "
  5. \n", " In order to obtain $| \\omega \\rangle$ we need $\\theta_t = \\frac{\\pi}{2}$, which with $\\theta=\\frac{\\pi}{6}$ inserted above results to $t=1$. This implies that after $t=1$ rotation the searched element is found.\n", "
  6. \n", "
\n", "\n", "We will now follow through an example using a specific oracle.\n", "\n", "#### Oracle for $\\lvert \\omega \\rangle = \\lvert 11 \\rangle$\n", "Let's look at the case $\\lvert w \\rangle = \\lvert 11 \\rangle$. The oracle $U_\\omega$ in this case acts as follows: \n", "\n", "$$U_\\omega | s \\rangle = U_\\omega \\frac{1}{2}\\left( |00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle \\right) = \\frac{1}{2}\\left( |00\\rangle + |01\\rangle + |10\\rangle - |11\\rangle \\right).$$\n", "\n", "or:\n", "\n", "$$\n", "U_\\omega = \n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & -1 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "which you may recognise as the controlled-Z gate. Thus, for this example, our oracle is simply the controlled-Z gate:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "#### Reflection $U_s$\n", "In order to complete the circuit we need to implement the additional reflection $U_s = 2|s\\rangle\\langle s| - \\mathbb{1}$. Since this is a reflection about $|s\\rangle$, we want to add a negative phase to every state orthogonal to $|s\\rangle$. \n", "\n", "One way we can do this is to use the operation that transforms the state $|s\\rangle \\rightarrow |0\\rangle$, which we already know is the Hadamard gate applied to each qubit:\n", "\n", "$$H^{\\otimes n}|s\\rangle = |0\\rangle$$\n", "\n", "Then we apply a circuit that adds a negative phase to the states orthogonal to $|0\\rangle$:\n", "\n", "$$U_0 \\frac{1}{2}\\left( \\lvert 00 \\rangle + \\lvert 01 \\rangle + \\lvert 10 \\rangle + \\lvert 11 \\rangle \\right) = \\frac{1}{2}\\left( \\lvert 00 \\rangle - \\lvert 01 \\rangle - \\lvert 10 \\rangle - \\lvert 11 \\rangle \\right)$$\n", "\n", "i.e. the signs of each state are flipped except for $\\lvert 00 \\rangle$. As can easily be verified, one way of implementing $U_0$ is the following circuit:\n", "\n", "![image-2.png](attachment:image-2.png)\n", "\n", "Finally, we do the operation that transforms the state $|0\\rangle \\rightarrow |s\\rangle$ (the H-gate again):\n", "\n", "$$H^{\\otimes n}U_0 H^{\\otimes n} = U_s$$\n", "\n", "The complete circuit for $U_s$ looks like this:\n", "\n", "![image-3.png](attachment:image-3.png)\n", "\n", "#### Full Circuit for $\\lvert w \\rangle = |11\\rangle$\n", "Since in the particular case of $N=4$ only one rotation is required we can combine the above components to build the full circuit for Grover's algorithm for the case $\\lvert w \\rangle = |11\\rangle$:\n", "\n", "![image-4.png](attachment:image-4.png)\n", "\n", "### 2.1 Qiskit Implementation\n", "\n", "We now implement Grover's algorithm for the above case of 2 qubits for $\\lvert w \\rangle = |11\\rangle$." ] }, { "cell_type": "code", "execution_count": 44, "id": "173963fa", "metadata": {}, "outputs": [], "source": [ "#initialization\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# importing Qiskit\n", "from qiskit import IBMQ, Aer, assemble, transpile\n", "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n", "from qiskit.providers.ibmq import least_busy\n", "\n", "# import basic plot tools\n", "from qiskit.visualization import plot_histogram" ] }, { "cell_type": "markdown", "id": "0c749364", "metadata": {}, "source": [ "We start by preparing a quantum circuit with two qubits:" ] }, { "cell_type": "code", "execution_count": 45, "id": "b8661268", "metadata": {}, "outputs": [], "source": [ "n = 2\n", "grover_circuit = QuantumCircuit(n)" ] }, { "cell_type": "markdown", "id": "ade34935", "metadata": {}, "source": [ "Then we simply need to write out the commands for the circuit depicted above. First, we need to initialize the state $|s\\rangle$. Let's create a general function (for any number of qubits) so we can use it again later:" ] }, { "cell_type": "code", "execution_count": 46, "id": "02034729", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def initialize_s(qc, qubits):\n", " \"\"\"Apply a H-gate to 'qubits' in qc\"\"\"\n", " for q in qubits:\n", " qc.h(q)\n", " return qc" ] }, { "cell_type": "code", "execution_count": 47, "id": "6f06218a", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grover_circuit = initialize_s(grover_circuit, [0,1])\n", "grover_circuit.draw()" ] }, { "cell_type": "markdown", "id": "52c70844", "metadata": {}, "source": [ "Apply the Oracle for $|w\\rangle = |11\\rangle$. This oracle is specific to 2 qubits:" ] }, { "cell_type": "code", "execution_count": 48, "id": "a5548335", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grover_circuit.cz(0,1) # Oracle\n", "grover_circuit.draw()" ] }, { "cell_type": "markdown", "id": "1608f774", "metadata": {}, "source": [ "We now want to apply the diffuser ($U_s$). As with the circuit that initialises $|s\\rangle$, we'll create a general diffuser (for any number of qubits) so we can use it later in other problems. " ] }, { "cell_type": "code", "execution_count": 49, "id": "1869da17", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Diffusion operator (U_s)\n", "grover_circuit.h([0,1])\n", "grover_circuit.z([0,1])\n", "grover_circuit.cz(0,1)\n", "grover_circuit.h([0,1])\n", "grover_circuit.draw()" ] }, { "cell_type": "markdown", "id": "695655ee", "metadata": {}, "source": [ "This is our finished circuit." ] }, { "cell_type": "markdown", "id": "8174e476", "metadata": {}, "source": [ "### 2.1.1 Experiment with Simulators \n", "\n", "Let's run the circuit in simulation. First, we can verify that we have the correct statevector:" ] }, { "cell_type": "code", "execution_count": 50, "id": "94c8acc6", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \n", "$$ |\\psi\\rangle =\\begin{bmatrix}\n", "0 \\\\\n", "0 \\\\\n", "0 \\\\\n", "1\\end{bmatrix} $" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sv_sim = Aer.get_backend('statevector_simulator')\n", "qobj = assemble(grover_circuit)\n", "result = sv_sim.run(qobj).result()\n", "statevec = result.get_statevector()\n", "from qiskit_textbook.tools import vector2latex\n", "vector2latex(statevec, pretext=\"|\\\\psi\\\\rangle =\")" ] }, { "cell_type": "markdown", "id": "e22169dd", "metadata": {}, "source": [ "As expected, the amplitude of every state that is not $|11\\rangle$ is 0, this means we have a 100% chance of measuring $|11\\rangle$:" ] }, { "cell_type": "code", "execution_count": 51, "id": "2eb1866e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grover_circuit.measure_all()\n", "\n", "qasm_sim = Aer.get_backend('qasm_simulator')\n", "qobj = assemble(grover_circuit)\n", "result = qasm_sim.run(qobj).result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "id": "add8a88f", "metadata": {}, "source": [ "### 2.1.2 Experiment with Real Devices \n", "\n", "We can run the circuit a real device as below." ] }, { "cell_type": "code", "execution_count": 75, "id": "eddf3e0c", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ibmqfactory.load_account:WARNING:2021-06-10 15:05:56,210: Credentials are already in use. The existing account in the session will be replaced.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Traceback \u001b[1;36m(most recent call last)\u001b[0m:\n", " File \u001b[0;32m\"\"\u001b[0m, line \u001b[0;32m3\u001b[0m, in \u001b[0;35m\u001b[0m\n", " provider = IBMQ.get_provider(\"ibm-q-internal\")\n", "\u001b[1;36m File \u001b[1;32m\"/opt/conda/lib/python3.8/site-packages/qiskit/providers/ibmq/ibmqfactory.py\"\u001b[1;36m, line \u001b[1;32m424\u001b[1;36m, in \u001b[1;35mget_provider\u001b[1;36m\u001b[0m\n", "\u001b[1;33m raise IBMQProviderError('No provider matches the specified criteria: '\u001b[0m\n", "\u001b[1;31mIBMQProviderError\u001b[0m\u001b[1;31m:\u001b[0m 'No provider matches the specified criteria: hub = ibm-q-internal, group = None, project = None'\n", "\n", "Use %tb to get the full traceback.\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load IBM Q account and get the least busy backend device\n", "provider = IBMQ.load_account()\n", "provider = IBMQ.get_provider(\"ibm-q-internal\")\n", "device = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and \n", " not x.configuration().simulator and x.status().operational==True))\n", "print(\"Running on current least busy device: \", device)" ] }, { "cell_type": "code", "execution_count": null, "id": "baad7134", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n", "from qiskit.tools.monitor import job_monitor\n", "transpiled_grover_circuit = transpile(grover_circuit, device, optimization_level=3)\n", "qobj = assemble(transpiled_grover_circuit)\n", "job = device.run(qobj)\n", "job_monitor(job, interval=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "5dd3c0d6", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [], "source": [ "# Get the results from the computation\n", "results = job.result()\n", "answer = results.get_counts(grover_circuit)\n", "plot_histogram(answer)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "4e8358d0", "metadata": {}, "source": [ "We confirm that in the majority of the cases the state $|11\\rangle$ is measured. The other results are due to errors in the quantum computation. \n", "\n", "## 3. Example: 3 Qubits \n", "\n", "We now go through the example of Grover's algorithm for 3 qubits with two marked states $\\lvert101\\rangle$ and $\\lvert110\\rangle$, following the implementation found in Reference [2]. The quantum circuit to solve the problem using a phase oracle is:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "
    \n", "
  1. \n", " Apply Hadamard gates to $3$ qubits initialised to $\\lvert000\\rangle$ to create a uniform superposition:\n", " $$\\lvert \\psi_1 \\rangle = \\frac{1}{\\sqrt{8}} \\left( \n", " \\lvert000\\rangle + \\lvert001\\rangle + \\lvert010\\rangle + \\lvert011\\rangle + \n", " \\lvert100\\rangle + \\lvert101\\rangle + \\lvert110\\rangle + \\lvert111\\rangle \\right) $$\n", "
  2. \n", "\n", "
  3. \n", " Mark states $\\lvert101\\rangle$ and $\\lvert110\\rangle$ using a phase oracle:\n", " $$\\lvert \\psi_2 \\rangle = \\frac{1}{\\sqrt{8}} \\left( \n", " \\lvert000\\rangle + \\lvert001\\rangle + \\lvert010\\rangle + \\lvert011\\rangle + \n", " \\lvert100\\rangle - \\lvert101\\rangle - \\lvert110\\rangle + \\lvert111\\rangle \\right) $$\n", "
  4. \n", "\n", "
  5. \n", " Perform the reflection around the average amplitude:\n", " \n", "
      \n", "
    1. Apply Hadamard gates to the qubits\n", " $$\\lvert \\psi_{3a} \\rangle = \\frac{1}{2} \\left( \n", " \\lvert000\\rangle +\\lvert011\\rangle +\\lvert100\\rangle -\\lvert111\\rangle \\right) $$\n", "
    2. \n", " \n", "
    3. Apply X gates to the qubits\n", " $$\\lvert \\psi_{3b} \\rangle = \\frac{1}{2} \\left( \n", " -\\lvert000\\rangle +\\lvert011\\rangle +\\lvert100\\rangle +\\lvert111\\rangle \\right) $$\n", "
    4. \n", "\n", "
    5. Apply a doubly controlled Z gate between the 1, 2 (controls) and 3 (target) qubits\n", " $$\\lvert \\psi_{3c} \\rangle = \\frac{1}{2} \\left( \n", " -\\lvert000\\rangle +\\lvert011\\rangle +\\lvert100\\rangle -\\lvert111\\rangle \\right) $$\n", "
    6. \n", "
    7. Apply X gates to the qubits\n", " $$\\lvert \\psi_{3d} \\rangle = \\frac{1}{2} \\left( \n", " -\\lvert000\\rangle +\\lvert011\\rangle +\\lvert100\\rangle -\\lvert111\\rangle \\right) $$\n", "
    8. \n", "
    9. Apply Hadamard gates to the qubits\n", " $$\\lvert \\psi_{3e} \\rangle = \\frac{1}{\\sqrt{2}} \\left( \n", " -\\lvert101\\rangle -\\lvert110\\rangle \\right) $$\n", "
    10. \n", "
    \n", "
  6. \n", "\n", "
  7. \n", " Measure the $3$ qubits to retrieve states $\\lvert101\\rangle$ and $\\lvert110\\rangle$\n", "
  8. \n", "
\n", "\n", "Note that since there are 2 solutions and 8 possibilities, we will only need to run one iteration (steps 2 & 3).\n", "\n", "### 3.1 Qiskit Implementation \n", "\n", "We now implement Grover's algorithm for the above [example](#3qubits) for $3$-qubits and searching for two marked states $\\lvert101\\rangle$ and $\\lvert110\\rangle$. **Note:** Remember that Qiskit orders it's qubits the opposite way round to this resource, so the circuit drawn will appear flipped about the horizontal.\n", "\n", "We create a phase oracle that will mark states $\\lvert101\\rangle$ and $\\lvert110\\rangle$ as the results (step 1)." ] }, { "cell_type": "code", "execution_count": 53, "id": "c3975d83", "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(3)\n", "qc.cz(0, 2)\n", "qc.cz(1, 2)\n", "oracle_ex3 = qc.to_gate()\n", "oracle_ex3.name = \"U$_\\omega$\"" ] }, { "cell_type": "markdown", "id": "1136cedb", "metadata": {}, "source": [ "In the last section, we used a diffuser specific to 2 qubits, in the cell below we will create a general diffuser for any number of qubits.\n", "\n", "
\n", " Details: Creating a General Diffuser (click to expand)\n", " \n", "Remember that we can create $U_s$ from $U_0$:\n", "\n", "$$ U_s = H^{\\otimes n} U_0 H^{\\otimes n} $$\n", "\n", "And a multi-controlled-Z gate ($MCZ$) inverts the phase of the state $|11\\dots 1\\rangle$:\n", "\n", "$$\n", "MCZ = \n", "\\begin{bmatrix}\n", " 1 & 0 & 0 & \\cdots & 0 \\\\\n", " 0 & 1 & 0 & \\cdots & 0 \\\\\n", " \\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " 0 & 0 & 0 & \\cdots & -1 \\\\\n", "\\end{bmatrix}\n", "\\begin{aligned}\n", "\\\\\n", "\\\\\n", "\\\\\n", "\\leftarrow \\text{Add negative phase to} \\; |11\\dots 1\\rangle\\\\\n", "\\end{aligned}\n", "$$\n", "\n", "Applying an X-gate to each qubit performs the transformation:\n", "\n", "$$\n", "\\begin{aligned}\n", "|00\\dots 0\\rangle & \\rightarrow |11\\dots 1\\rangle\\\\\n", "|11\\dots 1\\rangle & \\rightarrow |00\\dots 0\\rangle\n", "\\end{aligned}\n", "$$\n", "\n", "So:\n", "\n", "$$ U_0 = - X^{\\otimes n} (MCZ) X^{\\otimes n} $$\n", "\n", "Using these properties together, we can create $U_s$ using H-gates, X-gates, and a single multi-controlled-Z gate:\n", "\n", "$$ U_s = - H^{\\otimes n} U_0 H^{\\otimes n} = H^{\\otimes n} X^{\\otimes n} (MCZ) X^{\\otimes n} H^{\\otimes n} $$\n", " \n", "Note that we can ignore the global phase of -1.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 54, "id": "54f0b494", "metadata": {}, "outputs": [], "source": [ "def diffuser(nqubits):\n", " qc = QuantumCircuit(nqubits)\n", " # Apply transformation |s> -> |00..0> (H-gates)\n", " for qubit in range(nqubits):\n", " qc.h(qubit)\n", " # Apply transformation |00..0> -> |11..1> (X-gates)\n", " for qubit in range(nqubits):\n", " qc.x(qubit)\n", " # Do multi-controlled-Z gate\n", " qc.h(nqubits-1)\n", " qc.mct(list(range(nqubits-1)), nqubits-1) # multi-controlled-toffoli\n", " qc.h(nqubits-1)\n", " # Apply transformation |11..1> -> |00..0>\n", " for qubit in range(nqubits):\n", " qc.x(qubit)\n", " # Apply transformation |00..0> -> |s>\n", " for qubit in range(nqubits):\n", " qc.h(qubit)\n", " # We will return the diffuser as a gate\n", " U_s = qc.to_gate()\n", " U_s.name = \"U$_s$\"\n", " return U_s" ] }, { "cell_type": "markdown", "id": "20822b60", "metadata": {}, "source": [ "We'll now put the pieces together, with the creation of a uniform superposition at the start of the circuit and a measurement at the end. Note that since there are 2 solutions and 8 possibilities, we will only need to run one iteration. " ] }, { "cell_type": "code", "execution_count": 55, "id": "82d9a938", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 3\n", "grover_circuit = QuantumCircuit(n)\n", "grover_circuit = initialize_s(grover_circuit, [0,1,2])\n", "grover_circuit.append(oracle_ex3, [0,1,2])\n", "grover_circuit.append(diffuser(n), [0,1,2])\n", "grover_circuit.measure_all()\n", "grover_circuit.draw()" ] }, { "cell_type": "markdown", "id": "1a99a3ed", "metadata": {}, "source": [ "### 3.1.1 Experiment with Simulators \n", "\n", "We can run the above circuit on the simulator. " ] }, { "cell_type": "code", "execution_count": 56, "id": "2fed9692", "metadata": {}, "outputs": [ { "data": { "image/png": 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SmY2Urppt3fbjilUkSVKN6vLkBhFxeUQ8FhHbI2J8ue3jEfHfKl+eJEm1o6uTG3wY+CTwLSBaLXoK+LvKlSVJUu3p6p7m+4FLM/M6YFer9iZgUsWqkiSpBnU1NF8NLGmn/QWg//6XI0lS7epqaK4AprTT/mZg6f6XI0lS7erq1bP/C7ghIl5J6ZzmtIj478DHgIsrXZwkSbWkq/dp3hwRfYEvAa+kNNHBU8CVmXnnAahPkqSasS/3ac4GZkfEEcAhmbmx8mVJklR7uhyau2XmpkoWIklSrdtraEbEI8DMzNwSEY8C2VHfzDy5ksVJklRLiuxp3gM0t3rfYWhKktSb7TU0M/Nzrd5/9oBWI0lSDevqNHq/jIjD22kfFBG/rFhVkiTVoK5ObnAm0K+d9kOBM/a7GkmSalihq2cjovUsQCdHxNOtPvcBzgHWVrIwSZJqTdFbThopXQCUwH3tLN8BXFGpoiRJqkVFQ3McpWnzVgB/Afyx1bKdwMbMbKlwbZIk1ZRCoZmZT5bfdvmh1ZIk9RZFJjd4B/D/MvOF8vsOZeYPKlaZJEk1psie5t3ACGBj+X1HktJFQZIk9UpFJjc4pL33kiQdbAxBSZIKKnpOsxDPaUqSerOi5zSL8JymJKlX69I5TUmSDmYGoiRJBXmfpiRJBXmfpiRJBXmfpiRJBRmCkiQV1OXQjIgpEXFrRDSWX7e1ed6mJEm9UpdCMyIuAH4NHAX8R/k1HFgYEX9bcIzLI2JlRDwfEYsi4oxO+s6MiAcjYnNE7IiI30XE1e30e2dELI2I5vKfb+/K95IkqYiiz9Pc7YvApzLzS60bI+LvgS8A3+1s5Yg4H7gOuByYX/7zJxExMTP/0M4q24CvA48C24HTgW9GxPbM/EZ5zGnAncBngB8A7wDuiojTM3NBF7+fJEkd6urh2SOB/9tO+13AsALrXwXckpmzM/O3mXkFsA74QHudM3NRZt6RmY9l5srM/C7wM6D13umHgV9l5hfLY34RmFNulySpYroamr8Czmyn/UxgbmcrRkQ/4LXAfW0W3Qe8vsgPj4hTy31b/6xp7Yz5s6JjSpJUVFcnbP8JcE1E1AMPldteR+mQ6Gf3MtQRlO7j3NCmfQNw1l5qWENpL7cv8LnMvLHV4hEdjDmig7EuAy4DGDlyJHPmzAFg/PjxDBw4kMWLFwMwdOhQJk2axLx58wDo27cv06dPp6mpiWeffRaA+vp6NmzYABzTWfnqoRobG9m2bRsAU6dOZc2aNaxduxaACRMm0KdPH5YuXQrAiBEjGDduHA0NDQD079+fqVOnsmDBAnbs2AHAtGnTWLlyJevXrwdg4sSJtLS0sGzZMgBGjRrF6NGjWbCgdFZhwIAB1NfX09DQQHNzMwDTp0/n8ccfZ+PGjQCcdNJJNDc3s3z5cgDGjBnD8OHDaWxsBGDQoEFMmTKF+fPns2vXLgBmzJjBY489xubNmwGYPHkyW7duZcWKFQCMHTuWIUOG0NTUBMDgwYOZPHkyc+fOJTOJCGbOnMnixYvZsmULAFOmTOHpp59m1apVwP5tT6tXrwbguOOOo66ujiVLlgAwbNgwjj/+eObPnw9AXV0d06ZN26ffE9R18W+DeoJ169ZVZHvqTGRm5x0iXixYb2Zmh5MbRMRIYC0wMzPntWr/NHBBZk7oZN1xwABKAf1PwIcy87bysp3AJZl5a6v+7wFmZ2anW0Z9fX3u/sdlf1x67X4PoRo0+8PdXYEOFLfZ3qlS22xELMrM+vaWVXPC9k1AC6WrbVsbDqzfSw0ry28fjYjhlPZqbyu3rd+XMSVJ6qqqTW6QmTuBRcDZbRadDTzYhaEO4aXHVhoqMKYkSXvV1VtOiIjBwF8BRwP9Wi/LzM/vZfWvAbdFxELgAeD9wEjgxvLYt5bHeU/58xXASmBZef0ZwNXAN1qNeR0wLyI+Afwb8HbgL4HpXf1ukiR1pkuhGRGvA34MNFO6MGctpYkOmoFVQKehmZl3RsRQ4JPl9ZYAb87MJ8tdjm6zSh9K5zDHAruA3wOfoByy5TEfjIh3UbpP9PPlPud7j6YkqdK6uqf5z8D3gA8BzwJvAJ4Dvg/cVGSA8qQE3+hg2ZltPl8LXFtgzLvp/AkskiTtt66e0zwZuCFLl9y2AHWZuQH4OHu/5USSpB6tq6G5s9X7DcCry++3UTo3KUlSr9XVw7NNwGnA45SmqvtC+RaQvwUeqWxpkiTVlq7uaf4D8FT5/SeBPwLXA4Mpz7IjSVJv1aU9zcxsbPX+j5RuPZEk6aDQ5fs0ASLiGODE8selmbmiciVJklSbunqf5lBKt5bMAl78c3P8CLg4MzdXuD5JkmpGV89pfhs4ltLzLA8tv2YA44DZlS1NkqTa0tXDs+cAb8zMhlZtD0TE/wB+XrmyJEmqPV3d0/wjpRmA2toOeGhWktSrdTU0Pw9cGxGjdjeU33+Vvcw7K0lST7fXw7MR8SjQ+knV44BVEbG2/HkU8DwwjNI5T0mSeqUi5zSdCF2SJAqEZmZ+rhqFSJJU6/Z1coM3ABMpHbZ9LDPnVLIoSZJqUVcnNxgF/BB4LX+eg3ZkRDQCb8/MpzpcWZKkHq6rV89+ndJzNI/NzDGZOQY4rtz29UoXJ0lSLenq4dmzgTMzc+XuhsxcERFXAr+oaGWSJNWYru5pwktvP+msTZKkXqWrofkL4PqIGLO7ISKOBq7FPU1JUi/X1dC8EjgMWBERT0bEk8Dvy21XVro4SZJqSVfPaW4G/gI4Ezih3PbbzHSydklSr1c4NCOiD/AMMDkz7wfuP2BVSZJUgwofns3MFuBJoN+BK0eSpNrV1XOa/wh8OSKOOBDFSJJUy7p6TvNqSk85WRsRa2jzbM3MPLlShUmSVGu6Gpp3U7onMw5ALZIk1bRCoRkRrwT+Gfhr4BWU7sm8IjM3HbjSJEmqLUXPaX4OuBD4MfB94CzgXw9QTZIk1aSih2ffAbwvM+8AiIjvAQ9ERJ/yVbWSJPV6Rfc0xwD/uftDZi4EdgEjD0RRkiTVoqKh2QfY2aZtF/v4EGtJknqioqEXwHcjorlV26HA7IjYvrshM2dVsjhJkmpJ0dD8Tjtt361kIZIk1bpCoZmZFx3oQiRJqnX78hBqSZIOSoamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVFDVQzMiLo+IlRHxfEQsiogzOul7VETcHhG/i4iWiLilnT4XRkS28zr0gH4RSdJBp6qhGRHnA9cBXwJOBR4EfhIRR3ewSh2wCfgysKCTobcDR7V+ZebzlapbkiSo/p7mVcAtmTk7M3+bmVcA64APtNc5M1dl5pWZeQvwdCfjZmaub/2qfOmSpINd1UIzIvoBrwXua7PoPuD1+zl8/4h4MiLWRMSPIuLU/RxPkqSX6VvFn3UE0AfY0KZ9A3DWfoy7DLgYWAwMBD4EPBARkzNzedvOEXEZcBnAyJEjmTNnDgDjx49n4MCBLF68GIChQ4cyadIk5s2bB0Dfvn2ZPn06TU1NPPvsswDU19ezYcMG4Jj9KF+1qrGxkW3btgEwdepU1qxZw9q1awGYMGECffr0YenSpQCMGDGCcePG0dDQAED//v2ZOnUqCxYsYMeOHQBMmzaNlStXsn596UDIxIkTaWlpYdmyZQCMGjWK0aNHs2BB6UzEgAEDqK+vp6GhgebmZgCmT5/O448/zsaNGwE46aSTaG5uZvny0l/1MWPGMHz4cBobGwEYNGgQU6ZMYf78+ezatQuAGTNm8Nhjj7F582YAJk+ezNatW1mxYgUAY8eOZciQITQ1NQEwePBgJk+ezNy5c8lMIoKZM2eyePFitmzZAsCUKVN4+umnWbVqFbB/29Pq1asBOO6446irq2PJkiUADBs2jOOPP5758+cDUFdXx7Rp0/bp91Q686PeZt26dRXZnjoTmXkAv0KrHxQxElgLzMzMea3aPw1ckJkT9rL+j4BNmXnhXvr1AX4D/Cozr+ysb319fe7+x2V/XHrtfg+hGjT7w91dgQ4Ut9neqVLbbEQsysz69pZV85zmJqAFGN6mfThQsXOQmdkCNALHVWpMSZKgiqGZmTuBRcDZbRadTekq2oqIiABOpnSBkSRJFVPNc5oAXwNui4iFwAPA+4GRwI0AEXErQGa+Z/cKEXFK+e0g4MXy552ZubS8/DPAQ8Dycp8rKYVmu1fkSpK0r6oampl5Z0QMBT5J6X7KJcCbM/PJcpf27td8uM3ntwFPAmPLnw8HvgWMAJ4p95+RmQsrWrwk6aBX7T1NMvMbwDc6WHZmO22xl/E+AnykIsVJktQJ556VJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCqp6aEbE5RGxMiKej4hFEXHGXvrPLPd7PiJWRMT793dMSZL2RVVDMyLOB64DvgScCjwI/CQiju6g/zjgP8r9TgWuAa6PiHfu65iSJO2rau9pXgXckpmzM/O3mXkFsA74QAf93w88lZlXlPvPBr4DXL0fY0qStE+qFpoR0Q94LXBfm0X3Aa/vYLVp7fT/GVAfEa/YxzElSdonfav4s44A+gAb2rRvAM7qYJ0RwM/b6d+3PF50dcyIuAy4rPxxW0QsK1K89jgC2NTdRVTDtz/S3RVIFeE223Wv7mhBNUOzJmTmt4BvdXcdPVVENGZmfXfXIakYt9nKqmZobgJagOFt2ocD6ztYZ30H/XeVx4t9GFOSpH1StXOambkTWASc3WbR2ZSueG1PQwf9GzPzhX0cU5KkfVLtw7NfA26LiIXAA5Sujh0J3AgQEbcCZOZ7yv1vBP4uIq4FvgmcDlwIvLvomKo4D21LPYvbbAVFZlb3B0ZcDnwMOApYAnwkM+eVl80ByMwzW/WfCfxvYBLwFPBPmXlj0TElSaqUqoemJEk9lXPPSpJUkKEpSVJBhqYkSQUZmpIkFWRoSlIvFhGHtHof3VlLb2BoSlIvlpkvRsTA8ntvl9hP3nKivYqI2L2xRURf4MXMfLGby5LUiYg4kdKjE08FngD+ACwG5mXm6nKfMEi7xtDUXkXEkcCJrSeMKB/m6QO0uNFJtSUijgH+g9ITnx4ATqD01Kg6SgH67cxs+0hFFWBoaq8i4l8oPdR7I3AP8C+ZubTV8kOA0cBU4AeZ2dIthUoCICL+ldI2+TeZubXcNhz4K+BiSs8hvjIzb+q+Knsmz2mqiNMozeX7r8B0YElEPBER/zMihpQP1b6X0hSHBqbU/V4NNGXm1ojoExF9MnNDZt6SmTMobc+XRsQru7nOHsfQVKci4tXAFmAh8I/Amyn93+rPKE2OvykiHgA+AlzfXXVKeomfARdFxAmZ2ZKZLRHRLyL6lZffROkRilO7r8SeycOz6lREDALeDqzKzLmt2vtTeprMa4HLKe2BDszMHd1SqKQ9ImIc8APgcOAfM/P/tFl+EtAEHJ6Z26tfYc9laKqw3Rf/ZOauNu3fA0a1fjqNpO5Vvs3kGuAC4BXAfcDPgZMo/U/ub1o9hlEFGZrqstZXzgL9gXnANZl5T7cWJmn39nlI+ZDsocBrgBnAG4ApwErgu5Qu2lvffZX2TIamOlS+Kva/AEcCrwTWAnMzc2OrPnXAWZn54+6pUtLeREQfSvdXZ0S8KjOf6e6aeipDU+0qH9q5CfhL4EVgDZDA88Bc4LbM/F33VSiptYh4BTAOeDIzm9tZ7kQGFeDVs+rIlcAE4M2ZOZzSeZFrgUeBNwFfKU96IKk2fBB4GLgxIt4WESPKe5hAaQq9iBgUEX9VDljtA/c01a6I+E/gh5n5tTbtfYDTKe2F/j4zz+2O+iS9VEQ0UDoS1Bd4PaVp835I6SraRzPzmYh4P3BhZr6u+yrt2dzT1MuU55ddArxz995k+QbpQ8r3fM2jdI/m6IiY3J21Stoz1eULwOzMPIPS5AY3AW+ldKHeLyPi48CHgQXdVWdvYGjqZcq3lHyH0lyVV0fE8HJYtp6k/XFgLLCpG0qU9FJ9Ke1VbgbIzDWZ+YXMPJ7SvdQPAR8Djge+0m1V9gIentXLlK+aPQS4CPgSpQ3yHuBOSod8Tqb0f7ATM/O07qpT0p+VJxzJzHy+9XMzWz2h6IuUrlE4tbtq7A0MTXUqIg4HLgT+BjgF2ErpvMmvKd2b6aEeqUZ0dIVseY7ZJuDmzPyn6lfWexiaeonytHlbW2945T3PQ4EBlGYTec6wlGpDe9tsO30OBc4Hvp+ZO6tWXC9kaOolIuKblCZnX0jpfq9n2+kzODO3eN+X1P0KbrOHZ+afql1bb2Roao+IeDfwPeBZ4GngfkpPS3gEWJuZOyJiAKUpuD6VmY92W7GSOtpmf0ppm32qvM32B+4A/iEzl3Rbsb2Eoak9ImI2pflkvwK8g9IzMo8BllF6CvwvKE14cF1m9utoHEnV4TZbfYamgD33Zn4MGJSZn2jVPgm4FDiP0nnNw4HvZOb7uqNOSSVus93D0NQeETEYGJ6Zvys/rPaFNhcEnQ98H5iSmb/ppjIllbnNVl/f7i5AtSMztwBbyu93wp4rZyMzW4BBwPNufFJtcJutPkNTnWozC9BA4DPdVYukvXObPbA8PKvCyk9GaDudnqQa5TZbeYamJEkFOWG7JEkFGZqSJBVkaEqSVJChKUlSQYamJEkF/X9VRdT0IO+yBwAAAABJRU5ErkJggg==\n", 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" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qasm_sim = Aer.get_backend('qasm_simulator')\n", "transpiled_grover_circuit = transpile(grover_circuit, qasm_sim)\n", "qobj = assemble(transpiled_grover_circuit)\n", "results = qasm_sim.run(qobj).result()\n", "counts = results.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "id": "bde94427", "metadata": {}, "source": [ "As we can see, the algorithm discovers our marked states $\\lvert101\\rangle$ and $\\lvert110\\rangle$." ] }, { "cell_type": "markdown", "id": "97db39a1", "metadata": {}, "source": [ "### 3.1.2 Experiment with Real Devices \n", "\n", "We can run the circuit on the real device as below." ] }, { "cell_type": "code", "execution_count": 57, "id": "eeb65463", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "least busy backend: ibmqx2\n" ] } ], "source": [ "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and \n", " not x.configuration().simulator and x.status().operational==True))\n", "print(\"least busy backend: \", backend)" ] }, { "cell_type": "code", "execution_count": 62, "id": "b62a02f3", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":5: DeprecationWarning: Passing a Qobj to Backend.run is deprecated and will be removed in a future release. Please pass in circuits or pulse schedules instead.\n", " job = backend.run(qobj)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Job Status: job has successfully run\n" ] } ], "source": [ "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n", "from qiskit.tools.monitor import job_monitor\n", "transpiled_grover_circuit = transpile(grover_circuit, backend, optimization_level=3)\n", "qobj = assemble(transpiled_grover_circuit)\n", "job = backend.run(qobj)\n", "job_monitor(job, interval=2)" ] }, { "cell_type": "code", "execution_count": 63, "id": "4cf15e98", "metadata": { "tags": [ "uses-hardware" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get the results from the computation\n", "results = job.result()\n", "answer = results.get_counts(grover_circuit)\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "8c5b89a7", "metadata": {}, "source": [ "As we can (hopefully) see, there is a higher chance of measuring $\\lvert101\\rangle$ and $\\lvert110\\rangle$. The other results are due to errors in the quantum computation. " ] }, { "cell_type": "markdown", "id": "64e50ec1", "metadata": {}, "source": [ "## 4. Problems \n", "\n", "The function `grover_problem_oracle` below takes a number of qubits (`n`), and a `variant` and returns an n-qubit oracle. The function will always return the same oracle for the same `n` and `variant`. You can see the solutions to each oracle by setting `print_solutions = True` when calling `grover_problem_oracle`." ] }, { "cell_type": "markdown", "id": "4683da78", "metadata": {}, "source": [ "### Exercise 10\n", "\n", "Answer the questions below:" ] }, { "cell_type": "code", "execution_count": 64, "id": "ced95af4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit_textbook.problems import grover_problem_oracle\n", "## Example Usage\n", "n = 4\n", "oracle = grover_problem_oracle(n, variant=1) # 0th variant of oracle, with n qubits\n", "qc = QuantumCircuit(n)\n", "qc.append(oracle, [0,1,2,3])\n", "qc.draw()" ] }, { "cell_type": "markdown", "id": "b1d610d3", "metadata": {}, "source": [ "1. `grover_problem_oracle(4, variant=2)` uses 4 qubits and has 1 solution. \n", " a. How many iterations do we need to have a > 90% chance of measuring this solution? \n", " b. Use Grover's algorithm to find this solution state.\n", " c. What happens if we apply more iterations the the number we calculated in problem 1a above? Why?\n" ] }, { "cell_type": "markdown", "id": "9addc91d", "metadata": {}, "source": [ "### Answer 1\n", "a-\n", "\n", "b- fill in the cells below:" ] }, { "cell_type": "code", "execution_count": null, "id": "8b1a7dba", "metadata": {}, "outputs": [], "source": [ "n = 4\n", "# Initialize a quantum circuit 4 qubits\n", "\n", "# apply H to all qubits\n", "\n", "# append the oracle to your circuit as many times as needed,\n", "oracle = grover_problem_oracle(n, variant=2)\n", "\n", "# draw your circuit here\n" ] }, { "cell_type": "code", "execution_count": 76, "id": "23496e6f", "metadata": {}, "outputs": [], "source": [ "# Run your circuit on a qasm_simulator\n", "\n", "# get your results and plot them here !\n" ] }, { "cell_type": "markdown", "id": "0c462394", "metadata": {}, "source": [ "b - Discuss your results and answer: What happens if we apply more iterations the the number we calculated in problem 1a above? Why?" ] }, { "cell_type": "markdown", "id": "6cb0ef59", "metadata": {}, "source": [ "## Important \n", "\n", "The below part is not included in the course material but you are free to read it!" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "b43071c8", "metadata": {}, "source": [ "## 5. Solving Sudoku using Grover's Algorithm \n", "\n", "The oracles used throughout this chapter so far have been created with prior knowledge of their solutions. We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2×2 binary sudoku, which in our case has two simple rules:\n", "\n", "- No column may contain the same value twice\n", "- No row may contain the same value twice\n", "\n", "If we assign each square in our sudoku to a variable like so:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "we want our circuit to output a solution to this sudoku.\n", "\n", "Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical [decision problems](https://en.wikipedia.org/wiki/Decision_problem) into oracles for Grover's algorithm.\n", "\n", "### 5.1 Turning the Problem into a Circuit\n", "\n", "We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution. Similar to how we created a classical adder using quantum circuits in [_The Atoms of Computation_](https://qiskit.org/textbook/ch-states/atoms-computation.html), we simply need to create a _classical_ function on a quantum circuit that checks whether the state of our variable bits is a valid solution.\n", "\n", "Since we need to check down both columns and across both rows, there are 4 conditions we need to check:\n", "\n", "```\n", "v0 ≠ v1 # check along top row\n", "v2 ≠ v3 # check along bottom row\n", "v0 ≠ v2 # check down left column\n", "v1 ≠ v3 # check down right column\n", "```\n", "\n", "Remember we are comparing classical (computational basis) states. For convenience, we can compile this set of comparisons into a list of clauses:" ] }, { "cell_type": "code", "execution_count": 65, "id": "4536b865", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "clause_list = [[0,1],\n", " [0,2],\n", " [1,3],\n", " [2,3]]" ] }, { "cell_type": "markdown", "id": "a3009919", "metadata": {}, "source": [ "We will assign the value of each variable to a bit in our circuit. To check these clauses computationally, we will use the `XOR` gate (we came across this in the atoms of computation)." ] }, { "cell_type": "code", "execution_count": 66, "id": "7e31b3f7", "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "def XOR(qc, a, b, output):\n", " qc.cx(a, output)\n", " qc.cx(b, output)" ] }, { "cell_type": "markdown", "id": "adf4733b", "metadata": {}, "source": [ "Convince yourself that the `output0` bit in the circuit below will only be flipped if `input0 ≠ input1`:" ] }, { "cell_type": "code", "execution_count": 67, "id": "f8169e78", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We will use separate registers to name the bits\n", "in_qubits = QuantumRegister(2, name='input')\n", "out_qubit = QuantumRegister(1, name='output')\n", "qc = QuantumCircuit(in_qubits, out_qubit)\n", "XOR(qc, in_qubits[0], in_qubits[1], out_qubit)\n", "qc.draw()" ] }, { "cell_type": "markdown", "id": "267eff29", "metadata": {}, "source": [ "This circuit checks whether `input0 == input1` and stores the output to `output0`. To check each clause, we repeat this circuit for each pairing in `clause_list` and store the output to a new bit:" ] }, { "cell_type": "code", "execution_count": 68, "id": "8005edcb", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create separate registers to name bits\n", "var_qubits = QuantumRegister(4, name='v') # variable bits\n", "clause_qubits = QuantumRegister(4, name='c') # bits to store clause-checks\n", "\n", "# Create quantum circuit\n", "qc = QuantumCircuit(var_qubits, clause_qubits)\n", "\n", "# Use XOR gate to check each clause\n", "i = 0\n", "for clause in clause_list:\n", " XOR(qc, clause[0], clause[1], clause_qubits[i])\n", " i += 1\n", "\n", "qc.draw()" ] }, { "cell_type": "markdown", "id": "12cac3ef", "metadata": {}, "source": [ "The final state of the bits `c0, c1, c2, c3` will only all be `1` in the case that the assignments of `v0, v1, v2, v3` are a solution to the sudoku. To complete our checking circuit, we want a single bit to be `1` if (and only if) all the clauses are satisfied, this way we can look at just one bit to see if our assignment is a solution. We can do this using a multi-controlled-Toffoli-gate:" ] }, { "cell_type": "code", "execution_count": 69, "id": "5feb8bd8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create separate registers to name bits\n", "var_qubits = QuantumRegister(4, name='v')\n", "clause_qubits = QuantumRegister(4, name='c')\n", "output_qubit = QuantumRegister(1, name='out')\n", "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit)\n", "\n", "# Compute clauses\n", "i = 0\n", "for clause in clause_list:\n", " XOR(qc, clause[0], clause[1], clause_qubits[i])\n", " i += 1\n", "\n", "# Flip 'output' bit if all clauses are satisfied\n", "qc.mct(clause_qubits, output_qubit)\n", "\n", "qc.draw()" ] }, { "cell_type": "markdown", "id": "c4123660", "metadata": {}, "source": [ "The circuit above takes as input an initial assignment of the bits `v0`, `v1`, `v2` and `v3`, and all other bits should be initialised to `0`. After running the circuit, the state of the `out0` bit tells us if this assignment is a solution or not; `out0 = 0` means the assignment _is not_ a solution, and `out0 = 1` means the assignment _is_ a solution.\n", "\n", "**Important:** Before you continue, it is important you fully understand this circuit and are convinced it works as stated in the paragraph above.\n", "\n", "### 5.2 Uncomputing, and Completing the Oracle\n", "\n", "We can now turn this checking circuit into a Grover oracle using [phase kickback](https://qiskit.org/textbook/ch-gates/phase-kickback.html). To recap, we have 3 registers: \n", "- One register which stores our sudoku variables (we'll say $x = v_3, v_2, v_1, v_0$)\n", "- One register that stores our clauses (this starts in the state $|0000\\rangle$ which we'll abbreviate to $|0\\rangle$)\n", "- And one qubit ($|\\text{out}_0\\rangle$) that we've been using to store the output of our checking circuit. \n", "\n", "To create an oracle, we need our circuit ($U_\\omega$) to perform the transformation:\n", "\n", "$$\n", "U_\\omega|x\\rangle|0\\rangle|\\text{out}_0\\rangle = |x\\rangle|0\\rangle|\\text{out}_0\\oplus f(x)\\rangle\n", "$$\n", "\n", "If we set the `out0` qubit to the superposition state $|{-}\\rangle$ we have:\n", "\n", "$$\n", "\\begin{aligned}\n", "U_\\omega|x\\rangle|0\\rangle|{-}\\rangle \n", "&= U_\\omega|x\\rangle|0\\rangle\\otimes\\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle)\\\\\n", "&= |x\\rangle|0\\rangle\\otimes\\tfrac{1}{\\sqrt{2}}(|0\\oplus f(x)\\rangle - |1\\oplus f(x)\\rangle)\n", "\\end{aligned}\n", "$$\n", "\n", "If $f(x) = 0$, then we have the state:\n", "\n", "$$\n", "\\begin{aligned}\n", "&= |x\\rangle|0\\rangle\\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle)\\\\\n", "&= |x\\rangle|0\\rangle|-\\rangle\\\\\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "(i.e. no change). But if $f(x) = 1$ (i.e. $x = \\omega$), we introduce a negative phase to the $|{-}\\rangle$ qubit:\n", "\n", "$$\n", "\\begin{aligned}\n", "&= \\phantom{-}|x\\rangle|0\\rangle\\otimes\\tfrac{1}{\\sqrt{2}}(|1\\rangle - |0\\rangle)\\\\\n", "&= \\phantom{-}|x\\rangle|0\\rangle\\otimes -\\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle)\\\\\n", "&= -|x\\rangle|0\\rangle|-\\rangle\\\\\n", "\\end{aligned}\n", "$$\n", "\n", "This is a functioning oracle that uses two auxiliary registers in the state $|0\\rangle|{-}\\rangle$:\n", "\n", "$$\n", "U_\\omega|x\\rangle|0\\rangle|{-}\\rangle = \\Bigg\\{\n", "\\begin{aligned}\n", "\\phantom{-}|x\\rangle|0\\rangle|-\\rangle \\quad \\text{for} \\; x \\neq \\omega \\\\\n", "-|x\\rangle|0\\rangle|-\\rangle \\quad \\text{for} \\; x = \\omega \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "To adapt our checking circuit into a Grover oracle, we need to guarantee the bits in the second register (`c`) are always returned to the state $|0000\\rangle$ after the computation. To do this, we simply repeat the part of the circuit that computes the clauses which guarantees `c0 = c1 = c2 = c3 = 0` after our circuit has run. We call this step _'uncomputation'_." ] }, { "cell_type": "code", "execution_count": 70, "id": "b6720fab", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var_qubits = QuantumRegister(4, name='v')\n", "clause_qubits = QuantumRegister(4, name='c')\n", "output_qubit = QuantumRegister(1, name='out')\n", "cbits = ClassicalRegister(4, name='cbits')\n", "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit, cbits)\n", "\n", "def sudoku_oracle(qc, clause_list, clause_qubits):\n", " # Compute clauses\n", " i = 0\n", " for clause in clause_list:\n", " XOR(qc, clause[0], clause[1], clause_qubits[i])\n", " i += 1\n", "\n", " # Flip 'output' bit if all clauses are satisfied\n", " qc.mct(clause_qubits, output_qubit)\n", "\n", " # Uncompute clauses to reset clause-checking bits to 0\n", " i = 0\n", " for clause in clause_list:\n", " XOR(qc, clause[0], clause[1], clause_qubits[i])\n", " i += 1\n", "\n", "sudoku_oracle(qc, clause_list, clause_qubits)\n", "qc.draw()" ] }, { "cell_type": "markdown", "id": "d0bc3dba", "metadata": {}, "source": [ "In summary, the circuit above performs:\n", "\n", "$$\n", "U_\\omega|x\\rangle|0\\rangle|\\text{out}_0\\rangle = \\Bigg\\{\n", "\\begin{aligned}\n", "|x\\rangle|0\\rangle|\\text{out}_0\\rangle \\quad \\text{for} \\; x \\neq \\omega \\\\\n", "|x\\rangle|0\\rangle\\otimes X|\\text{out}_0\\rangle \\quad \\text{for} \\; x = \\omega \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "and if the initial state of $|\\text{out}_0\\rangle = |{-}\\rangle$,:\n", "\n", "$$\n", "U_\\omega|x\\rangle|0\\rangle|{-}\\rangle = \\Bigg\\{\n", "\\begin{aligned}\n", "\\phantom{-}|x\\rangle|0\\rangle|-\\rangle \\quad \\text{for} \\; x \\neq \\omega \\\\\n", "-|x\\rangle|0\\rangle|-\\rangle \\quad \\text{for} \\; x = \\omega \\\\\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "aaa5865c", "metadata": {}, "source": [ "### 5.3 The Full Algorithm\n", "\n", "All that's left to do now is to put this oracle into Grover's algorithm!" ] }, { "cell_type": "code", "execution_count": 71, "id": "5fc35320", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var_qubits = QuantumRegister(4, name='v')\n", "clause_qubits = QuantumRegister(4, name='c')\n", "output_qubit = QuantumRegister(1, name='out')\n", "cbits = ClassicalRegister(4, name='cbits')\n", "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit, cbits)\n", "\n", "# Initialise 'out0' in state |->\n", "qc.initialize([1, -1]/np.sqrt(2), output_qubit)\n", "\n", "# Initialise qubits in state |s>\n", "qc.h(var_qubits)\n", "qc.barrier() # for visual separation\n", "\n", "## First Iteration\n", "# Apply our oracle\n", "sudoku_oracle(qc, clause_list, clause_qubits)\n", "qc.barrier() # for visual separation\n", "# Apply our diffuser\n", "qc.append(diffuser(4), [0,1,2,3])\n", "\n", "## Second Iteration\n", "sudoku_oracle(qc, clause_list, clause_qubits)\n", "qc.barrier() # for visual separation\n", "# Apply our diffuser\n", "qc.append(diffuser(4), [0,1,2,3])\n", "\n", "# Measure the variable qubits\n", "qc.measure(var_qubits, cbits)\n", "\n", "qc.draw(fold=-1)" ] }, { "cell_type": "code", "execution_count": 72, "id": "ae23d7ac", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Simulate and plot results\n", "qasm_simulator = Aer.get_backend('qasm_simulator')\n", "transpiled_qc = transpile(qc, qasm_simulator)\n", "qobj = assemble(transpiled_qc)\n", "result = qasm_sim.run(qobj).result()\n", "plot_histogram(result.get_counts())" ] }, { "cell_type": "markdown", "id": "fad12ec8", "metadata": {}, "source": [ "There are two bit strings with a much higher probability of measurement than any of the others, `0110` and `1001`. These correspond to the assignments:\n", "```\n", "v0 = 0\n", "v1 = 1\n", "v2 = 1\n", "v3 = 0\n", "```\n", "and\n", "```\n", "v0 = 1\n", "v1 = 0\n", "v2 = 0\n", "v3 = 1\n", "```\n", "which are the two solutions to our sudoku! The aim of this section is to show how we can create Grover oracles from real problems. While this specific problem is trivial, the process can be applied (allowing large enough circuits) to any decision problem. To recap, the steps are:\n", "\n", "1. Create a reversible classical circuit that identifies a correct solution\n", "2. Use phase kickback and uncomputation to turn this circuit into an oracle\n", "3. Use Grover's algorithm to solve this oracle" ] }, { "cell_type": "markdown", "id": "741c5ab4", "metadata": {}, "source": [ "## 6. References \n", "\n", "1. L. K. Grover (1996), \"A fast quantum mechanical algorithm for database search\", Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC 1996), [doi:10.1145/237814.237866](http://doi.acm.org/10.1145/237814.237866), [arXiv:quant-ph/9605043](https://arxiv.org/abs/quant-ph/9605043)\n", "2. C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath & C. Monroe (2017), \"Complete 3-Qubit Grover search on a programmable quantum computer\", Nature Communications, Vol 8, Art 1918, [doi:10.1038/s41467-017-01904-7](https://doi.org/10.1038/s41467-017-01904-7), [arXiv:1703.10535 ](https://arxiv.org/abs/1703.10535)\n", "3. I. Chuang & M. Nielsen, \"Quantum Computation and Quantum Information\", Cambridge: Cambridge University Press, 2000." ] }, { "cell_type": "code", "execution_count": 73, "id": "bc7e0d21", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'qiskit-terra': '0.17.4', 'qiskit-aer': '0.8.2', 'qiskit-ignis': '0.6.0', 'qiskit-ibmq-provider': '0.13.1', 'qiskit-aqua': '0.9.1', 'qiskit': '0.26.2', 'qiskit-nature': '0.1.3', 'qiskit-finance': None, 'qiskit-optimization': '0.1.0', 'qiskit-machine-learning': None}" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import qiskit\n", "qiskit.__qiskit_version__" ] }, { "cell_type": "code", "execution_count": null, "id": "d64c620d", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }