From 056b6e5bc95129cad0c5c9ad15dc613b9b6bccc1 Mon Sep 17 00:00:00 2001 From: Jessie Yu Date: Tue, 9 Apr 2024 14:19:44 +0100 Subject: [PATCH] Add quantum-approximate-optimization-algorithm.ipynb Originally created in Qiskit/qiskit-ibm-runtime#888 Co-authored-by: Frank Harkins Co-authored-by: Hwajung Kang Co-authored-by: Ikko Hamamura Co-authored-by: Kevin Tian Co-authored-by: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Co-authored-by: Sanket Panda --- ...m-approximate-optimization-algorithm.ipynb | 680 ++++++++++++++++++ 1 file changed, 680 insertions(+) create mode 100644 tutorials/runtime/quantum-approximate-optimization-algorithm/quantum-approximate-optimization-algorithm.ipynb diff --git a/tutorials/runtime/quantum-approximate-optimization-algorithm/quantum-approximate-optimization-algorithm.ipynb b/tutorials/runtime/quantum-approximate-optimization-algorithm/quantum-approximate-optimization-algorithm.ipynb new file mode 100644 index 00000000000..6d762ddbcd3 --- /dev/null +++ b/tutorials/runtime/quantum-approximate-optimization-algorithm/quantum-approximate-optimization-algorithm.ipynb @@ -0,0 +1,680 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "f028436d", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid iterative method for solving combinatorial optimization problems. In this tutorial, we demonstrate how to implement the QAOA algorithm using Qiskit Runtime for solving a simple max-cut problem.\n", + "\n", + "In a max-cut problem, we want to partition nodes of a graph in a way that maximizes the number of edges between nodes in differing groups. The desired max-cut partition for the following graph is clear: the 0th-node on the left should be separated from the rest of the nodes on the right by a cut. We will find this answer by applying QAOA by using Qiskit Runtime primitives and sessions." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e291b6c0", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4a7d432c", + "metadata": {}, + "outputs": [], + "source": [ + "# General imports\n", + "import numpy as np\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Pre-defined ansatz circuit, operator class and visualization tools\n", + "from qiskit.circuit.library import QAOAAnsatz\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "from qiskit.visualization import plot_distribution\n", + "\n", + "# Qiskit Runtime\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, Session\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", + "from qiskit_ibm_runtime import SamplerV2 as Sampler\n", + "\n", + "# SciPy minimizer routine\n", + "from scipy.optimize import minimize\n", + "\n", + "# rustworkx graph library\n", + "import rustworkx as rx\n", + "from rustworkx.visualization import mpl_draw" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a2c3bce4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "cell_type": "markdown", + "id": "cb6f52f4", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "To demonstrate max-cut, we'll create a graph using the [rustworkx library](https://github.com/Qiskit/rustworkx), and create Pauli Hamiltonian that encodes the cost in a manner such that the minimum expectation value of the operator corresponds to the maximum number of edges between the nodes in two different groups." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1f8247c3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 499, + "width": 660 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "num_nodes = 5\n", + "# The edge syntax is (start, end, weight)\n", + "edges = [(0, 1, 1), (0, 2, 1), (0, 3, 1), (0, 4, 1)]\n", + "\n", + "G = rx.PyGraph()\n", + "G.add_nodes_from(range(num_nodes))\n", + "G.add_edges_from(edges)\n", + "mpl_draw(\n", + " G, pos=rx.bipartite_layout(G, {0}), with_labels=True, node_color=\"#EE5396\", font_color=\"#F4F4F4\"\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "987e72fd", + "metadata": {}, + "source": [ + "For this simple example, the operator is a linear combination of terms with `Z` operators on nodes connected by an edge (recall that the 0th qubit is farthest right): $IIIZZ + IIZIZ + IZIIZ + ZIIIZ$. Once the operator is constructed, the ansatz for the QAOA algorithm can easily be built by using the [`QAOAAnsatz`](https://docs.quantum-computing.ibm.com/api/qiskit/qiskit.circuit.library.QAOAAnsatz#qaoaansatz) circuit from the Qiskit circuit library." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b6dabf56", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": { + "image/png": { + "height": 753, + "width": 1722 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "# Problem to Hamiltonian operator\n", + "hamiltonian = SparsePauliOp.from_list([(\"IIIZZ\", 1), (\"IIZIZ\", 1), (\"IZIIZ\", 1), (\"ZIIIZ\", 1)])\n", + "# QAOA ansatz circuit\n", + "ansatz = QAOAAnsatz(hamiltonian, reps=2)\n", + "\n", + "ansatz.decompose(reps=3).draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "da92068c", + "metadata": {}, + "source": [ + "The previous image illustrates the ansatz in basic gates for clarity. However, it can be expressed in multiple levels of decomposition by changing the `reps` argument or by drawing the circuit without the `decompose` method. For example, the following representation directly shows the QAOA structure with the default `reps` value, which is `reps=1`. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8fbe14ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": { + "image/png": { + "height": 753, + "width": 1722 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz.decompose().draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "id": "abe6e493", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution." + ] + }, + { + "cell_type": "markdown", + "id": "26970208-6305-4338-93dd-e0dcb0aa8d36", + "metadata": {}, + "source": [ + "To reduce the total job execution time, V2 primitives only accept circuits (ansatz) and observables (Hamiltonian) that conforms to the instructions and connectivity supported by the target system (referred to as instruction set architecture (ISA) circuits and observables)." + ] + }, + { + "cell_type": "markdown", + "id": "cfdd9015-81ab-45de-bd0d-f99470d61992", + "metadata": {}, + "source": [ + "### ISA Circuit" + ] + }, + { + "cell_type": "markdown", + "id": "b136c1ed-6a3c-4767-b0de-d2738b43a778", + "metadata": {}, + "source": [ + "We can schedule a series of [`qiskit.transpiler`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend and make it compatible with the instruction set architecture (ISA) of the backend. This can be easily done using a preset pass manager from `qiskit.transpiler` and its `optimization_level` parameter.\n", + "\n", + "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3e08da25", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "\n", + "ansatz_isa = pm.run(ansatz)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1b707e64", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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JZPfT1tlCmUxUl6yKisXvx8o3n4j59/w8pnyrd8y69n+jcvWytNOxDTKZTPz90Zmx20n3p1LA+7SVqyvirCvGxDHfeiLe/2h1qlnYCOsAkOusg0Cusw42WlNmLov9vjE6fvLHcakU8D7tlgdmxO4nPxBPvPRBqjkgl1RVVcdvbp0UA097KJUC3qfNW7g2jvv2kzHi0hdi+cqyVLPkkuUry2LEpS/Ecd9+MpUC3qeNfWtRDDztofjNrZOiqirdxyQ+w3PBRu3Jlz+I3U9+IJUC3qeVV1THT/80Pvb9+uiY/M7SVLOwEdYBINdZB4FcZx1sFOyEBwAAsJXS3v0uyYpV5TH80hfin0/NsiteitoMPKrmgUwmKtcsj9L3p0Z16X/LUUv/87cofX9K9P7Ff6KgRes6Tsm2SnP3u8/zxMsfxu4nP2BXvJRZB4BcZx0Ecp11sPFLe/e7JB8sWBNHf+sJu+JBHZg+a3kM/1k6u999ntsffieeeuXDuMmueFn32Ivvx9kp7X6XpKy8Kn70+9fjgWdm2xUvRZ4L5oY0d7/7POOnLo7Bpz9sV7yUWQeAXGcdBHKddbBxUsIDAADYClVV1fGdq1+Jv/xzetpREv3rhfdj0LCH4om/HB179u2Qdpycs+sVj2/0eKaqKpa/+kC8f/P3omLZ/IiIWPvuGzFv1GWxw1nX1mVEttFbM5bGkec9Hh8tLkk7ykat2xXvlYkL48bLDoiCAm+y1zXrAJDrrINArrMONm5rSyrjlAuficfG1N8d5255YEaMeXNBPHXjMdF9Ox/SBLXtqVc+jBO/93SsLa1MO8pGffjJrni//N6Q+PGZe6Qdp1H61V8nxiV/GJd2jERj31oUQ05/OB78/eFx5P7d046TczwXbPw++GhNHHne4zHtveVpR9modbvivfjGgrh/5OHRorlLReuadQDIddZBINdZBxsnV18BAABsoYqK6vjGT56v1wW8dRYuLY1Dz/x3vPTmgrSj8Im8goJod8Cp0fv//Sfym/33ArhFj98QVSWrP+ee1CevTlwYh5zxr3pbwPu0vz44I07/4XNRVl6VdhQ+YR0Acp11EMh11sGGb8Wq8jjqvMfrdQFvnemzVsSBwx+Nd+asSDsKNCr3PzUrjvv2k/W2gPdpl/xhXPzo2tcik8mkHaXRyGQy8ePfv16vC3jrrC2tjOO/81Tc9+SstKPwCc8FG4eZc1fGgcMfrbcFvE97/KUP4sjzHo/lK8vSjsInrANArrMOArnOOtiw+XgTAACALVBZWR3DfvhsPPjMnLSjbLYVq8pj6LmPxRM3HB0HDd4u7Th8otn2vaPDYcNj0b//HBERmYqyWD3lhSgecmzKydiUVyYuiKHnPB5rSur/RVbr3PfU7CgteyYeuPaIKCrymUz1hXUgdw2ff1/aEWq4vespaUcgR1kHyVUeB1jHOtgwrVxdHkec81iMm7I47Sibbc681XHQ8H/Fi7cfF7vuVJx2HGjw7n3ivfjqj/4T1dUNp9T2m9veitKyqvj9j/aNvLy8tOM0aJlMJr7/m7Hxh7umpB1ls1VUVsewHz4Xo6ozMezoXdKOwyc8F2y4Zs5dGQcNf7RBfEjfOi+9uSCOOOfxeObmY6K4dZO04/AJ60Du8toQfMw6SK7yOMA61sGGyVVXAAAAm6m6OhNnXv5igyrgrVNSWhXHf/fJeGNqw7lALBe02u3gGrfLFvg04vpu0oylcez5TzaoAt46j77wfnzzZ89HVVV12lH4FOtA7skr8JIsfJp1kFzjcYDPsg42LCWllfHl/3uqQRXw1lmwpCSOOOex+OCjNWlHgQbtsRffj69f8nyDKuCt88dRU+OK699MO0aDd+UNbzaoAt461dWZ+PpP/hP/fvH9tKPwKZ4LNjwffLQmjjjnsQZVwFtn/NTF8eX/eypKGsAurrnEOpB7vDYENVkHyTUeB/gs62DDYyc8yKIPP/wwXn/99Xj99ddj3LhxMW7cuFi6dGmNc5577rk49NBDG/ScAAC54ocjX4s7R89MO8ZWW7m6Io761hPx2l1fjp27t047DhFR2KpdjdtVa5anE4TNMnf+6jjy3Mdj+arytKNstbsfey86tWsWf/jxfmlH4RPWgdzTZZ9+sWrOgrh/32+nHQXqBesgucbjAJ9lHWw4MplMnP7D5+L5cR+lHWWrzZ2/Joae+1i8+vcv2wEFtsJrby2Kr1z4TFRUNtwPOPr5jW9Glw7N4vzT+6cdpUG6/h9T48q/NNwiY2VlJr7yg2fiP389Nvb5Que04xCeCzY0K1eXx5HnPR5z5q1OO8pWe2H8RzHs4ufioT8cEfn5dkatD6wDucdrQ1CTdZBc43GAz7IONjxKeFDLfv7zn8e4cePi9ddfj48+qps34dKYEwAg1zzz6ry45s7JWRn7pssPjN171fwP9eSZy+KcK8fU+lyLl5XGiMteiGdvOdaba/VA5colNW4XtGiTUhI2JZP5eCfMBUuy8+m2dbkO/HHU1Dj2oB3iqAO61/rYbDnrQO7Z4ai94v2nxqUdA+oN6yC5xuMAn2UdbDhu/Of0eOQ/c7Mydl3+n3D6rBVx8cjX4qbLD6z1saExKymtjG/85PkoKa3Kyvh1uQ784HevxRf37hb9dmlb62M3ZtNnLY8f/O61rIxdl3/+pWVV8Y2fPh8T7j0pWjR32VjaPBdsWC4e+VpMe295Vsauy3Vg9PNz48Z/To9vDetX62Oz5awDucdrQ1CTdZBc43GAz7IONjxeTYFadvnll+fEnAAAuWTVmvI484oXszb+7r3axX571N2nzj4/7qO44d5p8W2fdpy61VNfqHG7+U4DUkrCptx8/9vx9KvzsjZ+Xa8DZ10xJiY/cLKdD+oB60Du2WHo4HjlhzelHQPqDesgucbjAJ9lHWwYZn+4Ki4e+XrWxq/r/xPefP/bccrQHnHk/j6cBTbXpdeNjxlzVmRt/LpcB8rKq2LEpS/ES3ceHwUF+XUyZ0NXVVUdIy59IcrKs1PCrOvHgXfmrIxL/zw+rrlonzqbk43zXLDheOqVD+Om+97O2vh1vQ5cPPK1OObA7tFj+9Z1NicbZx3IPV4bgpqsg+QajwN8lnWw4fFqGgAAwCb86NrXY8681WnHqFU/HPl6vPfByrRj5LTSD96OJc/esf52Ubuu0aq/T6Gvj+bMWxUXZulTrtPywYI1cdE1Y9OOkfOsA7mnuHf3aNa+TXz06tS0o0C9YB0k13gc4LOsgw1DJpOJs64YE6vXVqQdpVaddcWYWLm6PO0Y0CC8PGFBjPzb5LRj1Kqxby2KkXc2rp8pm67925R4ddKitGPUqmv/NjleenNB2jFymueCDcfK1eVxVhY/rDMNa0oq48zLX4zq6kzaUXKadSD3eG0IarIOkms8DvBZ1sGGSQkPsqhJkyYxaNCgOOecc+Lmm2+O0aNHN8o5AQAas2fHzosb7p2edoxat7a0Ms64zJtrachUVcWyl+6LGT/7YlSXrV1/vPuI30VegQ3r65vGerFlRMQtD8yIJ176IO0YOck6kLt2PHJIfPjchMhUZueT86GhsA6SqzwOsI51sGG58Z/T45mx2dsZPS3vf7QmLrqmcX3gDGRDSWlljLj0xcg0wpdRL/3zGzHtveVpx6j3ps9aHj+7bnzaMWpdJhMx4rIXYm1JZdpRco7ngg3PxSNfi7nz16Qdo9Y9+9r8uPGfje890IbAOpC7vDYEH7MOkqs8DrCOdbBh8ycEtWzEiBExZMiQGDJkSOyxxx7RtGnT9d+bPXt2o5kTACAXrFlbEWdc3rg+2fLTnh/3Ufzl3mlx/un9047SKL1zxdE1D2QyUbV2RZS8PzWqS1b993h+QWz/v7+K9od8rW4Dslluuf/tePrVxnex5TpnXTEmpj50crRu2STtKI2SdYDP6j50SEy//fG0Y0CdsQ5CTR4Hco91sOGbO391XDzy9bRjZM3N978dpx21cxyx7/ZpR4F667I/vxEz5qxIO0ZWlJVXxYhLX4iX//alyM/PSztOvVRdnYkRl74QZeWN8wLJd+asjMv+PD5+d9E+aUdplDwXbByeeXVe3HTf22nHyJqLR74Wxx7UPXbq1jrtKI2SdYDP8toQucY6CDV5HMg91sHGSQkPatmtt96aE3MCAOSCv//r3Zgzb3XaMbLql3+dFOec0jcKC22UXttWvvnEJs9pd9Dp0fWUn0TzHgPqIBFbqqqqOq6+ZWLaMbLqgwVr4o5HZsZ3vqqMmw3WAT6taYc20fELu8SHz7yRdhSoM9ZB+C+PA7nJOtjw/eGuKY1yZ/RP+8VNE5TwUjR/0dp4ecKCmDt/w9cgP1y4Np565cPYb4/O0apFUQrpWLayLK77x9S0Y2TV2LcWxTNj58XQ/awDG/Psa/Pi1UmL0o6RVX++Z1r85Ow9o31x002fzBbxXLBx+MXNE9KOkFVrSirjD3dNiZEX75t2lEbJOsCneW2IXGQdhP/yOJCbrIONkxIeAADARmQymbj+nmlpx8i6DxasiUdfmBsnHtYj7Sg5afW0l6Jy5eJNnjf7D8NjybN3bPH4TTrvFANunr0VyYiIePylD2J2Iy/iRkRcf8+0+Pbp/SIvzyeep8E6kDt2OGJwLBz3dpSvXJt2FKhXrIPkCo8DJLEO1l9rSyrjtodmpB0j654f91FMmbksduvVLu0oOaO6OhNPv/phXH/PtBj9/PtRXZ3Z6Hnvf7Qm/j979x0eRbX/cfyzu9kkpJICJPQOoUNCL9IROypgF8QCqNfee8VrwZ9eRQSlXbviVeygAko1oPTeew+k193fH8hqTELa7s5m5/16njxPZvbMOd+F7Dmzc+Y7Z/At3ys81K7rL2qmcSNaqlUT/p+8acaXW5Wd458roP3dpI83koRXAjPMEWTnFGjGl1t093Xc7GcEzgV924btKVqQfNDoMDxu+hdb9extSQqpxq2kRqAfMA+uDQHFox+EWTAOoCT0g1UP35y8aMuWLVq1apUOHjyojIwMxcTEqHXr1urWrZsCAvivKC+n0ymn0ymrlRU7AAAA4H5LVh3Rmi0njA7DKyZ9vJEkPA9I/LLwDVT56SnKPbpHKb9+pKPfv6WCjFPKO7ZXW585T80e/07hbfuWWJctJFIB1WuVqV1nfq4K0lMkSRZ7cIXjhzluspGkjTtOauGKQ+rbOd7oUPwO/QD+rt6QJO2dt9LoMACvoh8E/sI4YE70g1Xbxz/sUEpqrtFheMVbn2zUGw/3MDoMU9i5L01jnvhV88txQ39aRp7e+HCD3vxog+64urWeu52b5L3B4XDqrU/McW1ozoI92nsoXfXiwowOxafsO5ShL+fvMToMr3jrk02685o2slp5SJc7cS5Y9b31ySajQ/CKk2m5+uj7HbphWHOjQ/E79AP4O64NwYzoB4G/MA6YE/2gf+LKrIfl5ubqjTfe0LvvvqsNGzYUW6ZGjRq67777dPfdd8tms2nZsmXq3r276/XmzZtr8+bN3grZbd5//33dcsstru23335bV199tVvqdjqdGjNmjCTpnXfeIREPAAAAbmeW5BtJmrf0gLbsOqXmDSONDsWvBYRFKSAsSiGN2itmwGhtfqiX8k8dlTM3WzsnXq1Wr61WQERsscfWu+k11bvptVLbcDoc2vbshUpd+a1ktan+zW+4+22Yxo59qfpu0T6jw/CaSR9vJAnPC+gHzMsaGKDafdppxVOzSi3b9Ir+6vXqeNf2b0/M0IYpX5e5rcimtXXh3JcUUC1IkrR33kr9dN2E8gcNeAD9IMyKcQBn0A9WLWa6NjTrq22acEeSwkMDjQ7Fr82as1Xjn1uijKz8Ch3vdEr/9956ff3LXn36cn91aBnj5gjxdz8tP6Ctu1ONDsMrHA6npny2Wc/clmh0KD5lyuxNJa5U6W+27UnVj8v2a3CPukaH4tc4F6xa0jPzNHPOVqPD8Jo3P9qg0Zc0k8VCMq4n0Q+YF9eGgNPoB2FWjAM4g37QP5C55EELFy5UQkKC7rnnnhIT8CTp6NGjuv/++3XxxRcrLy9Pq1evLvR6YmLVvNCZl5enjIwM109eXp5b6j2TgDd9+nRNnz5dN954oxwOh1vqBgAAACTpyPEsfTp3p9FheJVZnursK4LrNFejuz9wbeedOKB9Mx+sdL0H3nvk9EUUSXVHv6yIDgMrXadZTf5kk5zmuMdGkvS/n3fpwJEMo8MwFfoBc4nv1Vbp+44pbffhUstu++jnQk9B7PTglYpoUrtM7VisVvV67XbXpEr2iTQtufetigUNeBj9IMyEcQDFoR/0bb+tPaoV648ZHYbXpGXk6f1vthsdhl/7v/+u0/WP/lLhBLy/27YnVefc8I2WrT7ihshQkjc/KvkeD380dfZm5eYVGB2Gz8jNK9CUz6rew7Ir482PmCPwJs4Ffd/732xXWoZ77nWrCn7feFy/rT1qdBimQj9gLlwbAoqiH4SZMA6gOPSDVRdJeB4ya9YsDRo0SDt27CjymtVqVVRUlGw2W6H933zzjZ555hm/ScLzlHfffVfTp093bZOIBwAAAHeb9dU25eWb6/xy+pdblZdnrvdstIgOAxXV50rX9vGfpytr19oK13fi1491aPYLkqSY/ter1kV3VjZE0yoocGjaF1uMDsOr8vOdmvGleZ7q6yvoB8yj/pDO2js3uczll9z7lnJS0iRJAdWC1Pu122Sxln4pt+2/hqlGp2au7eWPvKOsIyfLHS/gLfSDMAvGAZSEftB3vfO5uRIvJJku2cSbZny5RXe9tNytdaam52no+B+0ccdJt9aL0w4dy9RXC/caHYZXHT6epa8W7DE6DJ/xzS97dfh4ltFheNXXv+zVwaOZRodhKpwL+raps813bmTG92w0+gHz4NoQUDz6QZgF4wBKQj9YNZGE5wEffPCBRo0aVWjlt+joaD3wwANas2aNsrOzdeLECWVlZWn+/PkaMGCAq9zEiRO1cOHCQvWRhFfY6NGjddVVVxXaRyIeAAAA3GnRH4eMDsHrTqXlasOOFKPDMJ061zwnS4D99IbDof3vP1qhejJ3rNLu/9wgSQpt3lX1x7/trhBNafOuUzp+MsfoMLxu8arSn7oG96MfMIe6AxO194cVZS6fdeSklj86zbVdI7G52oy/6KzHRLVqoPZ3Xe7a3vX1Uu38YnH5gwW8jH4QZsA4gLOhH/RNi/4w3/ejVZuPKz3TPKu9eMv2vam69bmlHqn7ZFqurntkofJN9jAxb1i25ogcDqfRYXgd14b+YsZxwOFwatkaVtj0Ns4FfVNGZp7+2HTc6DC8jnHAGPQD5sC1IaBk9IMwA8YBnA39YNVDEp6brVixQqNHj5bT+dcF2aFDh2r9+vV64YUX1LZtW9ntpz8kdrtdffv21dy5czVq1ChJUkZGhjZs2OA61mKxqGPHjl59D77OZrNp1qxZxSbijRkzhkQ8AAAAVNrKDeabWJPM+76NFFSrkWL6j3Jtn/ptjjK2lv3CmyTlpx7T9gmXyJGTKXtUvBo/+Lms9iA3R2ouKzccMzoEQ6zccLzQ9Qx4B/2A/4tp11hWu01Hfy/fapM7Pv9Vu7/9a7WMDveOVPUW9Yota7UHqPfrt8sWePq6Y9bRk1r6wJSKBw14Ef0g/B3jAEpDP+h70jPztGnnSaPD8DqnU1plwpvNPcnhcGrME78qMzvfY22sWH9ML05f47H6zcqs10nN+r6LY97rg+Z830biXNA3rdp8wpTJ2Jt3nVJaRq7RYZgO/YD/49oQcHb0g/B3jAMoDf1g1UMSnhtlZmbqyiuvVG7uX19GL7roIs2ZM0dxcXElHme1WjVp0iTVqVOnyGtNmzZVZGSkR+KtykpKxJsxYwaJeAAAAKiUI8eztO9whtFhGIIJdmPEj3hUloBA1/aBDx8v87HOgnxt//flyj2yWxZ7kJo89D8FxtT2RJimYtYbjg4fz9KBI5lGh2FK9AP+rd7gJO378ffTdzWX09L731b28VOSJFuQXb1ev00WW9FLuh3uHaHo1g0LHZdzIq3CMQPeRj8If8Y4gLKgH/QtqzYdr8hH1i9wbci9vlu0VwtXHPJ4O89NXa1Tadww705m/Sz8vvG4KZNO/snhcOr3jea8PmjW66JG41zQ95h1HDj9UIYTRodhSvQD/o1rQ0Dp6AfhzxgHUBb0g1ULSXhuNGHCBG3bts213aJFC3388ccKCAgo9dhq1arpuuuuK7I/MTHRrTH6k7Ml4t1www0k4gEAAKBCzDqxJpn7vRspsEZ9xQy8wbWduvI7pW9aWqZj9069Q+nrFkqS6o+brNAWXT0So9mY+bNg5vduJPoB/1ZvcGftnZtcoWOzj6dq6QNTXdux7Zqo3R2XFSoT27GZ2oy/2LW9/bOF2vN9xdoDjEI/CH/GOICyoB/0LWb+XkTyhXtN+nijV9rJzM7XrK/K9zR1lMzpdGrFenP2A+mZedqy+5TRYRhu6+5TSsvIMzoMQ6zYcExOs2aiG4hzQd9j7vNB8753I9EP+DeuDQGlox+EP2McQFnQD1YtJOG5yZEjR/TKK68U2jdp0iQFBweXuY4ePXoU2ZeUlFTp2HzF8uXL9dFHH7n159NPP9V5552nBg0aFGpr5syZJOIBAACgQlZuNO/k0uotJ5Sfzzm0EeKHPyKLPci1feD9x0o95tjcd3T0u0mSpJoX3qHYAaM8FZ6pFBQ49Mcm8950yA2XxqEfqFqCYyPV+807FBB69mt/IfHRimxaWwcWrqlwW7u/WaadXyx2bbe741JFt2kkSbIFB6r367fJGmCTJGUcOK7lj7xb4bYAI9EPoiphHIAn0A/6DjN/LzLzdTF323MwXd8t2ue19t7+dJPX2vJ3+w5n6GhKttFhGIbkC3OPA8dSsrX3UIbRYZgS54K+xcx9IeeDxqEfqFq4NgS4H/0gqhLGAXgC/WDVUfoSbSiTN954Q1lZWa7tgQMHqn///uWqIz4+vsi+sqyEt3HjRr3zzjv64YcftG/fPuXn56tOnTrq16+fxowZo86dO5crDk+ZPHmyJk+e7LX2Zs6cqfj4eE2YMMFrbQIAAKDq+2PjCaNDMEx2ToE27TypNs2ijQ7FdAJj6yp28E06+s0bkqS0NT8pbd1Chbc5p9jy6RuXaM/bt0qSwtsNUN3RrxRbDuW3bU+qMrLyjQ7DMGZOQDQa/UDVUbNLS50z+S6Fxsdoz7fLtfubZSWWrTe4sw4uWqf8rJxKtbns4amK69FK1WpGyRZoV6/XbtPX5z6gxIevUmTTOq5yS+59S7mpmZVqCzAK/SCqCsYBeAr9oO8w8/eiTTtPKSs7X9WCuY2gshb/cVjeXExq/faTOn4yWzHVy/6QYBTvj43m7QOk0+//6vObGh2Gocw8Dkin33/9+DCjwzAdzgV9R3ZOvjbuNO+qoGYfB41EP1B1cG0I8Az6QVQVjAPwFPrBqoOr527gdDo1Y8aMQvvGjh1b7noCAgr/d1gsFnXs2PGsx7z88st65JFHlJubW2j/li1btGXLFk2dOlV33323XnzxRVkslnLHVNVt3brV6BBQiqFDh8putxsdBgAAgMuGrPMk1S7XMVOe6KU2TaMq3GZxx7ZpGqUl/72wwnVK0rptKbr5qUXlOmbk1WMUYTtUqXa9zVmtunTnd0aHUWnxlz+sY/PekTP39JO2D7z/mFpM+KVIudzj+7X935fJmZ+rwLjGanz/J7LYbN4Ot0yGDh0qS9ZJo8Mol7SCmpIuKtcxle0DJN/pBxb8+pu6d3+8Um36mqrUR1TFfsDXP+fBBVZdr6IPvqqopiP6qu7gJDkLTq8cW//czmedWKk/JEm7v/ut0u3mpKRryX1va8DMByVJ0a0aqN8796ruwE6uMpvfm6f981dVuq3yGnreecq2sZJuaapSX2SkqtgPGsnX+2Bf4c6xgHGgKF8fB6pa/1sV+0F/7Is2Z14pKbTM5f3pO6HD4VSvcwYr0JpVemGc1e6crpLaerXNXoOvUXXbfq+26Y+O5DWTVPzNTSXx1X6gIteHZ30wW4tn31nhNv3B9pzeklqU6xh/miO4+77H9IK9at1rU9XO+UpSFc8FS1MVzxVzndXkcFxdrmN8dRyQyt8PbNmxX927d69Um76mKvURVbUf8PXPOteGPMvXrw35iqrUFxmpqvaDRvH1/tdXMA54nq+PBVWpD66K/aC3+qK8vLwi++666y699957Hm/7n0jCc4Ply5dr7969ru2IiAhdfPHF5a7n+PHCT5Jp2rSpIiMjSyz/6quv6r777nNtd+nSRf3795fdbtfixYv1888/y+Fw6OWXX5bD4dArr5gvu7VBgwZGh4BSrFy50ugQAAAACmvSTwop3yFtmkape/uabg0jPNTu9jrLYsPGrVL6eq+3WxkBEbFqb3QQkmpf+aRqX/lkhY+3R8er06dnv8nNkZut7ROGKT/lkKzBYWr68JcKCPfdlQtXrlyh/NRjRodRPqEtpcblO8QTfYBkTD+Qlp6tZatLvkhcFXmzjzBjP+Drn/NwS6Cur1W5G1X+bscXi7TtkwWq3ryuLln4f6o7oJMsNqtrouXvAkKCVatbKy26a5Jb2t47d4W2fbJATUf0lSTVG5zkei1tz2ElPznTLe2U18oVK5TmzC29oMn5yvmKp5mxHzSSr/fBvsKdYwHjQFG+Pg54u/81Yz/ol31RwpXlmkX3p++EkvT7H2ukPFZAqbSG3aRw7za5aUeqdNy/vtMbIjpIqlN6sb/zp37g6LGTOrrX5H9H9dpI1ct3iD/NEezYuVc7TlStvwFf+c5txnPB0lTJc0V7tNSyfEl4/jQO5OVLy5ZVrT6gNMwReJ6vf9a5NuRZvn5tyFf4yvmKp5m1HzSKr/e/voJxwPN8fSzgfNCzjOyLNm3aZEi7JOG5wfz58wtt9+jRo8iqdmVx5MiRQtuJiYkllt20aVOhBLw333xT48ePL1Tmiy++0IgRI5SXl6eJEyfqwgsvVN++fcsdl7uMHj1aPXr0cHu9TqdTzz//vHbt2lVo/+WXX65///vfbm8PAAAAfs5i8lV6rSZ//z5u95s3K3NrsmSxqOGds1StQRujQ/I/Zv8MmP39VwH0A8Zy5OZLkk5u2afja3cqpm0j1eqaoENLiiaw1+nXXic371XW4RS3tf/bY9MU36utQmvHuPY5HQ4tvnOS8jOy3dYO4MvoB2EkxgH4AvpBL7CafArdGmh0BP7BGuT9Nm0GtOmPzH592OzvX+LfgOuDPo1zQS8wex9g4VzQ19EPGItrQ4Dx6AdhJMYB+AL6QeOZfAbBPf65kldFE82Sk5MLbZ8tCe/xxx9XQUGBJGnMmDFFEvAk6ZJLLtFjjz2mxx9/XJL00EMPaenSpRWKzR369OmjUaNGubVOp9OpW265pUgC3vDhw/XBBx9UKBkSAAAAZuc0OgBjOU3+/n3Y4S8n6sSC/0qS4q94QlHdhxkckZ8y/WfA7O/ft9EP+Ja9PyQrpm0j1T+3c7ETK/UGd9aeuSvc2mZuWpYyDx4vNLFyaOkGHVpatVaxBSqKfhC+hHEARqAfhFc4iz65GxVhwPdr01/TcBez/zua/f1Lpv83oC/xWZwLwjs4F/Rl9AO+hWtDgPfRD8KXMA7ACPSDvsFqdAD+YPv27YW269atW6F6Fi1aVGi7pCS81NRUzZkzR5JksVj08MMPl1jnHXfcobCwMEmnl4rftm1bhWLzRWcS8KZOnVpoPwl4AAAAqBRHntERGMtp8vfvo1JX/ah9M+6XJFXvNkzxIx83OCI/ZvbPgNn7QB9GP+B79vxw+oFa9YZ0LvqixaK6Azpqn5snVtqMu0g1EpsX2hfXvZXievJ0O/g/+kH4GsYBeBv9oBc5co2OwFhm/17sLgWZ5mjTH5n92ojZ37/Ev4HT5OOgj+Jc0IvM/hkwex/ow+gHfA/XhgDvoh+Er2EcgLfRD/oOspTc4Pjx44W2Y2Njy13Hpk2b9Ntvv7m2LRaLOnXqVGzZH374QTk5OZKkjh07qnHjxiXWGxERoUGDBul///ufJOnLL7/UPffcU+74fE1JCXgjRozQ+++/TwJeFZKYmCi73W50GAAAAC4bsqoptZwPeVy3LaVSbbZpGqXw0MLnRGkZeZWutyLHt0popghbRKXa9TZnterKNzoID9sz5TbJcXo19LT1C7VmVHyZj014OVmBNep5KrSzSkxMkiXrpCFtV1RaQQ2tzy7fMZX9rEq+0w+EhwWrdbdulWrT1/hLH+Gr/YCvf86DC6zSXs/UfWLdTqXvP6rw+rUUldBAKRt3u16r2bmF8rNydWL9Lre1V715XXW8b2SR/RarVT0njtOX/e5RfmY5OzA3SExKUraNJ2SXxl/6IiP5aj9oJF/vg32Fp8YCxoHTfH0c8Kf+11f7QX/si37PtCi3HIsA+dN3QklK7NROdov3+xN/szfXof1evoe9dZNwhTf3r+/0RjiaV1/by5l/4av9QEWOrVEjSk3qmvvvaEdOlI6U8wTCn+YImjRqoBpVrC/xp3O+kvjquWBpquK5Yp4zWCvLmdfuq+OAVP7YAu0WdWKOwCf5cj/g6591rg15lq9fG/IV/tIXGcmX+0Gj+Hr/6ysYBzzP18cCf+mDfbUf9FZflJeXp5UrVxba17JlS4+3WxwyldwgN7fwFdi8vPJfTX/jjTcKbTdt2lSRkZHFlv3jjz9cv/fs2bPUunv16uVKwvv7sVUVCXj+5bvvvlONGjWMDgMAAMDlmocW6P1vtpde8G9ufmpR6YXOYsl/L1T39jUL7Vu3LUU9rv2qUvVWxJzZs9SkXtVKwkvJkQb9YHQUnuXM++tCWUHaifId++cFGCN89913igoyrPkK2XMwXQ2GfFyuYyrbB0i+0w8MHdRDH7/0qFfb9DR/6SN8tR/w9c959rFT+qjtGI/Vv/eHFUq4Yajqndu50MRKvcFJ2uvGJxtabFb1ev122YIDJUlZR09q+SPv6pzJd8litSq8fi0lPX6tlj04tZSa3O+7b79VcGzx1zHxF3/pi4zkq/2gkXy9D/YVnhwLGAd8fxzwp/7XV/tBf+yLulz1pZLXHStzeX/6ThgUaNPSX3+S3W71arv+6Mv5u3XJHT96rT2r1aLfFs5WSDXmyitr3tL9GnzL9+U6xp/6gVtuGKlnbnvRq236msffXKln3l5VrmP8aY5g0uvPa3CPul5vtzL86ZyvJL56LliaqniumJfnUHj3WcrJLfu/mz+NA+1aNdDSD5d6tU1P85c+wpf7AV//rHNtyLN8/dqQr/CXvshIvtwPGsXX+19fwTjgeb4+FvhLH+yr/aC3+qKjR4+qZs3C35leffVVzzdcDK7AukFkZKQOHz7s2t6/f3+5jl+zZo2mTJlSaF9iYmKJ5Tds2OD6vWnTpqXW36RJE9fv69evL1dsvujdd98lAQ8AAAAek9gqttxJeP6ienigGtcNNzoMFKPt1F1Gh2Aa9eJCFRsVrGMp5nzqf2JCrNEhoAT0A75p79zTEyv1h3TWmlc/c+2vP6Szlj86zW3ttPvXpYpt/9c1vqUPTtWeb5erVrdWSrhhqCSpxbWDtPvrZTq4aK3b2gV8Cf0gfBHjALyJftB7EhNiy5WE50/aNY8iAc9N+iTGKTjIpuwc79zo17tTLRLw3KRTQozRIRgqsZW53790eo7AzMz+/n0V54LeY7db1b55tH5bd9ToUAxBH+C76Ad8E9eGAO+hH4QvYhyAN9EP+g6uoLtBXFxcoe0lS5aU+dicnByNGTOmyOp5Z0vCO3TokOv3OnXqlNrG38v8PVmwqho9erRGjBjh2h45cqQ++OADEvAAAADgFokmvsmiU0KMLBaL0WEAhrJYLKbuB5hgB8rn0JL1yk3NUGz7JgqJj5YkhTeKU7VaUTq0xD0Pw4pu3VDt7rzMtb3981+159vlkqSVz76n1F2nrxVarFb1nDhOAaHBbmkXAFA6xgHAP5n5exEPZnGfqIggXTm0sdfaGz8ywWtt+buY6sFqWDvM6DAMY+Y+8Awz94UNaocppjrnk4CZE5LNPD8CVATXhgDA3BgHAHMiCc8NunTpUmh7zpw5Onq09KfhFBQUaOTIkVqxouhyo2dLwktPT3f9HhoaWmo7ISEhrt/T0tJKLe/rbDabPvjgA40YMUIjR47U+++/L5vNZnRYAAAA8BMdE2Jk1jw0brAATjPzZ6GTiW8uACrCkZev/fNXSZLqDe4sSao/uLMOLFgtR15+peu32gPU67XbZAu0S5IyD6do+SPvul7Pz8rR4rsnyelwSJLC6tVU58evq3S7AICyYRwA/JOpb7o28fdhT/BWYlx8jRBd0r+BV9oyi6TW5vws1IwOVt1apd+D4u/q1ApRrZhqRodhiCTGAUCSuc+JzPzegYrg2hAAmBvjAGBOJOG5wXnnnVdoOzMzs9jV7f7u4MGDOv/88/Xll18Wec1isahTp04lHpuVleX6PTAwsNT4goP/ymj++7GeNmrUKDmdTtfPqFGj3Fb3mUQ8EvAAAADgbuGhgWreINLoMAzBxBpwmlk/C43rhisqIsjoMIAqZ88PyZKk+ueenlipNyRJe+Ymu6XuDveOUHTrhq7tJfdNVu7J9EJlDi/doI3Tvndtt7husOJ7t3VL+wCA0jEOAP6nddMoBdrNOY1u5gRET0hqXUM3DGvu8XZee6CbAu3MmbuTWa8NJbaKlcWsT6j7G4vFYtr+0Kx/+8A/mfWzEGi3qk2zKKPDAKocrg0BgLkxDgDmE2B0AP6gX79+atu2rdauXeva99VXX+mcc87RU089pb59+8putysvL09btmzRe++9pylTpujEiROSpKSkpEKr4TVt2lSRkSXf9Fut2l9P3MrNzS01vuzs7GKPrep8Nflu8+bNmj9/frGvHT9+vMi+OXPmaNOmTcWWb9Gihfr16+eTbQIAAPizxFax2rzrlNFheJ1ZJxWBf+ImGwDlsf+n3+XIy1dc99YKq1dTNTo20883vFTpemM7NFWb8Re7trd9PF/75q0stuzK599T3QEdFdEoXpLUc+J4fdH3LuVnZBdbHgDgPowDgP8JtNvUrnm0Vqw/ZnQoXhVot6p1U266drdX7umiHxbv0/4jmR6p//JBDTV8cCOP1G1mZr1GYtb3XZzEVrH69td9RofhdWa9Lgr8U+smUQoKtCknt8DoULyqbbNoEvuBCuDaEACYG+MAYD4k4bnJ1KlT1atXL+Xn/7V06NKlSzV48GDZbDZFRETo1KlTcvy53OcZ11xzjRITEwsl4SUmJp61rbCwMNfvGRkZpcaWmfnXBf3w8PBSy6Nyli5dqnHjxpW5/Kuvvlria9dff32ZEuKMaBMAAMCfDehaWx98u93oMLyqQe0wNanH9wVAkurHh6lp/Qht25NqdCheNaBrbaNDAKqk3NRMHVq2UbV7t1XX58fo6B9bizyBsLxsQXb1ev02WQNO3/SSsf+Yfnt8eonlC7JyteiuSRr6+VOyWK0Kq1tDnZ+4Tkvvn1KpOAAApWMcAPzTgK61TZeE1ycxjpuuPaB6RJA+ebm/Bt78nbKy3Xsjf0Lj6pr8WE+31onTurWroZDgAGVm55de2I9wbegvA7rW1jNvrzI6DK8KCQ5Qt3Y1jQ4D8Al2u1V9Emtp3tIDRofiVQO6xhsdAlAlcW0IAMyNcQAwH6vRAfiLrl27aubMmbLb7UVeKygoUEpKSqEEvMDAQD3//POaNWuWVq1aVah8aUl4cXFxrt/3799famx/L1OrVq1SywMAAABmd8W5jRUZHmh0GF41dnhLWSwWo8MAfILFYtHY4S2NDsOrwkPtuuq8xkaHAVRZe+cmS5LqDUzU3h9WlFK6dJ0eukrVm9V1bS+5b7JyU8++csaR5Ru18d1vXdstrh2s+D7tKh0LAKB0jAOA/7n58hYy22WScSMSjA7Bb/XoUEtfvT5YodXc94zkhMbVNe/tcxVTPdhtdeIv4aGBuuaCJkaH4VUtG0XqnKS40guaRJ/EOCU0rm50GF519flNFBFmrnkR4GzMdm5ksUg3X26ueRHAnbg2BADmxjgAmAtJeG501VVXadGiRerTp0+JZUJCQjR69GitX79eDz30kCwWi1auLLw0aGlJeK1atXL9vm3btlLj2r79rxU8WrduXWp5AAAAwOxCqgVo9MXNjA7DawLtVt1wSXOjwwB8yqiLmyk4yDwrAFx3YVOFh3KTDVBRe79P/uv3eZWbWKnZNUEJN57n2t783jztn7+qTMeunPCBTm3/6wndPV8ZJ3tYtUrFAwAoHeMA4H8a143Q0F51Sy/oJ+rUDNFFfesbHYZfG9Cttn6Zfr5bknqGDWigX2ecrzq1QisfGEpktuSL8SMTeEjb31gsFo0fab6/AQB/ufCc+qprorH23J511aRehNFhAFUW14YAwNwYBwBzIQnPzbp06aKFCxdq9+7deu+99/TSSy/pueee01tvvaUFCxboxIkTmjZtmpo2bSpJyszM1MaNG13HWywWderU6axtdOzY0fX7kiVLSo1p0aJFxR4Lzxg1apScTqdbfmbMmOGzbQIAAPg7M91kMXxwI9WM4aIL8Hcx1YN1xbnmWRmOm2yAyknfd1QnNuzWqW37lbrjYIXrCagWpF6vjpfVdjoJOH3vESU/ObPMxxdk5WrxXW/KUVAgSQqrW0NJT1xX4XgAAGXDOAD4JzN9T7pleEsFBHDrgKd1ahWr3z++WA+OaadAe/n/vWtGB+vDf/fV7IkDWAHPCzq0jFGPDjWNDsMrQoIDdN2F5nkoXVlde0FTt65g6cu6t6+pDi1jjA4D8CkBAVbdMryF0WF4jZnOfQFP4NoQAJgb4wBgLlxJ95D69evr6quv1r333quHH35YY8eO1TnnnKOgoKBC5VavXq2CPzs6SWrSpIkiIyPPWveQIUMUGHj66fR//PGHdu7cWWLZtLQ0/fjjj67tiy66qCJvBwAAADCd5g0jNah7baPD8Aom1oDimeWz0bdzvFo1iTI6DKDK2/7pQm37ZEGl6kh87FpFNIqXJDkdDi2++y3lZ2SXq44jyZu18Z1vXdstrhmk2ue0r1RcAIDSMQ4A/ufcnnXVsHaY0WF4XECARTdeap4bzI0WHBSgCXd01t65V2jCHUll+hvr0aGm3ptwjvbMvUJXDG3CamVeZJZrQ9dc0ESR4YFGh+FzIsMDdc0FTY0OwyvM8rcOlNeNl7ZQQID/j7sNaoeZahVowFO4NgQA5sY4AJiHOR7Z5MNWrlxZaDsxMbHUYyIiInThhRdq9uzZcjgcmjBhgqZMmVJs2ddff11paWmSpK5du6pZM55eBgAAAJTV+JEJmrf0gNFheFT7FtHq3t4cT3Q2gwMfPqmDHz1VaF+bKTsVVKthpes+POf/tO/duzxSt6/q3KaGklrHasX6Y0aH4lHcZAO4x/rJcypdx/KH39Hyh9+pdD3JT84s11MRgcooyEzVwU+e1cmlnyv32F5Z7EGqVq+VYgbeoNjBNxW5STzn8C6tu7lRoX3xVzyh2lc+6ZZ4NtzZQVk7V7u2w9qcoxbPLXBL3cDZMA4A/sdms2rsiJZ68P9WGB2KR106oKHia4QYHYbp1IyppgfHtNcDN7TTgSOZWrHhmNZvS1FGVr5sNouqhweqU0KsOraMITnKQJcPaqQ7X1yuYynlu+Gtqhk3gmtDJRk3oqXe/nST0WF4VGxUsC4f1NDoMOAmzBG4V1xsiC4b2FAff1/yA/L9wdjhLWWzsZYDUFlcG4JZMUcAnMY4AJgHSXgG+2cSXlJSUpmOe+aZZ/TFF1+ooKBAU6dOVadOnTR27NhCZb788ks9/fTTru3nn3++8gEDAAAAJnLhOfXVo0NNLVl1xOhQPGbCv5L8/unZTqdTGRsX6+TyL5W+4Vdl798kR06mAsJjFdqyu2qed5vC2/WrUN3pm5bq0OwXlLFpiQqy0xVUs5Gi+1ypWsPukzUw+KzHrr2poeKveFKxA0ZVqO2zscfWU2CN+pJUJI789JNK/eMHZWz9TRlblitz++9y5mYpvN0ANX/mx+KqkyQFxtRRaEJPSVLmthVy5uW4PW5f9MIdnTXw5u+MDsNjurSpoWH9GxgdBkqw//3HdOiTZ9X4/k9UvcflHuvLABjLk+cqknRqxbc6/OVEZe74Xc68HAXVaaHYAaNV47xbZbGWfIPVmYnws91Q58jL1ZbHBihz2wrJalVQ3OlVIjK2JStjy3Jl7Vyl+mMnFXusxR6kkKanr4efOW8p3P5Opa7+UZlbflPG1t+UtWe95ChQ7aufUfyIR0uMO6RRR1mDw1SQeUrZu9eVWA4A3GHXa6N0/Oez38zQ8dOsUr8flhfnid4zbkSCJn28UXsOZhgdikcEBdr05LhORodhahaLRXVqhapOrVBd3I/v574mKNCmZ27tpHHPLjE6FI+54tzG6tAyxugwfFb7FjG66rwm+uDb7UaH4jFPjeuo4CD/vn2MOQLmCCrjyXGd9MXPe5STW2B0KB5RLy6UB/X5ML77AebAHAFzBACqLuYIzMm/r6JUARVZCU+SEhIS9MILL+i+++6TJI0bN04zZ85U//79FRAQoCVLlujHH/+6MHLHHXeof//+7gscAAAAMAGbzarpT/dR++H/U3aO/02u3TCsuYb2rmd0GB6XtuZnbX184OmNPy/8WoNDlXNgq04u/Vwnl36uuBGPqs7Vz5Sr3uML3teu166XHAWyx9RRcGw9Ze9ZpwMfPK6TyV+pxXMLZA0y5knysQNvKPFJcenrFmjny1eUu86onsMV1XO4pNM3B+Qe2V2ZEKuMAd1q65bh/vnE60C7VdOf6a2AAJ5w66tOJX8tS4BdER2HeKwvA2A8T36+D332gvb/9yFJUmBcY9mCw5S1a7X2Tv2XUlf/qCYP/e+sk+ylOf7TdGVuW6GAqDg1e/w7hTTuIEnK2Lxcmx/tq6PfT1bNC+9UcJ3mRY61R8Wp5QuLSqz7yFev6chXr5U7poZ3TJckpa1doC2PMqEEwDuCajdTQGQJq8xb3H++zXmi90SEBeqdJ3tr8C3fGx2KRzw9vpMSGlc3OgzAp918eUt9Onenfv7toNGhuF3N6GD956HuRofh815/sJt+Wn5Ah49nGR2K2/XrHK+xJlgJkTmCwpgjKJ+WjarrmVs76f5Xk40OxSPeebKXIsJYdddX8d0PMAfmCIrHHAGAqoQ5AnMhCc9AWVlZ2rBhg2vbYrGoU6eyP2nw3nvvVUFBgR577DHl5eVp2bJlWrZsWaEyFotFd955p15++WW3xQ0AAACYSfOGkXru9kTd8/JvRofiVnVrhWrivV2NDsM7nE4FxTdVrYvvVlTvKxQQFiXp9FPZDn70pA59NkGHPnlWoc27qnrnC8pUZc7hXdr9xhjJUaA617+oWsPulcViUc6R3dr65BBlbk3Wvhn3q/4tb7iO2fHKVYrpe60iE4cWqa8g45T2Trtb0X2uUkT7Ae553yWwBFZTWOs+Cm3WRaHNuyj74DYd+O/DHm2zqnvp7s76fvE+7T6QbnQobvX0rZ3UqkmU0WGgBLnH9ytr5yqFt+svW0iER/oyAD7CQ5/v9E1Ltf+9hyWrVY3uek/Rfa6UJGXuXK2tTw7Rqd/m6PCXExU37F5JUn7qce38v+tU74aJCq7bokh92fs2a++0u9XozlkKiDi9UsapFV9LkuIufcA1uS5JoS26KqrH5Tqx4D2lrVtQ7AR7aQIiYhXZ+QKFNuuikGaddWzuOzq5dHa563GXM0+ybP7sfIW37WtYHAB8U9zlD3tkBZPicJ7ofYO619HNl7fQlM82Gx2KW3VtW0P3XN/G6DAAn2e1WvTuU73V9rL/KT0zz+hw3GryYz0VG+XeJ7H7o5jqwZr8WA8Nu/Mno0Nxq9BqAXr3qd6yWi1Gh+J5zBEUwhxB+d19XRt9/tMuLVtz1OhQ3Oqmy1pocI+6RoeBEvDdDzAR5giKxRwBgKqEOQJz4VHnBlq9erUKCv5aTaNJkyaKjIwsVx0PPPCAVq1apTvvvFOtWrVSeHi4QkND1axZM910001atmyZJk6cKGslnlQAAAAAmN0dV7dWjw4lPK2minrnyV6KDDfHky1Dm3dR6zc3qsbQca4LDZJktQeqzrXPK+LPCe9jc6eWuc7D/3tJzrwcRXQYrLhL75PFcvpGhaCaDdTw9ml/1jdFeScPS5IceTmyBYdp27MXaOf/Xa/89BRXXSd/+0rrb2ultHULZPHA04/+KbLTELV4fqHqjn5JUT2Hyx4V7/E2q7rw0EC9+2Rvo8Nwqy5tauie69oaHQbO4lTy6UmryKTTF0E90ZcB8A2e+nwf/ORZyelU7KAbXZPrkhTSqL3q3TBRknRo9gty5p++kbggO12OnExtuKuDDs3+t+T489q1o0CHZv9bG+7qIEdOpgqy/0pKzzm0Q5IU1qLo6hn26NqSpPzUY+WK+4z4EY+q6aNfKX7kY4rsdK5s1cIqVA8A+BvOE43x0t1dVD8+1Ogw3CYo0Kbpz/SRzcYcMlAWDeuE66W7OxsdhltdObSxhg1oaHQYVcYl/RvqqvOaGB2GW710dxc1qhtudBhewRxBYcwRlJ/NZtX0Z/ooKNBmdChuUz8+VC/f08XoMHAWfPcDzIM5guIxRwAAxeM80XishGeglStXFtpOTEysUD2tWrXSq6++6o6QAAAAABTDZrNq+tN91H74/5SdU1D6AeW0bltKmfa5y5hhzTWkp3mebGkLiTjr6xHtByl15XfKObClTPU5nU6dXPY/SVLMoDFFXg9L6KHgui2VvW+TTi7/UjWG3CyrPUgNbp2iGueO1Z6p/9L621rJkZWuQ589r7wTBxR32UOqNexeWe1BSlu7QFueGKRqdRNUd/TLiug4uNg4js6dqj1v3qzw9gPV/Ol5ZYodFTegW22NHd5Skz/d5JH6vdkPBNqtmv5MbwUEcLOlJ+WnHtPqa2uUuXzNC+9UvRv/ur5z5smRkX8+iczdfRkA3+GJz3dBZqrSVv8oSYodWPR8JarncO2ePE4FaceVtna+IjoOVlDNBmrx3HylLP5U+6bfq2M/vitJ2vr0UDnzctTozlmK6jm8UD2OnExJUkD1og+syD28s0zvz2wqOz4AqPo4T6yaIsIC9e5TvTXo5u89Ur+3rw09Pb6TEhpX91j9gD+6ZXhLfTZvl35afsAj9XuzH6gVU03/eajoTbI4u9cf7Kaflh/Q4eNZbq/b2+NA/y7xumV4S4/V72uYI4A7tGxUXc/c2kn3v5rskfq93Q+882RvRYSZ42GdRuG7H4CyYo7AXJgjAMB5YtVHEp6B3JWEBwAAAMDzmjeM1NuP9dT1j/7i9rpvfmqR2+ssSYeW0Zp4X1evtVcVOPKyJUmWwGplKp97dI/yUg5KksISehZbJrRlT2Xv26SMLctVY8jNrv0hTTqpxYRftePFETq55DPlHtunFs8tUGjzv542aguNVHCdFsravVbbnr9EbafskD0qrkgbx3+aIUmKHTC6THGj8l66p4tWbDimFesr9rS+s/FmPzDpkR5q1SSq9IKolJzDOxWa0FOZ23+XMzdL1Rq1lzX4ryc0FqSdUPa+jbKFVldw/daK6HSu6zVHbrbS1vysoNrNFVy7WZnaK29fBqDqqMjnO3PHH3Lm58oSGKyQJp2KvG4JsCu0aWelrflJGVuWF7qhL6rncIW3G6BN93dz7Ut49Q8FhEcX05LzTI2F9uanHlPqmp8kSdXqtS5z3GZQmfEBgO86ueQznVz+hRyZqQqIrKmwhJ6K6XedbKGRRcpynlh1DexWR4/e3EHPTlnl9rq9+Z3wgj71dM/1bbzWHuAvLBaLZjzTRz2v/0p7Dma4vX5v9QOBdqven9BXMdWDvdKeP4mpHqwPXuiroeN/UG6ew611e3McqBcXqhnP9pHVaim9sEkwR4Cyuvu6Nvr198P6auEet9ftzX7g4Rvba1D3Ol5rz6z47gfAXZgj8C/MEQD+iTkCc+GR5waaNm2anE6n6+e+++4zOiQAAAAAZ3HdRc30f/dX3QS25g0i9cNb5/Jky79xOp1KWfyppJIny/8p58BWSZLFHiR7dO1iywTFNS5U9ozMHau05eFzlL5xkazBYQqMqaMtjw3Qoc9ekCMvV5IU0rijWv9nnWoMHS9nbpaO/TitSP3Z+7coY9MS2UIjVb3bsLK9WVRaWIhd300aolZNqhsdSoW9dHcXjbm0hdFhmEJos85q+cIiWe2n+9ymj32rli8scv3UOO9WSVL1bsPU8oVFiuw0xHVs2pqf5MjJdD25rDQV6csAVA0V/XyfOQcJjK0vi634Z/GdOV/J/sf5SsrSz7Xx7sKT8hvv7qSUpZ+Xqe3s/Vu0/YXLVJB2QoE1GyqsVa8yx20GlRkfAPiuUyu+0anlXypt7XylLPpYe6f+S2tvbqRTvxddNY3zxKrt6Vs76dYrEowOo8LOSYrTJy/3l83GbQJARdSNC9W8t4eqZnTVTGCzWi366MV+GtCt+GuaKF3/rrX10Yv9ZLNVzQS2GlHBmvf2uaoXF1Z6YZNgjgDlYbNZ9cnL/dS3c7zRoVTYuBEt9eztLBTgDXz3A+AOzBH4H+YIAP/EHIG5cHUdAAAAAMrhjmva6Nnbqt7kVMPaYZo35VzVjOGpNn93bO5UZe34Q5aAQNW68M4yHVOQkSJJsoVWl8VS/M0WAWGnVxnL/7OsIy9HeyaP18Z7khRYs6Fav7FBARExihv+iBrd84GOfPMfbfhXG6WtW+iqo9al90uS62LI3x3/eYYkKarXFbIG8X/qTbFRwZo7+Vw1qRdudCjl9tgtHXTvqLZGh2EquUf3qCDjlGzhMQqMKXxDTtau1ZKkag2K/p+cTP5aklQ9qWwXTivSlwGoGir6+c5PP30OcuacpDi2P187c26Te3SPtjw2UDsnXq0aQ8aq2ePfSZKaPf6dagwZq50Tr9aWxwYq92jxT3s/8cuHWnNDXa2/taXS1/8iW1iUGt39viwB9jLHbRYVHR8A+J6guCaqfe3zSnhttTp8mKoOH6Wp2VNzFdq8qwrSU7T9+UuUsXVFkeM4T6y6LBaLXn+wu66/qGxPGfYlXdvW0JzXB6lacPE33wEom+YNI/XD5HMVHRlkdCjlYrVaNP3p3ho2oKHRoVR5wwY01PSne1e5leSiI4P0w+QhatGoutGh+BTmCFBewUEBmvP6QHVrV8PoUMrt2gua6o2He5T4dwv347sfgMpijsA/MUcA+A/mCMyJJDwAAAAAKKdHbu6gifdVnRXxWjWprkUzL1D9eJ5u+3eZ23/X3nfukCTVvvpZBcU3KdNxjtxsSZIloOQVBS320zfhOHOyJElWe5Dy01PU9NGv1OiuWYUudlfvcqFa/We9whJ6yZmf59ofVLOBQpp1VtbOVco+uM213+lw6Pj8WZKk2AGjyxQz3KtOrVD9OuMCtWla8qSFr3nhziQ9fWvVSyCu6rJ2r5VU/MXRzJ0lXzhNXfmtbKGRZXoyZEX7MgC+rzKfb2de6ecr1oDT5yuOM+crQSGy2APV6tVVirv8Qclq+7OgTXGXP6hWr66SxR4oa1BosfXlnTysvOP7JafzdAz5eUpZ/KkKstLLHLdZVHR8AOB74kc+pvjLH1JIw3ayhYTLVi1MER0GqfnzvyikWRc583K0f9YDRY7jPLFqs1otmvZ0b40fWXVWxOvfJV7zppyriLCSzw0AlF2HljH6Zfr5iq8RYnQoZWIPsOqjF/vpuiqYQOyrrr2wmT5+sZ/sAVXjtqv4GiFaOO08dUyINToUn8IcASoqPDRQ86YMVf8uVWdFvHEjWmrGs32qXAJxVcd3PwCVwRyB/2KOAPAfzBGYE4+5AwAAAIAKuOvaNooItWvss4uVn+80OpwSdWlTQ9+8OVixUcFGh+JTcg7v1LZnLpAzN1vRfa5SrWH3lvlYa+Dpf0tnfm6JZZx5OZIky9+eQNv43g9LLB8QVl0N/zWtyP6oHpcrc2uyUhZ9ovjhD0uSUlfNU97x/Qqu21KhLapOMqi/ia8RooXTz9eFt8/VklVHjA6nRDabRW8+3EO3DG9pdCimlLWr+AunTodD2XvWnX6tYeHXMneuVu7RPYrqOaLUJ0NWpi8D4Nsq+/m22Es/X3Hknz5fOfPE/ICIWDV7/NsSywfXbXHW12teeIdqDLlZuUf3KG3tAh364iUd+er/lL5xkVq+uFQWW9WYjtj12igd/3lmia9vebRfsfubPztf4W37lqmNiowPAKoWqz1Qda5+RlufHKK0dQuUn55S6EZrzhOrPqvVojce7q7oyCA9O2WV0eGc1SX9G+jDf/dVcFDVGIuBqqJ10ygtmnm+hoz9Qdv2pBodTonCQuz69OX+OrdXXaND8TuXD26k8FC7Lr/nZ6Vn5pV+gEGa1AvXD5PPVZN6EUaH4lOYI0BlhYXY9c2bg3X1gwv1+U+7jA7nrB6+sb2evT2RFfAMwHc/ABXFHIFxmCMA4A7MEfi3qvFIJgAAAADwQWMubaEVH16sDi2jjQ6liIAAi54a30mLZl5AAt4/5KUc0tbHBykv5aAik85XwztmlGvi0RZ6+qJIQcZJOZ3FJ2Dmp6dIkgJCK7dSWlT3yyRJKYs/de07/tN0SVIMT7g1XHRkkBa8e76evS3RJ5963bZZlH57/yIS8AyUVcLF0ZwDW+TIyVRAZA3Zq9cq9Nqp5K8lSZGdLzhr3ZXtywD4Lnd8vs9M4pw5JylOwZ+v2Sp5vnKGxWKRNShEwXVbqsbQsUp4ZaUCa9RX5rYVOvFLyTca+pqg2s0VmtCzyE9AZE1JUnCDNsW+bguNLHMbFRkfAFQ9oS26n/7F4VDOoR2FXuM80T9YLBY9c1ui5k05V/Xji38KvJHCQ+2a8nhPff7qABLwAA9pXDdCf3xyiW69wjdXxuzfJV5rZw8jAc+DhvSsq7Wzh2lA19pGh1Ks8SMTtOrTYSTg/QNzBHCX4KAAfTaxv6Y+0UvhoWe/CdYI9UTXdukAAQAASURBVONDNW/KuXruX0l8JzAI3/0AVARzBMZ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+ "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": { + "image/png": { + "height": 1140, + "width": 1776 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz_isa.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "id": "da6d7c8b-0d45-453e-a36d-ae19dccda76e", + "metadata": {}, + "source": [ + "### ISA Observables" + ] + }, + { + "cell_type": "markdown", + "id": "df6ff51e", + "metadata": {}, + "source": [ + "Similarly, we need to transform the Hamiltonian to make it backend compatible before running jobs with [`Runtime Estimator V2`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2#run). We can perform the transformation using the `apply_layout` the method of `SparsePauliOp` object." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e856e5c0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['IIIIIIIIIIIIZIIIIIZIIIIIIII', 'IIIIIIIIIIIIZIIZIIIIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIIIIIIII', 'IIIIIIIIIIZIZIIIIIIIIIIIIII'],\n", + " coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hamiltonian_isa = hamiltonian.apply_layout(ansatz_isa.layout)\n", + "hamiltonian_isa" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b58c33dc", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "fe36b13c", + "metadata": {}, + "source": [ + "As with an iterative optimization procedure, we now need to define our cost function over which to minimize. We proceed in an identical manner to the [Variational Quantum Eigensolver tutorial](https://learning.quantum-computing.ibm.com/tutorial/variational-quantum-eigensolver), computing the expectation value of our Hamiltonian with respect to the parameterized ansatz circuit using the [Qiskit Runtime `Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) primitive:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "2f3e4de4", + "metadata": {}, + "outputs": [], + "source": [ + "def cost_func(params, ansatz, hamiltonian, estimator):\n", + " \"\"\"Return estimate of energy from estimator\n", + "\n", + " Parameters:\n", + " params (ndarray): Array of ansatz parameters\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (EstimatorV2): Estimator primitive instance\n", + "\n", + " Returns:\n", + " float: Energy estimate\n", + " \"\"\"\n", + " pub = (ansatz, [hamiltonian], [params])\n", + " result = estimator.run(pubs=[pub]).result()\n", + " cost = result[0].data.evs[0]\n", + "\n", + " return cost" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "32035dc8", + "metadata": {}, + "source": [ + "Any classical optimizer can be used to minimize the cost function. On a real quantum system, an optimizer designed for non-smooth cost function landscapes usually does better. Here we use the [COBYLA routine from SciPy through the minimize function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).\n", + "\n", + "Because we are iteratively executing many calls to Runtime, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all calls within a single block. Moreover, for QAOA, the solution is encoded in the output distribution of the ansatz circuit bound with the optimal parameters from the minimization. Therefore, we will need a [`Sampler`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.SamplerV2) primitive as well, and will instantiate it with the same [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f2fffe34", + "metadata": {}, + "outputs": [], + "source": [ + "# To run on local simulator:\n", + "# 1. Use the StatevectorEstimator from qiskit.primitives instead.\n", + "# 2. Remove the Session instantiation below.\n", + "session = Session(backend=backend)\n", + "\n", + "# Configure estimator\n", + "estimator = Estimator(session=session)\n", + "estimator.options.default_shots = 10_000\n", + "estimator.options.dynamical_decoupling.enable = True\n", + "\n", + "# Configure sampler\n", + "sampler = Sampler(session=session)\n", + "sampler.options.default_shots = 10_000\n", + "sampler.options.dynamical_decoupling.enable = True" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b0b5aa51", + "metadata": {}, + "source": [ + "We can set an initial set of random parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "1631f250", + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 2 * np.pi * np.random.rand(ansatz_isa.num_parameters)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "43520f43", + "metadata": {}, + "source": [ + "We can run our minimization routine:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "0076beb6", + "metadata": {}, + "outputs": [], + "source": [ + "res = minimize(cost_func, x0, args=(ansatz_isa, hamiltonian_isa, estimator), method=\"COBYLA\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "95404ae5", + "metadata": {}, + "source": [ + "In the end, we have a result in the standard [SciPy `OptimizeResult`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html) format." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "7a299ed5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " message: Optimization terminated successfully.\n", + " success: True\n", + " status: 1\n", + " fun: -2.482839158666561\n", + " x: [ 5.054e-01 5.090e+00 2.655e+00 5.840e+00]\n", + " nfev: 47\n", + " maxcv: 0.0" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d162e690", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "677cf16b", + "metadata": {}, + "source": [ + "The solution vector of parameter angles (`x`), when plugged into the `ansatz` circuit, yields the graph partitioning that we were looking for." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "29cff98d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 14, + "metadata": { + "image/png": { + "height": 1333, + "width": 1776 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "# Assign solution parameters to ansatz\n", + "qc = ansatz.assign_parameters(res.x)\n", + "# Add measurements to our circuit\n", + "qc.measure_all()\n", + "qc_isa = pm.run(qc)\n", + "qc_isa.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "c6225876-62cb-42be-8814-de40d002f407", + "metadata": {}, + "outputs": [], + "source": [ + "result = sampler.run([qc_isa]).result()\n", + "samp_dist = result[0].data.meas.get_counts()\n", + "# Close the session since we are now done with it\n", + "session.close()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "38c59bdc", + "metadata": {}, + "source": [ + "For small problem instances, the solution can be visually obtained:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "9c61fa56", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 16, + "metadata": { + "image/png": { + "height": 479, + "width": 1260 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "plot_distribution(samp_dist, figsize=(15, 5))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b2dd6e37", + "metadata": {}, + "source": [ + "The most probable bit-strings, up to finite-sampling deviations, encode the solution. Here we see that `00001` and `11110` are found, and are indeed correct. There are two solutions because the labeling of the two partitions with `'0'` or `'1'` is arbitrary." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "9a75683e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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AlJ5JN9SXQAkAAACUmkk31JuJNwAAAFBKJt3QDG5QAgAAAKVj0g3NIVACAAAApWLSDc1i4g0AAACUgkk3NJMblAAAAEDhTLqhuQRKAAAAoFAm3dBsJt4AAABAIUy6gQg3KAEAAIACmHQDTxEoAQAAgJEy6Qb2Z+INAAAAjIRJN7AQNygBAACA3Jl0A4ciUAIAAAC5MukGDsfEGwAAAMiFSTfQDzcoAQAAgMyZdAP9EigBAACATJl0A4th4g0AAABkwqQbGIQblAAAAMDQTLqBQQmUAAAAwFBMuoFhmHgDAAAAAzHpBrLgBiUAAACwaCbdQFYESgAAAGBRTLqBLJl4AwAAAH0x6Qby4AYlAAAAcEQm3UBeBEoAAADgsEy6gTyZeAMAAAALMukGRsENSgAAAOAgJt3AqAiUAAAAwAFMuoFRMvEGAAAAIsKkGyiGG5QAAACASTdQGIESAAAAGs6kGyiSiTcAAAA0lEk3UAZuUAIAAEADmXQDZSFQAgAAQMOYdANlYuINAAAADWHSDZSRG5QAAADQACbdQFkJlAAAAFBzJt1AmZl4AwAAQE2ZdANV4AYlAAAA1JBJN1AVAiUAAADUjEk3UCUm3gAAAFATJt1AFblBCQAAADVg0g1UlUAJAAAAFWfSDVSZiTcAAABUlEk3UAduUAIAAEAFmXQDdSFQAgAAQMWYdAN1YuINAAAAFWHSDdSRG5QAAABQASbdQF0JlAAAAFByJt1AnZl4AwAAQEmZdANN4AYlAAAAlJBJN9AUAiUAAACUjEk30CQm3gAAAFASJt1AE7lBCQAAACVg0g00lUAJAAAABTPpBprMxBsAAAAKYtIN4AYlAAAAFMKkG2APgRIAAABGzKQbYB8TbwAAABgRk26Ag7lBCQAAACNg0g2wMIESAAAAcmbSDXBoJt4AAACQE5NugCNzgxIAAAByYNIN0B+BEgAAADJm0g3QPxNvAAAAyIhJN8DiuUEJAAAAGTDpBhiMQAkAAABDMukGGJyJNwAAAAzIpBtgeG5QAgAAwABMugGyIVACAADAIpl0A2THxBsAAAD6ZNINkD03KAEAAKAPJt0A+RAoAQAA4AhMugHyY+INAAAAh2DSDZA/NygBAABgASbdAKMhUAIAAMDTmHQDjI6JNwAAADzJpBtg9NygBAAAgDDpBiiKQAkAAEDjmXQDFMfEGwAAgMYy6QYonhuUAAAANJJJN0A5CJQAAAA0jkk3QHmYeAMAANAYJt0A5eMGJQAAAI1g0g1QTgIlAAAAtWfSDVBeJt4AAADUlkk3QPm5QQkAAEAtmXQDVINACQAAQO2YdANUh4k3AAAAtWHSDVA9blACAABQCybdANUkUAIAAFB5Jt0A1WXiDQAAQGWZdANUnxuUAAAAVJJJN0A9CJQAAABUjkk3QH2YeAMAAFAZJt0A9eMGJQAAAJVg0g1QTwIlAAAApWfSDVBfJt4AAACUlkk3QP25QQkAAEApmXQDNINACQAAQOmYdAM0h4k3AAAApWHSDdA8blACAABQCibdAM0kUAIAAFA4k26A5jLxBgAAoDAm3QC4QQkAAEAhTLoBiBAoAQAAKIBJNwBPMfEGAABgZEy6AXg6NygBAAAYCZNuABYiUAIAAJA7k24ADsXEGwAAgNyYdANwJG5QAgAAkAuTbgD6IVACAACQOZNuAPpl4g0AAEBmTLoBWCw3KAEAAMiESTcAgxAoAQAAGJpJNwCDMvEGAABgYCbdAAzLDUoAAAAGYtINQBYESgAAABbNpBuArJh4AwAA0DeTbgCy5gYlAAAAfdmyZYtJNwCZEygBAAA4ok2bNsW5555r0g1A5ky8AQAAOCSTbgDy5gYlAAAAC1po0n3ZZZeZdAOQKYESAACAgxxq0v2hD33IpBuATJl4AwAAsJdJNwCj5gYlAAAAEWHSDUAxBEoAAABMugEojIk3AABAg5l0A1A0NygBAAAayqQbgDIQKAEAABrIpBuAsjDxBgAAaBCTbgDKxg1KAACAhjDpBqCMBEoAAIAGMOkGoKxMvAEAAGrMpBuAsnODEgAAoKZMugGoAoESAACghky6AagKE28AAIAaMekGoGrcoAQAAKgJk24AqkigBAAAqAGTbgCqysQbAACgwky6Aag6NygBAAAqyqQbgDoQKAEAACrIpBuAujDxBgAAqBCTbgDqxg1KAACAijDpBqCOBEoAAIAKMOkGoK5MvAEAAErMpBuAunODEgAAoKRMugFoAoESAACghEy6AWgKE28AAIASMekGoGncoAQAACgJk24AmkigBAAAKAGTbgCaysQbAACgQCbdADSdG5QAAAAFMekGADcoAQAACrFp06a4/PLLY3p6OiL2TLqvuOKKeP3rX1/wyQCylc52onvXQ9HZ+lD07nkk0t3zkc53I5KIZLwdybLJaJ9yTLTXrY72M4+JZKxd9JEZMYESAABghEy6gSbobN0es5/fEt1b7o/uPY9G9NL+fuN4O9qnHBtjZ6+JyR95TrRPWpnrOSmHJE3TPv8VAgAAwDC2bNkSl1566d4vwonYM+l+73vf64twgMpLZzsx9/XbY/Yzm6N7+4OZPHPs+Wtj8pKzY/yFp0TS9kmFdSVQAgAAjIBJN1BXabcXs5/6bsz87fWR7pzN5R3Jcctj2etfHOMXrI8kSXJ5B8URKAEAAHJk0g3UWfe+HbHr/V+M7i33j+R94+edFst+4YejdbRb53UiUAIAAOTEpBuoq6duTe7+q2sj5rojfXdy1JJY9pYLY+KC9SN9L/kRKAEAAHJg0g3UVTrfjV2/f3XMX3dnoeeYfO3zY+kbX2LyXQMCJQAAQIZMuoE6S2fmY+d7PhOd79xT9FEiImLiFWfGsl94mS/QqTh/9QAAADKyZcuW2Lhx4wFx8rLLLotrr71WnAQqL53vxs7fuao0cTIiYu7zt8T0h74c7t9Vm0AJAACQgU2bNsW555679/Mmp6am4sorr4wPfehDPm8SqLw0TWPXez8fnRvvLvooB5m7ekvM/PV1RR+DIQiUAAAAQ5ieno7LLrssfu7nfm7v501u2LAhvvnNb/q8SaA25r5wS8x/fWvRxzikmb/9Vsxvua/oYzAgn0EJAAAwIN/SDTRB76Gd8dg7PhoxPbf43zw1Eclpx0Zy2nHROu3YiGOnIjlqScRRkxFpREzPRXrPjujdcn/0vro14tHdA5+zdcKKWPG7l0ayZHzgZ1AMgRIAAGAAvqUbaII0TWPnf/mH6Nww2LR77NdeHq1zTu7vXfPd6H3ypuj+nxv3xMsBTL76ubHszS8d7DdTmLGiDwAAAFAlvqUbaJK5a24dOE4+Xbpjd6TbHov0kV0Rs52IibFITjgqktOOi2SsFcl4O9o/+fyI46ai+6GvDfSO2U99NyZecnqMPeekTM7MaAiUAAAAfTLpBpok7aUx8zfXD/WM3i33R+9bd0dv87aIh3Yu/ENHL4n2z26M9nmnRkRE+8L10bvhnki/+YOB3rn7b6+Po37rNQOemCL4khwAAIA++JZuoGk6N94dvQceH+oZvU9vid6Xbjt0nIyIeGwmuu//x+jdfP/ef6h98RkDv7Nzw93Rvf+xgX8/oydQAgAAHIZv6Qaaavaqm0b6vt4/3r737yenHDPUs2Y/u/nIP0RpCJQAAACHsGXLlti4ceMBnzd52WWXxbXXXuvzJoFa6z74eMxff9dI35k+PrPvF0N+E/fcF26JdLYz5IkYFYESAABgASbdQJPNffm2gb9Je1DJmqP3/eLhXUM9K905G/PfGm1gZXACJQAAwH5MugEiurc9MNoXrlwa7R87a+8ve98cPi52Rv1nYGC+xRsAAOBJvqUbYI/OHQ/l/5LxdsTq5dF63jOi/eqzIzl6aUREpNsei+4nh//8y+4d24d+BqMhUAIAAMSeSffll1++99bk1NRUXHHFFW5NAo3Te3Q60keGm1gvJHnW8TH+W686/Lu/c290rvhyxO75od/XveOhSNM0kiQZ+lnkS6AEAAAabXp6Ot7+9rcf8EU4GzZsiI9//OO+CAdopCJuHqa7ZqO76brofePO7J45PRe9+x+P9klHH/mHKZRACQAANJZJN8DBuvftyOW56Y7p6H7uln3/wNLxSE5cEckpx0YyNRljl18YvZetj86ffyPigScyeWdv2w6BsgIESgAAoJFMugEWls518nnw9p3RvfK6g//xlUuj/dM/FO0L10frrJNi/F2vjs67Pxvp3Y8O/cp0Nqc/C5nyLd4AAECj+JZugCOY6472fTt2R/dDX4vuZ2+OiIhk+Z7blJHBZ0fmFlvJlEAJAAA0xpYtW2Ljxo0HfN7kZZddFtdee63PmwR4SquYL5XpfvxbkU7PRURE8oyVkTxvzdDPTNrSVxX4qwQAADTCpk2b4txzz937eZNTU1Nx5ZVXxoc+9CGfNwmwn2SioE8EnOtGevu+L+hpnXH88M8s6s/CovirBAAA1Jpv6QZYnGT5ZGHvTnfN7ftFBuco8s9C/9ygBAAAasukG2Dx2qcdV9i7k5VL9/1i59yhf7BPY6ccO/QzyJ9ACQAA1JJJN8Bg2qccGzFWQDKamozk9NV7f5net2Oox7VOOjqSKTcoq0CgBAAAasW3dAMMJxlvR/uZxwz/oKmJRf14+40bI5loR0REOteN3g33DvX69n6xk3LzGZQAAEBtbNmyJS699NK9tyYj9ky63/ve97o1CbAI7XWro3vHQ0M9o3XB6dF6yWnR+9wt0bv+7oiZ+QV/Llm7MtqXvjBaz3vG3n+s9+nNEbtmh3r/2DqBsioESgAAoBY2bdoUl19++d5bk1NTU3HFFVe4NQkwgPHnr425z9089HNa646L1i+8NNJOL9Jtj0Xc//iTX4STRjI1GcnaVZGcuOKA39P7p7ui+3c3Dv3useetHfoZjIZACQAAVJpv6QbI3vi5p0ayclmkO6YHf0inu/fvJmOtSNauili76pA/nu6ei+4nbozeZ2+JSNPB3xsR7TNPjLFTfUFOVQiUAABAZZl0A+QjGWvH3Hknx/hV3xv4Gb0vfC/mNm+L1tlrIjn9uEiecXQkx05FLHvysyl3z0e6Y3ekP3gk0s3bovfNH0TMdjI5/5JLzs7kOYxGkqZDJmkAAIACmHQD5OPee++Nd7/73fH3mz4a//SKd8VYq130kRYlWbEkjv7TN0YyXq1zN5kblAAAQKWYdAPk46kw+YEPfCDm5uYiIuIf7rsxfuLkFxR8ssWZfOVZ4mTFCJQAAEBlmHQDZG+hMBmx52b6tgtOiPT+diSz3cM8oTxaq4+KJf/8h4o+BoskUAIAAJVg0g2QrcOFybe97W3xzne+M1avXh2zV90U0x/8coEn7d+yyy+KZOlE0cdgkQRKAACg1Ey6AbLVb5h8ysQrz465r2+Nzk33FXHcvk288qwYf97JRR+DAfiSHAAAoLRMugGys9gwub/uA4/H4+/8WMTM/KiOuyit1UfFit+71O3JihIoAQCAUjLpBsjGMGFyf/M3/CB2vvvTEZ1ensddtGT5ZBz1n34i2s88tuijMCCBEgAAKBWTboBsZBUm9zf39a2x6/evjuiVJCctGY+j3vXaGDvjhKJPwhAESgAAoDRMugGGl0eY3N/cdXfGrt/7bOE3KZPlk7H8t14TY+uPL/QcDE+gBAAASsGkG2A4eYfJ/c3fdG/s+oPPRbpjOpPnLVZrzcpY/huXRHvtMYW8n2wJlAAAQKFMugGGM8owub/eEzOx+yNfibkv35b5sw+plcTka58fSy89N5LJsdG9l1wJlAAAQGFMugEGV1SYfLq56+6M6Q98KdIdu3N9T2vNyph628UxdsaJub6H0RMoAQCAQph0AwymLGFyf70nZmL209+N2c/dHOkjuzJ9dmvNypi85OyY/JGz3JqsKYESAAAYKZNugMGUMUw+Xdrpxvw3vx+zn9kcnZvuHfxBrSTGzz01Jl+1IcY2PCOSJMnukJSOQAkAAIyMSTfA4lUhTC6k+8Dj0bn1/ujesT26d2yPzh0PRczML/izyfLJaK9bHWOnr4726atj7NknRWuV/15oCoESAAAYCZNugMWpapg8lLSXRu/hnREz85HOdSOSiGRiLJKl45EcM+WWZIMJlAAAQK5MugEWp25hEo7EJ4sCAAC5MekG6J8wSVMJlAAAQC5MugH6I0zSdAIlAACQKZNugP4Ik7CHQAkAAGTGpBvgyIRJOJBACQAAZMKkG+DwhElYmEAJAAAMxaQb4PCESTg8gRIAABiYSTfAoQmT0B+BEgAAGIhJN8DChElYHIESAABYFJNugIUJkzAYgRIAAOibSTfAwYRJGI5ACQAA9MWkG+BAwiRkQ6AEAAAOy6Qb4EDCJGRLoAQAAA7JpBtgH2ES8iFQAgAACzLpBthDmIR8CZQAAMABTLoB9hAmYTQESgAAYC+TbgBhEkZNoAQAACLCpBtAmIRiCJQAANBwJt1A0wmTUCyBEgAAGsykG2gyYRLKQaAEAICGMukGmkqYhHIRKAEAoGFMuoGmEiahnARKAABoEJNuoImESSg3gRIAABrCpBtoGmESqkGgBACAmjPpBppGmIRqESgBAKDGTLqBJhEmoZoESgAAqCmTbqAphEmoNoESAABqxqQbaAphEupBoAQAgBox6QaaQJiEehEoAQCgJky6gboTJqGeBEoAAKg4k26g7oRJqDeBEgAAKsykG6gzYRKaQaAEAICKMukG6kqYhGYRKAEAoGJMuoG6EiahmQRKAACoEJNuoI6ESWg2gRIAACrCpBuoG2ESiBAoAQCg9Ey6gboRJoH9CZQAAFBiJt1AnQiTwEIESgAAKCmTbqAuhEngcARKAAAoGZNuoC6ESaAfAiUAAJSISTdQB8IksBgCJQAAlIRJN1B1wiQwCIESAAAKZtINVJ0wCQxDoAQAgAKZdANVJkwCWRAoAQCgICbdQFUJk0CWBEoAABgxk26gqoRJIA8CJQAAjJBJN1BFwiSQJ4ESAABGxKQbqBphEhgFgRIAAHJm0g1UjTAJjJJACQAAOTLpBqpEmASKIFACAEBOTLqBqhAmgSIJlAAAkDGTbqAqhEmgDARKAADIkEk3UAXCJFAmAiUAAGTEpBsoO2ESKCOBEgAAhmTSDZSdMAmUmUAJAABDMOkGykyYBKpAoAQAgAGZdANlJUwCVSJQAgDAIpl0A2UlTAJVJFACAMAimHQDZSRMAlUmUAIAQJ9MuoGyESaBOhAoAQDgCEy6gbIRJoE6ESgBAOAwTLqBMhEmgToSKAEA4BBMuoGyECaBOhMoAQDgaUy6gbIQJoEmECgBAGA/Jt1AGQiTQJMIlAAA8CSTbqBowiTQRAIlAACNZ9INFE2YBJpMoAQAoNFMuoEiCZMAAiUAAA1m0g0URZgE2EegBACgcUy6gaIIkwAHEygBAGgUk26gCMIkwKEJlAAANIZJNzBqwiTAkQmUAADUnkk3MGrCJED/BEoAAGrNpBsYJWESYPEESgAAasukGxgVYRJgcAIlAAC1Y9INjIowCTA8gRIAgFox6QZGQZgEyI5ACQBAbZh0A3kTJgGyJ1ACAFB5Jt1A3oRJgPwIlAAAVJpJN5AnYRIgfwIlAACVZdIN5EWYBBgdgRIAgMox6QbyIkwCjJ5ACQBApZh0A3kQJgGKI1ACAFAZJt1A1oRJgOIJlAAAlJ5JN5A1YRKgPARKAABKzaQbyJIwCVA+AiUAAKVl0g1kRZgEKC+BEgCA0jHpBrIiTAKUn0AJAECpmHQDWRAmAapDoAQAoDRMuoFhCZMA1SNQAgBQOJNuYFjCJEB1CZQAABTKpBsYhjAJUH0CJQAAhTHpBgYlTALUh0AJAMDImXQDgxImAepHoAQAYKRMuoFBCJMA9SVQAgAwMibdwGIJkwD1J1ACAJA7k25gsYRJgOYQKAEAyJVJN7AYwiRA8wiUAADkxqQb6JcwCdBcAiUAAJkz6Qb6JUwCIFACAJApk26gH8IkAE8RKAEAyIxJN3AkwiQATydQAgAwNJNu4EiESQAORaAEAGAoJt3A4QiTAByJQAkAwMBMuoFDESYB6JdACQDAopl0A4ciTAKwWAIlAACLYtINLESYBGBQAiUAAH17+qR72bJlccUVV8Qb3vCGgk8GFEWYBGBYAiUAAEd0qEn3xz72sXjOc55T4MmAogiTAGRFoAQA4LBMuoH9CZMAZE2gBADgkEy6gacIkwDkRaAEAOAgJt3AU4RJAPImUAIAcACTbiBCmARgdARKAAD2MukGhEkARk2gBADApBsQJgEojEAJANBwJt3QbMIkAEUTKAEAGsykG5pLmASgLARKAIAGMumG5hImASgbgRIAoGFMuqGZhEkAykqgBABoEJNuaB5hEoCyEygBABrApBuaR5gEoCoESgCAmjPphmYRJgGoGoESAKDGTLqhOYRJAKpKoAQAqCGTbmgOYRKAqhMoAQBqxqQbmkGYBKAuBEoAgBox6Yb6EyYBqBuBEgCgBky6of6ESQDqSqAEAKg4k26oN2ESgLoTKAEAKsykG+pLmASgKQRKAIAKMumG+hImAWgagRIAoGJMuqGehEkAmkqgBACoEJNuqB9hEoCmEygBACrApBvqR5gEgD0ESgCAkjPphnoRJgHgQAIlAECJmXRDfQiTALAwgRIAoIRMuqE+hEkAODyBEgCgZEy6oR6ESQDoj0AJAFAiJt1QfcIkACyOQAkAUAIm3VB9wiQADEagBAAomEk3VJswCQDDESgBAApk0g3VJUwCQDYESgCAAph0Q3UJkwCQLYESAGDETLqhmoRJAMiHQAkAMEIm3VA9wiQA5EugBAAYAZNuqB5hEgBGQ6AEAMiZSTdUizAJAKMlUAIA5MikG6pDmASAYgiUAAA5MOmG6hAmAaBYAiUAQMZMuqEahEkAKAeBEgAgQybdUH7CJACUi0AJAJABk24oP2ESAMpJoAQAGJJJN5SbMAkA5SZQAgAMwaQbykuYBIBqECgBAAZg0g3lJUwCQLUIlAAAi2TSDeUkTAJANQmUAACLYNIN5SNMAkC1CZQAAH0w6YbyESYBoB4ESgCAIzDphnIRJgGgXgRKAIDDMOmG8hAmAaCeBEoAgAWYdEN5CJMAUG8CJQDA05h0QzkIkwDQDAIlAMB+TLqheMIkADSLQAkAECbdUAbCJAA0k0AJADSeSTcUS5gEgGYTKAGARjPphuIIkwBAhEAJADSUSTcUR5gEAPYnUAIAjWPSDcUQJgGAhQiUAECjmHTD6AmTAMDhCJQAQCOYdMPoCZMAQD8ESgCg9ky6YbSESQBgMQRKAKDWTLphdIRJAGAQAiUAUEsm3TA6wiQAMAyBEgCoHZNuGA1hEgDIgkAJANSKSTfkT5gEALIkUAIAtWDSDfkTJgGAPAiUAEDlmXRDvoRJACBPAiUAUGkm3ZAfYRIAGAWBEgCoJJNuyI8wCQCMkkAJAFSOSTfkQ5gEAIogUAIAlWLSDdkTJgGAIgmUAEAlmHRD9oRJAKAMBEoAoPRMuiFbwiQAUCYCJQBQaibdkB1hEgAoI4ESACglk27IjjAJAJSZQAkAlI5JN2RDmAQAqkCgBABKxaQbhidMAgBVIlACAKVg0g3DEyYBgCoSKAGAwpl0w3CESQCgygRKAKBQJt0wOGESAKgDgRIAKIRJNwxOmAQA6kSgBABGzqQbBiNMAgB1JFACACNl0g2LJ0wCAHUmUAIAI2HSDYsnTAIATSBQAgC5M+mGxREmAYAmESgBgFyZdEP/hEkAoIkESgAgFybd0D9hEgBoMoESAMicSTf0R5gEABAoAYCMmXTDkQmTAAD7CJQAQCZMuuHIhEkAgIMJlADA0Ey64fCESQCAQxMoAYChmHTDoQmTAABHJlACAAMx6YZDEyYBAPonUAIAi2bSDQsTJgEAFk+gBAAWxaQbDiZMAgAMTqAEAPpi0g0HEyYBAIYnUAIAR2TSDQcSJgEAsiNQAgCHZdIN+wiTAADZEygBgAWZdMM+wiQAQH4ESgDgICbdsIcwCQCQP4ESADiASTcIkwAAoyRQAgARYdINEcIkAEARBEoAwKSbxhMmAQCKI1ACQMOZdNNkwiQAjE7a7UXv4Z0Rs51IZzsRSRLJRDuSZRORHDMVSZIUfUQKIlACQEOZdNNkwiQA5K/7wOPRufX+6G7dHt07tkfnzociZuYX/Nlk+WS0162OsdNX7/nbM0+K1ipLnqZI0jRNiz4EADBaJt00lTAJAPlKO92Y/6fvx+xVN0XnpvsGf1ArifEXnRqTr9oQY899htuVNSdQAkDDmHTTRMIkAOSr98RMzH76uzH7uZsjfWRXps9urVkZk5ecHZM/clYkk8bAdSRQAkBDmHTTRMIkAORv7ro7Y/oDX4p0x+5c39NaszKm3nZxjJ1xYq7vYfQESgBoAJNumkaYBID89Z6Yid0f/krMfeW20b20lcTka54XS39mo9uUNSJQAkDNmXTTJMIkAIzG/E33xq4/uDr3W5OH0lqzMpb/xiXRXntMIe8nWwIlANSUSTdNIkwCwOjMXXdn7Pq9z0Z0eoWeI1k+Gct/6zUxtv74Qs/B8ARKAKghk26aQpgEgNGa+/rW2PX7V0f0SpKTlozHUe96bYydcULRJ2EIAiUA1IxJN00gTALA6M3f8IPY+e5PF35z8umS5ZNx1H/6iWg/89iij8KABEoAqAmTbppAmASAYnQfeDwef+fHImbmiz7Kglqrj4oVv3dpJEsnij4KA/B1RwBQAybd1J0wCQDFSXtpTP/JF0sbJyMietufiOlNX4+pX3xZ0UdhAAIlAFScSTd1JkwCQPHmrt4cnZvuG/wBx01F6+w1kZx5QiQnr4zk2KmIyfGImflIH52O9Pbt0fv6nZHe+sCQ59wSEy85Pcafd/JQz2H0TLwBoKJMuqkzYRIAymHPtPujETOdRf/e5JnHRPtN50Xr9P7+O7t38/3R+cBXIx7Zteh3PcXUu5rcoASACjLppq6ESQAol91Xfn2gOBkRkZy04qA4mW57LNJ7dkS6czZi2US01q/ec6MyIlrPOTHG3/VjMf9fPhOxfedA7+xtfyJm/u7bsfT/Om+g308xBEoAqBiTbupImASA8uk9vDPmr7tz6Oek9z8e3S/dFr2v3xHx6O4D/rluEtG6cH20X39uJJPjkaxaFmO/dGF0fvvTA79v9uotseSnXxTJeHvYozMiAiUAVIRJN3UkTAJAec1+bktEb/BPBkx37I7OB78ava/eEXGoTxhMI3r/eHuku2Zj/JcvjojYc6tyw5pIB/zcy/TxmZj/xtaYuPCMQY/OiAmUAFABJt3UjTAJAOWWdroxe/XNwz3j1gf6/uKb9Pq7o7d1+95JeOv5z4juEF/MM3PVZoGyQgRKACg5k27qRJgEgGqY/6fvR7pjeqTvTG/bHvFkoExWLx/qWd1b7o/O9x+OsVOPzeJo5EygBICSMummToRJAKiW+RvvHv1L95+BJ8nQj+t8526BsiIESgAoIZNu6kKYBIBq6t6xfeTvTNau2vv300d2Df28TgF/BgYjUAJAyZh0UwfCJABUVzrfje4PHhntS49ZFslzTtz7y97mbUM/srtVoKwKgRIASsKkmzoQJgGg+rp3PRzR6Y30nWP/6txI2q2IiEgf2hnpDfcM/czetsci3TUbydTk0M8iXwIlAJSASTdVJ0wCQH1073xopO9rXbAuWueesu/9H/92ZoG0c9fDMX7WmkyeRX4ESgAomEk3VSZMAkD9pDtnR/au5NRjo/2mF+/9dfcbd0bvG3dm9vxR/lkYnEAJAAUx6abKhEkAqK90rjOaFx23PMZ+7eJIJvbkqd7dj0b3z7+R7TtG9WdhKAIlABTApJuqEiYBoAF6af7vOHppjP/mj0Sycs//75s++ER0fudzEbvnM31N2h3tZ2kyGIESAEbMpJsqOlyYfOtb3xq//uu/LkwCQF1MtPN9/tRkjP3mj0RywoqIiEgfnY75/351xGO7M3/VU7czKTd/lQBgREy6qSI3JgGgeXKNekvGY+zXXxGtk1dFRET6xEx0fufqiId25vK6ZFL6qgJ/lQBgBEy6qRphEgCaq71mZT4PnhiLsXe+IlrrjouIiHR6Ljr/43OR3vtYPu+LiNZJK3N7NtkRKAEgZybdVIkwCQC01+Xw3/XjrRj71YujdcbxERGRzs5H5/c+H+n3H8n+XU9Klk1E68QVuT2f7AiUAJATk26qRJgEgGbbtm1bfOlLX4prrrkmrrnmmvjb038u1ixdmc3D20mMve2iaJ19UkREpHPd6PzBNZHetj2b5x/qteuOiyRJcn0H2RAoASAHJt1UhTAJAM309CB56623HvDP33jMD7IJlEkSY790YbTOOTkiItJOLzrv/1KkW7YN/+wjyOUmKLkQKAEgYybdVIEwCQDNcqQgub+xsbF4cHk3k/e2L3tJtDaeGhERaa8X3Q98JdJv35PJs49k7FknjOQ9DE+gBICMmHRTBcIkADTDYoPkxo0b46KLLoqLLroozj///Fgy3YvH/83/ikgHP0Pr5c+O9oXr9/0DD+6M5Izjo/3k51Ae1s7Z6H7ixoHfnSyfjPEXnDLw72e0BEoAyIBJN2UnTAJAvQ0bJKempg78oamI8ReeEvPfvGvgMyUrlhz46xNXRLvPL61Jt+8cKlBOvPzMSCZlr6rwVwoAhmTSTZkJkwBQT5kHyQVMXrJhqEBZpMkfPbvoI7AIAiUADMikmzITJgGgXkYRJA96zvPXRuuEFdF74PGBztz9uxuj+3eD34Ic1Ng5a6N94tEjfy+DEygBYAAm3ZSVMAkA9VBEkHy6pJXEkp9+YUy/74tDP2uUlv7UC4s+AoskUALAIpl0U0bCJABUWxmC5EImLnp2zH319ujccHcuz8/a5KufG2PPOanoY7BISZqmQ3wfEwA0h0k3ZSRMAkA1lTVILqT30M547B0fjZieO/IPF6h14opY8T8ujWTJeNFHYZHcoASAPph0UzbCJABUS5WC5NO1jlsey37u/Jj+k2sKO0M/lv2bi8XJihIoAeAITLopE2ESAKqhykFyIRMvPzPmb7g75r++teijLGjJT70gxs9aU/QxGJBACQCHYNJNmQiTAFBudQuST5ckSUz98iti5/RcdG4s1+dRTrzyrFjyLzcWfQyG4DMoAWABJt2UhTAJAOVU9yB5KOnMfOx8z2ei8517ij5KRERMvOLMWPYLL4uk3Sr6KAxBoASApzHppgyESQAol6YGyYWk893Y9ftXx/x1dxZ6jsnXPj+WvvElkSRJoedgeAIlADzJpJsyECYBoBwEycNLe2nMfuo7sfsvr4uY64z03cmKJbHsLRfGxPnrR/pe8iNQAkCYdFM8YRIAiiVIDqa7bUfset8Xo3vL/SN53/iL18Wyf31htI72/6PXiUAJQOOZdFMkYRIAiiFIZift9mL209+Nmb+5PtKds7m8IzlueSx7w0ti/PzTTbprSKAEoLFMuimSMAkAoyVI5i+d7cTc17fG7FU3Rfe2BzN55tg5a2PykrNj/AWn+CKcGhMoAWgkk26KIkwCwGgIksXqbN0ec1+4OTq33B/dux+J6PWZn8bb0T7l2Bg7e01M/shzon3SylzPSTkIlAA0jkk3RRAmASBfgmR5pbOd6N71cHS2bo/ePY9EOjMf6Vw3IkkimWhHsnQi2qceG+11q6O9dlUkY+2ij8yICZQANIZJN0UQJgEgH4Ik1MdY0QcAgFEw6WbUhEkAyJYgCfUlUAJQeybdjJIwCQDZECShOQRKAGrLpJtREiYBYDiCJDSXQAlALZl0MyrCJAAMRpAEniJQAlA7Jt2MgjAJAIsjSAKHIlACUBsm3YyCMAkA/REkgX4JlADUgkk3eRMmAeDwBElgUAIlAJVn0k2ehEkAWJggCWRFoASgsky6yZMwCQAHEiSBvAiUAFSSSTd5ESYBYA9BEhgVgRKAyjHpJg/CJABNJ0gCRREoAagMk27yIEwC0FSCJFAWAiUAlWDSTdaESQCaRpAEykqgBKD0TLrJkjAJQFMIkkBVCJQAlJZJN1kSJgGoO0ESqCqBEoBSMukmK8IkAHUlSAJ1IVACUDom3WRBmASgbgRJoK4ESgBKw6SbLAiTANSFIAk0hUAJQCmYdDMsYRKAqhMkgaYSKAEonEk3wxAmAagqQRJgD4ESgMKYdDMMYRKAqhEkARYmUAJQCJNuBiVMAlAVgiRAfwRKAEbOpJtBCJMAlJ0gCTAYgRKAkTHpZhDCJABlJUgCZEOgBGAkTLpZLGESgLIRJAHyIVACkDuTbhZDmASgLARJgNEQKAHIjUk3iyFMAlA0QRKgGAIlALkw6aZfwiQARREkAcpBoAQgcybd9EOYBGDUBEmAchIoAciMSTf9ECYBGBVBEqAaBEoAMmHSzZEIkwDkTZAEqCaBEoChmXRzOMIkAHkRJAHqQaAEYGAm3RyOMAlA1gRJgHoSKAEYyM033xyve93rTLo5iDAJQFYESYBmECgBWDSTbhYiTAIwLEESoJkESgD6ZtLNQoRJAAYlSAIQIVAC0CeTbp5OmARgsQRJABYiUAJwRCbd7E+YBKBfgiQA/RAoATgkk272J0wCcCSCJACDECgBWJBJN08RJgE4FEESgCwIlAAcxKSbCGESgIMJkgDkQaAEYC+TbiKESQD2ESQBGAWBEoCIMOlGmARAkASgGAIlACbdDSdMAjSXIAlAGQiUAA1m0t1swiRA8wiSAJSRQAnQUCbdzSVMAjSHIAlAFQiUAA1k0t1MwiRA/QmSAFSRQAnQICbdzSRMAtSXIAlAHQiUAA1h0t08wiRA/QiSANSRQAnQACbdzSJMAtSHIAlAEwiUADVm0t0swiRA9QmSADSRQAlQUybdzSFMAlSXIAkAAiVALZl0N4MwCVA9giQAHEygBKgRk+5mECYBqkOQBIAjEygBasKku/6ESYDyEyQBYPEESoAaMOmuN2ESoLwESQAYnkAJUGEm3fUmTAKUjyAJANkTKAEqyqS7voRJgPIQJAEgfwIlQAWZdNeTMAlQPEESAEZPoASoEJPuehImAYojSAJA8QRKgIow6a4fYRJg9ARJACgfgRKgAky660WYBBgdQRIAyk+gBCgxk+56ESYB8idIAkD1CJQAJWXSXR/CJEB+BEkAqD6BEqCETLrrQZgEyJ4gCQD1I1AClIhJdz0IkwDZESQBoP4ESoCSMOmuPmESYHiCJAA0j0AJUAIm3dUmTAIMTpAEAARKgAKZdFebMAmweIIkAPB0AiVAQUy6q0uYBOifIAkAHIlACVAAk+5qEiYBjkyQBAAWS6AEGCGT7moSJgEOTZAEAIYlUAKMiEl39QiTAAcTJAGArAmUACNg0l0twiTAPoIkAJA3gRIgRybd1SJMAgiSAMDoCZQAOTHprg5hEmgyQRIAKJpACZADk+5qECaBJhIkAYCyESgBMmTSXQ3CJNAkgiQAUHYCJUBGTLrLT5gEmkCQBACqRqAEyIBJd7kJk0CdCZIAQNUJlABDMOkuN2ESqCNBEgCoG4ESYEAm3eUlTAJ1IkgCAHUnUAIMwKS7nIRJoA4ESQCgaQRKgEUw6S4nYRKoMkESAGg6gRKgTybd5SNMAlUkSAIAHEigBOiDSXe5CJNAlQiSAACHJ1ACHIZJd7kIk0AVCJIAAIsjUAIcgkl3eQiTQJkJkgAAwxEoARZg0l0OwiRQRoIkAEC2BEqA/Zh0l4MwCZSJIAkAkC+BEuBJJt3FEyaBMhAkAQBGS6AECJPuogmTQJEESQCAYgmUQKOZdBdLmASKIEgCAJSLQAk0lkl3cYRJYJQESQCAchMogUYy6S6GMAmMgiAJAFAtAiXQKCbdxRAmgTwJkgAA1SZQAo1h0j16wiSQB0ESAKBeBEqgEUy6R0uYBLIkSAIA1JtACdSaSfdoCZNAFgRJAIBmESiB2jLpHh1hEhiGIAkA0GwCJVBLJt2jIUwCgxAkAQDYn0AJ1IpJ92gIk8BiCJIAAByOQAnUhkl3/oRJoB+CJAAAiyFQArVg0p0vYRI4HEESAIBhCJRApZl050uYBBZy3333HRAkv/e97x3yZwVJAACORKAEKsukOz/CJLA/QRIAgDwJlEAlmXTnQ5gEIhYfJM8777y9QfIlL3mJIAkAwKIIlEClmHTnQ5iEZhMkAQAokkAJVIZJd/aESWgmQRIAgDIRKIFKMOnOljAJzSJIAgBQZgIlUGom3dkSJqEZBEkAAKpEoARKy6Q7O8Ik1JsgCQBAlQmUQCmZdGdDmIR6EiQBAKgTgRIoFZPubAiTUC+CJAAAdSZQAqVh0j08YRLqQZAEAKBJBEqgFEy6hyNMQrUJkgAANJlACRTKpHs4wiRUkyAJAAD7CJRAYUy6BydMQrUIkgAAcGgCJVAIk+7BCJNQDYIkAAD0T6AERsqkezDCJJSbIAkAAIMTKIGRMelePGESykmQBACA7AiUwEiYdC+OMAnlIkgCAEB+BEogVybdiyNMQjkIkgAAMDoCJZAbk+7+CZNQLEESAACKI1ACuTDp7o8wCcUQJAEAoDwESiBTJt39ESZhtARJAAAoL4ESyIxJ95EJkzAagiQAAFSHQAlkwqT78IRJyJcgCQAA1SVQAkMx6T48YRLyIUgCAEB9CJTAwEy6D02YhGwJkgAAUF8CJTAQk+6FCZOQDUESAACaQ6AEFsWke2HCJAxHkAQAgOYSKIG+mXQfTJiEwQiSAADAUwRKoC8m3QcSJmFxBEkAAOBQBErgsEy6DyRMQn8ESQAAoF8CJXBIJt37CJNweIIkAAAwKIESWJBJ9x7CJCxMkAQAALIiUAIHMOneQ5iEAwmSAABAXgRKYC+TbmESniJIAgAAoyJQAhFh0i1M0nSCJAAAUBSBEhqu6ZNuYZKmEiQBAICyECihwZo86RYmaRpBEgAAKCuBEhqqqZNuYZKmECQBAICqECihYZo66RYmqTtBEgAAqCqBEhqkiZNuYZK6EiQBAIC6ECihIZo26RYmqRtBEgAAqCuBEmquaZNuYZK6ECQBAICmECihxpo06RYmqTpBEgAAaCqBEmqqKZNuYZKqEiQBAAD2ECihZpoy6RYmqRpBEgAAYGECJdRIEybdwiRVIUgCAAD0R6CEmqj7pFuYpOwESQAAgMEIlFBxdZ90C5OUlSAJAACQDYESKqzOk25hkrIRJAEAAPIhUEJF1XXSLUxSFoIkAADAaAiUUDF1nXQLkxRNkAQAACiGQAkVUsdJtzBJUQRJAACAchAooSLqNukWJhk1QRIAAKCcBEooubpNuoVJRkWQBAAAqAaBEkqsTpNuYZK8CZIAAADVJFBCSdVl0i1MkhdBEgAAoB4ESiiZuky6hUmyJkgCAADUk0AJJVKHSbcwSVYESQAAgGYQKKEkqj7pFiYZliAJAADQTAIlFKzqk25hkkEJkgAAAEQIlFCoKk+6hUkWS5AEAABgIQIlFKSqk25hkn4JkgAAAPRDoIQRq+qkW5jkSARJAAAABiFQwghVcdItTHIogiQAAABZEChhRKo26RYmeTpBEgAAgDwIlJCzqk26hUmeIkgCAAAwCgIl5KhKk25hEkESAACAIgiUkJOqTLqFyeYSJAEAACgDgRIyVpVJtzDZPIIkAAAAZSRQQoaqMOkWJptDkAQAAKAKBErISNkn3cJk/QmSAAAAVJFACUMq+6RbmKwvQRIAAIA6EChhCGWedAuT9SNIAgAAUEcCJQyorJNuYbI+BEkAAACaQKCERSrrpFuYrD5BEgAAgCYSKGERyjjpFiarS5AEAAAAgRL6VrZJtzBZPYIkAAAAHEyghCMo26RbmKwOQRIAAACOTKCEwyjTpFuYLD9BEgAAABZPoIRDKMukW5gsL0ESAAAAhidQwtOUZdItTJaPIAkAAADZEyhhP2WYdAuT5SFIAgAAQP4ESnhS0ZNuYbJ4giQAAACMnkBJ4xU96RYmiyNIAgAAQPEEShqtyEm3MDl6giQAAACUj0BJYxU16RYmR0eQBAAAgPITKGmcoibdwmT+BEkAAACoHoGSRili0i1M5keQBAAAgOoTKGmMUU+6hcnsCZIAAABQPwIltTfqSbcwmR1BEgAAAOpPoKTWRjnpFiaHJ0gCAABA8wiU1NaoJt3C5OAESQAAAECgpHZGNekWJhdPkAQAAACeTqCkVkYx6RYm+ydIAgAAAEciUFIbeU+6hckjEyQBAACAxRIoqby8J93C5KEJkgAAAMCwBEoqLc9JtzB5MEESAAAAyJpASWXlNekWJvcRJAEAAIC8CZRUTl6TbmFSkAQAAABGT6CkUvKYdDc5TAqSAAAAQNEESioj60l3E8OkIAkAAACUjUBJ6WU96W5SmBQkAQAAgLITKCm1LCfdTQiTgiQAAABQNQIlpZXVpLvOYVKQBAAAAKpOoKR0spp01zFMCpIAAABA3QiUlEoWk+46hUlBEgAAAKg7gZLSGHbSXYcwKUgCAAAATSNQNtCOXWnccFfEDd+P2HxPxOO7I2bmI9I0Ysl4xNSSiDPXRJxzSsQ5p0accHSS63mGnXRXOUwKkgAAANRd79Hp6N6xPTp3bI/u3Y9EOjMfMdeNSCKS8bFIlk1E+5Rjo3366mivWx2t5ZNFH5kRS9I0TYs+BPlK0zSuvzPiz78U8ZVbI76/fXG//6SVEeetj3jjhREXnRXRamUXLIeZdFcxTAqSAAAA1F3aS6PznXti9vM3R+fW+yN9ZNeifn/rhBUxdvaamPyRs6L9rOMjSfK9OEXxBMoam55N42+ui/jwFyNuvCubZ647PuLNF0X87AURq5YP9x8Qg066qxQmBUkAAACaovfETMxdc2vMXrU5evc/lskz2+tWx+QlZ8fES9dHMjmeyTMpH4Gyhnq9ND58TcR/+UTEjul83rFkPOJtl0T8xmsiJscXFyoHnXRXIUwKkgAAADRNOt+Nmb+5Pmb+/oY90+0cJMsnY8nPbIzJS86OJMNlJ+UgUNbM97en8bY/2zPlHoWznhHx/jdHnHNqf//hMMiku8xhUpAEAACgyTpbt8eu930hej94ZCTvG9uwJpZdfnG0T1gxkvcxGgJlTaRpGh/+YsR//JuIXbOjfXe7FfFrr474zddGTIwdOlQudtJdxjApSAIAAMBTtya/GTOf+HZEb8RpaclYLH39S/bcpvT5lLUgUNZAp5vG2/884q++Vuw5fvjMiL94W8RRSw/8D4fFTrrLFCYFSQAAADhQunsudv73z0TnpnsLPcfERc+OZZdfFEm7Veg5GJ5AWXFznTTe/KcRn/xW0SfZ40XrIv7mVyNWTu2JlIuZdJchTAqSAAAAcGi9nbOx8z9/Mrq3P1j0USIiYvy802LqV18ZyXi76KMwBIGywrq9NN7ygYhP/FPRJznQxtMjPvHOiL/96JV9TbqLDJOCJAAAAPQn3T0fT/z230f3ew8UfZQDjJ+/PqZ+5RVuUlaYQFlhv/EXaXzwC0WfYmEnxE3xvY88PyL2/MtroUl3EWFSkAQAAIDFS3tp7Pyv/xCdG+4u+igLmvyxDbHssguLPgYDGiv6AAzmqhvLGycjIh6IDTFx1ttjbst7D5p0jzJMCpIAAAAwvNlPfae0cTIiYvbTN8X4Dz0zxl9wStFHYQBuUFbQjuk0XvIfIrbtGO454+00fvwF3fiJF3Ti2SelcdxRaTw2HXH3I6341I3t+Ni1Y/HorsG/DSvtTMd/PP+z8Y5f/MmIGE2YFCQBAAAgW91tO+Lxd348Yq4z2AOSJJKTj47ktOMiOe3YPf+3dlUkY3s+N7J38/3Refdnhz5ncsxUrPj9n4nW1OTQz2K03KCsoH/318PHydOP78X7fm42nrv2wD695OiIE47uxYtO68XlL5+Pd/zlZHxhy2AfNJuMLYurH/3n8bq77433vCefMClIAgAAQH7SXhrT7/viwHEyecHaGPull0YyOZ7xyQ6WPrIrdv/512LqrRfn/i6yJVBWzBduSuMvvzrcM05a2YuPvm02Tlq5J072ehHf2NqK7z+UxHHLIy58djeWTkSsXhHx4bfMxhuumIyvfG+wSPn12yKe/er3xO6b/njvPzZMmBQkAQAAYHRmr7opOrfcP/DvT5ZNjCROPmXui7fExAXrY/yctSN7J8MTKCvmdz81/DP+6I1ze+Pk3Q8n8fMfnIyb79v3TVerptL4kzfNxoXP7sXEWMQVPz8b5/+npfH47sHm3mNnvSNi8/tiatmSRYdJQRIAAACKkXZ7MfN3387mWTt2R3rnQ9G78+FI73woWhvWRPuSszJ59tPNfOJbAmXFCJQVcvO9aXz11uGe8fKzuvGS9b2IiJjtRLzpA5Nxy7bWAT/z6K490fJz/3YmTj0ujVVTEf/mFfPx7k9ODPTO1vJnxqW/8uH443/36iOGSUESAAAAymH++rsifXjXUM/offfemPu1v4145GnPWZfNl+MupLP5vuje/Ui01x6T2zvIlkBZIR+5ZvhnvOnC+b1//+PXtg+Kk0/ZPZfE//jUePzxG/d8ZuTrL+jE73xqPLq9wW5Rzq99Y6xeffDvFSQBAACgnGY/c9PwD3lsZvhnDGD2s5tj2WUXFvJuFk+grIgndqfx118b7hnLJtK44Ize3l9/7NrD/+X/hxva8d8ujThqScSqqYgXn96Lr9422GdRfmFzxNYH0lja3SZIAgAAQMl179sRne/cU/QxBjZ7za2x9F+9OJKlo/v8SwYnUFbEZ26MeGLI/9HhRet6seTJf1/umo244QcL3558ylwniW99vxUvO3NP1LzgjO7AgTIi4od/9o/ivs//yiH/eUESAAAAymHuy7cVfYTh7J6P+eu/HxMvfVbRJ6EPAmVFXH/n8M941gn7bk/ecl+rr7n2d+/eFyjXn5AO9f4drXUH/FqQBAAAgHLq3P5g0UcYWue2BwXKihAoK+LGu4Z/xunH7wuM9zzS32dJ3vfovp9bv1/gHET7uBfG+RdcEBcLkgAAAFBaaZpG947tRR9jaHX4MzSFQFkB3V4a3/nB8M9ZNbUvUG5/or9A+eDj+35u5bLhblC2lp4YH//7L8eaVYN90Q4AAACQv/SRXZE+trvoYwytc+dDkfbSSFo6RNkd/kMIKYXb79/zmZHDmprcFxhn5g/zg/uZmd/3b+KpyeHPcEMGN0EBAACA/HS21uTm4cx89LbtKPoU9EGgrIA7M/rPhcn97svOd/v7PXOdfX9/SQZffLX1geGfAQAAAOSnd/9jRR8hM91t9fmz1JmJdwXMzGXznNn9YuN4n1/GPbHfv0L6vXV5OB/+s/8VV7/v48M/CAAAAMjFj7dOj58aO6PoY2Sj3xtaFEqgrIAswmBExK7ZfXPtfm9DLhnfNwvPYmZ+y23fjxu/9ffDPwgAAADIxXPPek3Ec+oRKNP9p6GUlol3BYz1edvxSB7dtS9Qrj6qvy+8OX7Fvp/bMZ3Bh8r2MqqtAAAAQC46aa/oI2QmaUtfVeAGZQVk8dmPERFbH9wXGE8+pr9AuWbVvp+7/YHh/039H/79b8YvvOztQz8HAAAAyEdy1S0Rf3dT0cfIxoT0VQX+KlXAcUdl85zb9guMZ67pRbuVRrd3+FuRz1277381uf2B4W9QnnLiVKxevXzo5wAAAAD5mD3poZgu+hAZaa1YUvQR6IN7rhWwYW1EksG6+pt3tPZ+nuXUZMTzn3n4K9sTY2m84NR9P/PV7w2/NX/+KUM/AgAAAMhRe93qoo+QjSSifcpxRZ+CPgiUFbB8SRLPOnH450zPJfHV7+37S37pxsN/k9WPPa8bRz35PzQ8uiviG1uH+5fL5FjEmScN9QgAAAAgZ+21qyLGM/pCjAK1nrEqkqUZfW4euRIoK+KcjG4e/s8v7/s35qUv7sQZJy58i3LJeBq/8ep9X2jzv742dsQ5+JFsWBsxPpbBVVAAAAAgN8lYO9qnHFv0MYY2VpeboA0gUFbEOadm85zPb2nHN27f85d9cizif/7ibJx50oGRctWyND7yr2fjtOP3fEHOo7si3v+54f8Xh6wiKwAAAJCvsdOrH/fa68y7qyJJ07S/r3OmUN/blsbG38rmWSet7MUn3zkbJx695y99txfxjdtbcdfDSRy7POLCM7qxbHLPz853I17/J5PxlQw+f/KvfzniVc93gxIAAADKbu6b349d7/50Js8ae8fLI1YuO+AfS45eGsnKpRERkc7MR/rAEwf9vs7vfT5ix+6B37viD/9ltJ+xauDfz+j4Fu+KOOOkJH74zDT+8Zbhn7VtRysu/aPJeP+bZmPDyWm0WxEXnNGLC572cw89EfGOv8gmTq49NuKVzx36MQAAAMAIjP/QM6N13PLoPbRz6Gcla1ZGsnr5of/5JeORnHLMwf/E2ODD37HnPkOcrBCBskIuuzgyCZQREVsfbMVrfndJ/MQLuvETL+zEs09M47gVaTw+HfGDh1vx6e+046+/MRaP7srmxuObL4pot9yeBAAAgCpI2q2Y+NGzY+Yvry36KAOZvGRD0UdgEUy8K2S+k8bz/u+IbTuKPsniTIxFbP6diNUrBEoAAACoit5j0/HYL14Z0Vn4C3bLKjlmKo7+k9dH0vbVK1Xhr1SFjI8l8eaLij7F4v2LjeIkAAAAVE3r6GUxcf76oo+xaJOXnC1OVoy/WhXztksinnVi0afo38plEf/PTxV9CgAAAGAQS9/w4kiWTxZ9jL611qyMJa95ftHHYJEEyopZOpHE+34+IqnIhcT3/GzEiSsrclgAAADgAK1VU7H0zS8t+hj9aSUx9baLI5n0lStVI1BW0Mb1Sbz1lUWf4sh+7JyI151X9CkAAACAYUxc+KwYf9EpRR/jiCZf87wYO6NCs1P2Eigr6t//ZMQZJxV9ikNbNRXx+2+ISKpy1RMAAABYUJIksewXXlbqqXfrGStj6c9sLPoYDEigrKilE0l87FciTjy66JMcbNlExEd/2bQbAAAA6qJ1zFQs/7evjijhfDpZtSyW/7t/ZtpdYQJlhZ26Oon//Y6IY5YXfZJ9Jsci/uJte2boAAAAQH2MnXliLP/NV0WMt4s+yl7JUUviqHe9NtonrCj6KAwhSdM0LfoQDOeW+9L4yd+N2Laj2HMsn4z4q1+OuPBMcRIAAADqav6me2Pnuz8dMTNf6DmSY6b2xMmTVxV6DoYnUNbEXQ+l8fNXRHzrzmLef9rxEX/2ixHnnCpOAgAAQN11bn8wdv3B1dG7//FC3t9ef3xMveOV0T7ezck6EChrpNNN44+uivhv/ydirjOadyZJxC++IuJd/yJi2aQ4CQAAAE2RzszH7r+8NmY/9d3RvXSsFUt/ZmNM/vjzI2n75MK6EChr6OZ703jrn+V/m/K04yP++E0RFzxbmAQAAICmmt9yX0y/74vReyDf25Tt9cfH1FsvjvbaY3J9D6MnUNZUp5vG314X8eEvRly3Ndtnn7km4s0XRbz+pW5NAgAAABHp7HzMfuGWmL1qc/TueTTTZ7fPOCEmX7UhJi5Y79ZkTQmUDXDjXWl85JqIj38jYnpusGeMtSNe+4KIyy6OuOCMiCQRJgEAAIADpWkanc33xexVm2P+ujsjur3BHjQ5FhMXPismf/TsGFu3OttDUjoCZYPsnEnj29+PuOGuiBue/NutDyz8sycfE3HOqRHnnLLn/15wWsQxy0VJAAAAoD+9J2aie/uD0blje3S3bo/uHduj99DOBX+2ddLR0V63OsZOX/3k3x4fydLxEZ+YogiUDTc9m8au2YjdcxFpRCwdj1g6EXHUUjESAAAAyFa6ey7S2U6kc52IJIlkoh3JkvFIJsXIJhMoAQAAAIDC+GRRAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABRGoAQAAAAACiNQAgAAAACFESgBAAAAgMIIlAAAAABAYQRKAAAAAKAwAiUAAAAAUBiBEgAAAAAojEAJAAAAABTm/wfiLAzgdQQAHQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 499, + "width": 660 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Reverse 11110 to convert quantum result to classical solution\n", + "solution = [0, 1, 1, 1, 1]\n", + "\n", + "mpl_draw(\n", + " G,\n", + " pos=rx.bipartite_layout(G, {0}),\n", + " with_labels=True,\n", + " node_color=[\"#EE5396\" if kk else \"#0F62FE\" for kk in solution],\n", + " font_color=\"#F4F4F4\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "071d7e49", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.21.1'" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "f3f06a12", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.1'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.11.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}