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| 1 | { |
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| 2 | "cells": [ |
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| 3 | { |
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| 4 | "cell_type": "code", |
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| 5 | "execution_count": 167, |
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| 6 | "metadata": { |
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| 7 | "colab": { |
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| 8 | "base_uri": "https://localhost:8080/", |
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| 9 | "height": 0 |
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| 10 | }, |
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| 11 | "id": "TS6zWfrlNVpz", |
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| 12 | "outputId": "89232223-f6d8-4123-980f-de9259a97a71" |
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| 13 | }, |
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| 14 | "outputs": [ |
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| 15 | { |
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| 16 | "output_type": "stream", |
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| 17 | "name": "stdout", |
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| 18 | "text": [ |
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| 19 | "Time in seconds since beginning of run: 1693414138.8077796\n", |
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| 20 | "Wed Aug 30 16:48:58 2023\n" |
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| 21 | ] |
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| 22 | } |
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| 23 | ], |
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| 24 | "source": [ |
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| 25 | "# This cell is added by sphinx-gallery\n", |
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| 26 | "# It can be customized to whatever you like\n", |
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| 27 | "%matplotlib inline\n", |
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| 28 | "# !pip install pennylane\n", |
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| 29 | "import time\n", |
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| 30 | "seconds = time.time()\n", |
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| 31 | "print(\"Time in seconds since beginning of run:\", seconds)\n", |
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| 32 | "local_time = time.ctime(seconds)\n", |
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| 33 | "print(local_time)" |
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| 34 | ] |
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| 35 | }, |
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| 36 | { |
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| 37 | "cell_type": "markdown", |
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| 38 | "metadata": { |
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| 39 | "id": "x7Q73jKsNVp0" |
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| 40 | }, |
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| 41 | "source": [ |
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| 42 | "An equivariant graph embedding\n", |
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| 43 | "==============================\n", |
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| 44 | "\n", |
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| 45 | "::: {.meta}\n", |
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| 46 | ":property=\\\"og:description\\\": Find out more about how to embedd graphs\n", |
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| 47 | "into quantum states. :property=\\\"og:image\\\":\n", |
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| 48 | "<https://pennylane.ai/qml/_images/thumbnail_tutorial_equivariant_graph_embedding.png>\n", |
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| 49 | ":::\n", |
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| 50 | "\n", |
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| 51 | "::: {.related}\n", |
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| 52 | "tutorial\\_geometric\\_qml Geometric quantum machine learning\n", |
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| 53 | ":::\n" |
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| 54 | ] |
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| 55 | }, |
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| 56 | { |
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| 57 | "cell_type": "markdown", |
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| 58 | "metadata": { |
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| 59 | "id": "7wijfDxKNVp1" |
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| 60 | }, |
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| 61 | "source": [ |
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| 62 | "A notorious problem when data comes in the form of graphs \\-- think of\n", |
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| 63 | "molecules or social media networks \\-- is that the numerical\n", |
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| 64 | "representation of a graph in a computer is not unique. For example, if\n", |
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| 65 | "we describe a graph via an [adjacency\n", |
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| 66 | "matrix](https://en.wikipedia.org/wiki/Adjacency_matrix) whose entries\n", |
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| 67 | "contain the edge weights as off-diagonals and node weights on the\n", |
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| 68 | "diagonal, any simultaneous permutation of rows and columns of this\n", |
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| 69 | "matrix refer to the same graph.\n", |
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| 70 | "\n", |
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| 71 | "{.align-center\n", |
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| 72 | "width=\"60.0%\"}\n", |
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| 73 | "\n", |
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| 74 | "For example, the graph in the image above is represented by each of the\n", |
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| 75 | "two equivalent adjacency matrices. The top matrix can be transformed\n", |
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| 76 | "into the bottom matrix by swapping the first row with the third row,\n", |
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| 77 | "then swapping the third column with the third column, then the new first\n", |
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| 78 | "row with the second, and finally the first colum with the second.\n", |
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| 79 | "\n", |
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| 80 | "But the number of such permutations grows factorially with the number of\n", |
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| 81 | "nodes in the graph, which is even worse than an exponential growth!\n", |
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| 82 | "\n", |
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| 83 | "If we want computers to learn from graph data, we usually want our\n", |
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| 84 | "models to \\\"know\\\" that all these permuted adjacency matrices refer to\n", |
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| 85 | "the same object, so we do not waste resources on learning this property.\n", |
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| 86 | "In mathematical terms, this means that the model should be in- or\n", |
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| 87 | "equivariant (more about this distinction below) with respect to\n", |
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| 88 | "permutations. This is the basic motivation of [Geometric Deep\n", |
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| 89 | "Learning](https://geometricdeeplearning.com/), ideas of which have found\n", |
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| 90 | "their way into quantum machine learning.\n", |
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| 91 | "\n", |
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| 92 | "This tutorial shows how to implement an example of a trainable\n", |
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| 93 | "permutation equivariant graph embedding as proposed in [Skolik et al.\n", |
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| 94 | "(2022)](https://arxiv.org/pdf/2205.06109.pdf). The embedding maps the\n", |
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| 95 | "adjacency matrix of an undirected graph with edge and node weights to a\n", |
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| 96 | "quantum state, such that permutations of an adjacency matrix get mapped\n", |
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| 97 | "to the same states *if only we also permute the qubit registers in the\n", |
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| 98 | "same fashion*.\n", |
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| 99 | "\n", |
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| 100 | "::: {.note}\n", |
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| 101 | "::: {.title}\n", |
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| 102 | "Note\n", |
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| 103 | ":::\n", |
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| 104 | "\n", |
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| 105 | "The tutorial is meant for beginners and does not contain the\n", |
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| 106 | "mathematical details of the rich theory of equivariance. Have a look [at\n", |
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| 107 | "this demo](https://pennylane.ai/qml/demos/tutorial_geometric_qml.html)\n", |
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| 108 | "if you want to know more.\n", |
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| 109 | ":::\n", |
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| 110 | "\n", |
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| 111 | "Permuted adjacency matrices describe the same graph\n", |
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| 112 | "===================================================\n", |
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| 113 | "\n", |
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| 114 | "Let us first verify that permuted adjacency matrices really describe one\n", |
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| 115 | "and the same graph. We also gain some useful data generation functions\n", |
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| 116 | "for later.\n", |
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| 117 | "\n", |
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| 118 | "First we create random adjacency matrices. The entry $a_{ij}$ of this\n", |
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| 119 | "matrix corresponds to the weight of the edge between nodes $i$ and $j$\n", |
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| 120 | "in the graph. We assume that graphs have no self-loops; instead, the\n", |
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| 121 | "diagonal elements of the adjacency matrix are interpreted as node\n", |
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| 122 | "weights (or \\\"node attributes\\\").\n", |
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| 123 | "\n", |
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| 124 | "Taking the example of a Twitter user retweet network, the nodes would be\n", |
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| 125 | "users, edge weights indicate how often two users retweet each other and\n", |
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| 126 | "node attributes could indicate the follower count of a user.\n" |
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| 127 | ] |
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| 128 | }, |
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| 129 | { |
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| 130 | "cell_type": "code", |
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| 131 | "execution_count": 168, |
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| 132 | "metadata": { |
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| 133 | "colab": { |
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| 134 | "base_uri": "https://localhost:8080/", |
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| 135 | "height": 0 |
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| 136 | }, |
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| 137 | "id": "RD3UyP_ONVp2", |
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| 138 | "outputId": "067100c4-e388-4fe1-f053-dffe91869d2d" |
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| 139 | }, |
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| 140 | "outputs": [ |
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| 141 | { |
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| 142 | "output_type": "stream", |
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| 143 | "name": "stdout", |
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| 144 | "text": [ |
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| 145 | "[[0.23 0.1 0.43]\n", |
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| 146 | " [0.1 0.71 0.46]\n", |
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| 147 | " [0.43 0.46 0.24]]\n" |
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| 148 | ] |
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| 149 | } |
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| 150 | ], |
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| 151 | "source": [ |
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| 152 | "import numpy as np\n", |
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| 153 | "import networkx as nx\n", |
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| 154 | "import matplotlib.pyplot as plt\n", |
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| 155 | "\n", |
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| 156 | "\n", |
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| 157 | "def create_data_point(n):\n", |
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| 158 | " \"\"\"\n", |
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| 159 | " Returns a random undirected adjacency matrix of dimension (n,n).\n", |
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| 160 | " The diagonal elements are interpreted as node attributes.\n", |
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| 161 | " \"\"\"\n", |
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| 162 | " mat = np.random.rand(n, n)\n", |
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| 163 | " A = (mat + np.transpose(mat))/2\n", |
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| 164 | " return np.round(A, decimals=2)\n", |
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| 165 | "\n", |
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| 166 | "A = create_data_point(3)\n", |
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| 167 | "print(A)" |
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| 168 | ] |
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| 169 | }, |
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| 170 | { |
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| 171 | "cell_type": "markdown", |
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| 172 | "metadata": { |
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| 173 | "id": "cuOQH6WINVp2" |
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| 174 | }, |
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| 175 | "source": [ |
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| 176 | "Let\\'s also write a function to generate permuted versions of this\n", |
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| 177 | "adjacency matrix.\n" |
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| 178 | ] |
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| 179 | }, |
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| 180 | { |
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| 181 | "cell_type": "code", |
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| 182 | "execution_count": 169, |
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| 183 | "metadata": { |
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| 184 | "colab": { |
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| 185 | "base_uri": "https://localhost:8080/", |
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| 186 | "height": 0 |
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| 187 | }, |
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| 188 | "id": "i9RRz3GrNVp2", |
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| 189 | "outputId": "7eb0cf27-79e5-4995-c4bf-119854171dcb" |
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| 190 | }, |
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| 191 | "outputs": [ |
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| 192 | { |
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| 193 | "output_type": "stream", |
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| 194 | "name": "stdout", |
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| 195 | "text": [ |
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| 196 | "[[0.71 0.46 0.1 ]\n", |
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| 197 | " [0.46 0.24 0.43]\n", |
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| 198 | " [0.1 0.43 0.23]]\n" |
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| 199 | ] |
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| 200 | } |
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| 201 | ], |
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| 202 | "source": [ |
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| 203 | "def permute(A, permutation):\n", |
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| 204 | " \"\"\"\n", |
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| 205 | " Returns a copy of A with rows and columns swapped according to permutation.\n", |
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| 206 | " For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n", |
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| 207 | " \"\"\"\n", |
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| 208 | "\n", |
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| 209 | " P = np.zeros((len(A), len(A)))\n", |
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| 210 | " for i,j in enumerate(permutation):\n", |
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| 211 | " P[i,j] = 1\n", |
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| 212 | "\n", |
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| 213 | " return P @ A @ np.transpose(P)\n", |
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| 214 | "\n", |
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| 215 | "A_perm = permute(A, [1, 2, 0])\n", |
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| 216 | "print(A_perm)" |
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| 217 | ] |
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| 218 | }, |
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| 219 | { |
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| 220 | "cell_type": "markdown", |
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| 221 | "metadata": { |
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| 222 | "id": "nD0puQC9NVp2" |
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| 223 | }, |
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| 224 | "source": [ |
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| 225 | "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n", |
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| 226 | "and plot them, we see that they are identical as claimed.\n" |
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| 227 | ] |
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| 228 | }, |
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| 229 | { |
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| 230 | "cell_type": "code", |
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| 231 | "execution_count": 170, |
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| 232 | "metadata": { |
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| 233 | "colab": { |
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| 234 | "base_uri": "https://localhost:8080/", |
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| 235 | "height": 487 |
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| 236 | }, |
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| 237 | "id": "p5NZCKEfNVp2", |
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| 238 | "outputId": "e3fd5d80-0eba-4f72-c895-66e07da93537" |
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| 239 | }, |
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| 240 | "outputs": [ |
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| 241 | { |
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| 242 | "output_type": "display_data", |
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| 243 | "data": { |
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| 244 | "text/plain": [ |
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| 245 | "<Figure size 640x480 with 2 Axes>" |
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| 246 | ], |
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| 247 | "image/png": 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tGm7fvo0VK1bAxMREI/uQyWQcZ0evZNDFzsTEBB4eHlpf66d169Y4ffo0Hjx4AF9fX1y6dEmr+yciIjEuXryImTNnYuLEiahSpYpG9yVJEiIiIjj0h15g0MUO0OySJ29Sq1YtREZGokiRIvD398exY8e0noGIiLQnOzsbffr0QaVKlTB+/HiN70+SJCQnJ+Pvv//W+L5IfxhFsVPn3ScKo1SpUggJCYGvry9atGiBNWvWCMlBRESa99NPP+HcuXNYvny5Vm43WbduXZiZmXGcHb3AKIrdrVu3oFQqhey/SJEi2Lt3L3r16oVevXrhq6++EpaFiIg04+bNm/jqq68wYsQI+Pj4aGWfVlZWqF27NsfZ0QtMRQfQNIVCgdTUVMTExMDV1VVIBjMzMwQHB8PT0xMTJkzA7du3sXz5clhYWAjJQ0RE6qNUKtGvXz+4ublh6tSpWt23JEnYtWuXVvdJus3gz9h5enoC0M6SJ28ik8kwfvx4bN68GVu3bkXz5s0RFxcnNBMREb2/FStW4Pjx4wgODoaNjY1W9y1JEm7fvo1Hjx5pdb+kuwy+2Hl4eAAQX+zyfPzxxzh69CguXboESZJ0JhcRERXew4cPMXr0aPTq1QtNmzbV+v4lSQIAhIeHa33fpJsMvtjZ2dmhWLFiwiZQvIq/vz/Cw8ORk5MDX19fREREiI5ERETvYOjQobC0tMScOXOE7N/d3R1lypThBArKZ/DFDhC35MmblC9fHuHh4ahQoQIaNWqE7du3i45ERESFsH37duzcuRMLFy6Ek5OTsBz+/v6cQEH5WOwEcnZ2xpEjR9C+fXt06tQJc+bM4YxZIiI9EBcXhyFDhqB9+/bo2LGj0CySJOGPP/5Aenq60BykG4yi2Hl6eupksQMAS0tLbNiwAePHj8fo0aMxZMgQZGdni45FRERvMHr0aKSnp2PRokWQyWRCs0iShKysLPzxxx9Cc5BuMIpip1Ao8ODBA539NCOXyzF9+nQEBwcjODgY7dq1Q3JysuhYRET0CkeOHMGqVaswe/ZsuLu7i46D6tWrw8bGhpdjCYARFTsAuH37tuAkb9avXz/8+uuvOH36NOrXr48HDx6IjkRERM9JSUlB//790ahRI/Tt21d0HACAqakpfHx8OIGCABhZsdPVy7HPa9GiBUJCQhAbGwtfX1/8+eefoiMREdG/Jk+ejEePHiE4OFj4Jdjn5U2g4DhtMopi5+7uDnNzc70odgBQo0YNREZGolixYggICMDBgwdFRyIiMnpnzpzBvHnzMGXKFJQrV050nBdIkoQnT57o1NJeJIZRFDsTExN4eHjoTbEDVGX01KlTaNCgAVq3bo1ly5aJjkREZLQyMzPRp08f1KpVCyNHjhQd5yW+vr4AwHF2ZBzFDtDdJU/exNbWFrt27cKAAQPQv39/TJgwAbm5uaJjEREZnZkzZ+Kff/7BihUrYGqqe7dZd3BwQNWqVVnsCLr37tQQhUKBEydOiI5RaKampli4cCE8PT0xevRo3L59G6tXr4alpaXoaERERuHy5cuYOnUqxo4di5o1a4qO81qSJHECBRnfGTt9HFgqk8kwatQobN26Fbt370bTpk0RGxsrOhYRkcHLyclB3759oVAoMHnyZNFx3sjf3x+XLl1CQkKC6CgkkFEVu7S0NDx+/Fh0lHfWsWNHHD9+HNeuXYOfnx+uX78uOhIRkUFbvHgxwsPDsWzZMp2/UiJJEpRKJSIjI0VHIYGMpth5enoC0I8lT97E19cXERERMDExgZ+fH0+7ExFpyJ07dzBhwgQMHjwY9evXFx3nrcqVKwdnZ2eOszNyRlPsPDw8AOh/sQNUZx/DwsJQrVo1NGnSBL/88ovoSEREBkWpVGLAgAFwdHTEjBkzRMcpEJlMBkmSWOyMnNEUO1tbW7i4uBjMGj9OTk44ePAgOnXqhC5duuD777/Xy/GDRES6aP369Th48CCWLl2KIkWKiI5TYP7+/oiIiOA9x42Y0cyKBfRzyZM3sbCwwNq1a6FQKDBhwgTcvHkTixcvhpmZmehoRER6KyYmBiNGjEDXrl3RunVr0XEKRZIkJCcn4++//4aXl5foOCSA0ZyxAwyv2AGqU+/ffvstVq1ahdWrV6NNmzZISkoSHYuISG8NHz4cMpkM8+bNEx2l0OrUqQMzMzNejjViRlXsPD09Da7Y5enVqxd+++03REZGIiAgAPfu3RMdiYhI7+zduxebN2/GvHnzUKxYMdFxCs3Kygq1a9dmsTNiRlXsFAoFHj58iLS0NNFRNKJJkyYICwtDUlISfHx8cO7cOdGRiIj0RmJiIgYNGoRWrVrhk08+ER3nnXGhYuNmdMUOAG7fvi04ieZUqVIFERERKFGiBBo0aIBff/1VdCQiIr0wfvx4JCYmYunSpZDJZKLjvDN/f39ERUXh4cOHoqOQAEZZ7Az1cmweNzc3nDhxAk2bNkXbtm2xePFi0ZGIiHTaqVOnsHTpUnz//fcoXbq06Djvxc/PDwAQHh4uOAmJYFTFzt3dHRYWFgZf7ADAxsYG27dvx7BhwzBkyBCMHj0aubm5omMREemctLQ09O3bF/7+/hg0aJDoOO/N3d0dZcuW5Tg7I2VUy53I5XJ4eHgYRbEDABMTE/z444/w8PDAiBEjcPv2baxbtw7W1taioxER6YwpU6bgzp072LNnD+RywzjfwYWKjZdhvIMLwRCXPHmbYcOGYdeuXfjtt9/QuHFjxMTEiI5ERKQTzp8/j9mzZ2Py5MmoVKmS6DhqI0kS/vjjD4OdLEivZ5TFzlDuPlEYbdu2xcmTJxEVFQVfX1/8888/oiMREQmVnZ2NPn36oGrVqhg7dqzoOGrl7++PrKws/PHHH6KjkJYZZbG7deuWUd5+q27duoiMjIS1tTX8/Pxw8uRJ0ZGIiISZM2cOLl68iBUrVsDc3Fx0HLWqVq0abG1teTnWCBllsUtPT0d0dLToKEKUKVMGISEhqFOnDpo1a4b169eLjkREpHXXr1/HN998g5EjR6Ju3bqi46idqakpfHx8WOyMkNEVO09PTwCGv+TJmzg4OGD//v3o3r07evTogalTpxrlGUwiMk65ubno168f3N3dMWXKFNFxNCZvAgV/vxsXoyt2Hh4eAIy72AGAubk5VqxYgWnTpuGrr75C7969kZmZKToWEZHGLV++HCdPnsSyZcsMepUASZLw5MkT3LhxQ3QU0iKjK3Y2NjZwdXU1ygkU/yWTyTBx4kSsX78eGzduRKtWrZCQkCA6FhGRxjx48ABjxoxBnz590LhxY9FxNMrX1xcymYyXY42M0RU7wDiXPHmTbt264dChQzh//nz+rWiIiAyNUqnE4MGDYW1tjdmzZ4uOo3EODg6oWrUqi52RYbEjAEBgYCDCw8ORnp4OX19f/P7776IjERGp1datW7Fnzx4sWrQIjo6OouNoBRcqNj5GWew8PT1Z7F6hYsWKiIiIgIeHBwIDA7F7927RkYiI1OLp06f4/PPP0bFjR3To0EF0HK2RJAmXLl3iMBsjYpTFTqFQ4NGjR0hNTRUdRecUK1YMx44dQ6tWrRAUFIR58+aJjkRE9N5GjRqFzMxMLFy4UHQUrfL394dSqURERIToKKQlRlvsAOD27duCk+gmKysrbNmyBaNHj8aIESMwfPhw5OTkiI5FRPRODh48iLVr12LOnDlwc3MTHUerPD09UaxYMV6ONSJGXex4Ofb15HI5Zs2ahcWLF2PhwoXo0KEDUlJSRMciIiqU5ORkDBgwAE2aNMFnn30mOo7WyWQyjrMzMkZZ7IoXLw4LCwsWuwIYNGgQ9u7di6NHjyIwMBBxcXGiIxERFdikSZMQExOD4OBgyGQy0XGEkCQJkZGRyM7OFh2FtMAoi51cLufM2EL44IMPcPr0aZiZmcHc3LxAq5jzFwgRiXbx4kXMnz8f06ZNy79SY4wkSUJycjL++usv0VFIC0xFBxCFxa5watWqhVOnTkEmk73xU++hQ4dw6NAhxMfHo2TJkvj222+1mJKISEWpVKJKlSqYM2cOhg0bJjqOUHXr1oWZmRnCwsJQq1Yt0XFIw4zyjB2gKna8+0ThmJmZwdT09Z8Fpk+fjgEDBuDYsWNwcnLC1q1b0bBhQ84+JiKtk8lkMDMzw8iRI2FiYiI6jlCWlpaoU6cOx9kZCaMudrdv30Zubq7oKAZh9erVmDRpEoYPH47Dhw9j9uzZ2Lt3L54+fYo//vhDdDwiIqPGCRTGw6iLXXp6OqKjo0VH0Xs3btzA4MGDMXHiRAwePBhFixYFoJpmHxMTg3PnzglOSERk3CRJQlRUFB4+fCg6CmmY0RY7T09PAFzyRB169+4NX19fjBo1Cubm5vmPHzp0CCYmJvD29haYjogMUUJCAs6ePYtffvkFjx49AoACTewyVpIkAQDP2hkBoy12Hh4eAFjs3tdff/2FhIQEDB06FI6Ojvm/WB8+fIgdO3agatWqKFasmOCURGRoOnfujH79+qFr165o2rQpnj59arTLmRRE8eLF4eHhwWJnBIy22FlbW8PNzY0TKN5TTk4Orl+/nr+au0wmQ0pKCtatW4eQkBB06NAB5cqVE5ySiAxJ9+7dkZGRgbVr1yIhIQFpaWmIjIxEYmIiMjIyuNzSa3CcnXEw2mIHcMkTdbC3t0fVqlURGxub/9js2bOxa9cuBAYGYtCgQQBefYmEl02IqLAOHjyIY8eO4eeff0aNGjVQpEgR+Pv7Y8mSJahcuTKaN2+OWbNmITk5WXRUnSNJEs6dO4e0tDTRUUiDWOxY7N6Lh4cHgoKC8PHHH6Njx46oWLEiVq5ciQYNGmD27NkAVGf1nr9Eklfo8h6LiYlBRkaG9sMTkV7JyclBREQE+vXrlz+c5tq1a9i0aRMUCgWCg4NRrVo1LFq0COfPnxecVvdIkoSsrCyuVGDgZEojPm3yzTff4Oeff84feEvv7siRIzh+/DgAoFu3bvD09ISFhQVycnIgl8tfKHZxcXF4+vQp1q1bh+vXryM8PBypqamIiIgw6tXhiejtHj9+jAcPHqB27doAgP79+0OpVGLZsmX5rylfvjz69u2LcePGiYqpk7Kzs+Ho6IhJkybx78aAGe2dJwDVGbvo6GikpqbC2tpadBy91rRpUzRt2jT/z+Hh4cjKykKDBg3yHztw4AAuXLiAlStXomzZsqhRowZq166NjIwMXL9+HY8fP2axI6I3cnV1haurKwDVGbyxY8eidOnSAICsrCxkZ2ejcuXKb1xM3ViZmprC19eX4+wMnNFfigU4M1bdEhMT8fnnn2PatGm4d+8eAODMmTNo3bo1Hj9+jM2bN+Pw4cOYM2cOkpKSEBsbi2HDhsHPz09wciLSRdevX8cvv/yS/+e8heVNTExQrlw5mJmZAVDdHSckJASRkZFo06aNkKy6Lm8ChRFfrDN4LHZgsVM3e3t7fP311+jWrRtKlSoFQLVu4Mcff4y1a9fmLwq9aNEi/PbbbwgICEC/fv3yv/7ixYuYMWMGL5ETEQCgVatWGDNmDEaPHo0HDx5ALlcdunJycgCoxuump6cjPDwcgwYNwueff46KFSuKjKyzJElCbGwsbty4IToKaYhRFzs3NzdYWlqy2GnAhx9+iE8//RSA6tN10aJFsXbtWowZMyZ/ssWePXtQo0YNjBw5EoDql3Rubi4ePHiAf/75B7Vq1cKuXbsEfhdEJFp6ejrc3d1RsWJFXLhwAUOGDMGvv/4KAHj27Fn+mae//voLkyZNgp+fHyZNmiQysk7z8fGBTCbj5VgDZtSTJwCgatWqaNKkCebPny86isFTKpWQyWRYsmQJvvjiC9ja2uLgwYOoVasWcnJy8m/UrVQqkZycjM2bN2P8+PGYMWMG+vfvLzg9EYkyZ84cxMbGwtvbGz///DPS0tLQvHlzzJgxA3v27EHjxo0BqG5vWKpUKVhYWAhOrNuqV68OPz8/BAcHi45CGmDUZ+wALnmiLXml7unTp7hy5QqqVq0KU1NTfPfdd8jOzs4vdenp6ZDJZLCzs0O/fv0wYsQIHDx4EFlZWYK/AyISpWbNmjh+/Dg++OADfPfdd6hXrx5++uknWFlZwcrKKv915cqVY6krAH9/f56xM2AsdgoF7z6hBXnLnSxfvhwHDhxA9+7d8fDhQyxYsCB/9lpubi527979wjR8d3d3HDp0CImJiUJyE5F4TZs2RalSpRAZGYk6derA3d0dKSkpKFeuHL799lssWbJEdES9IkkSLl26hISEBNFRSANY7BQK3L59O3+WFWnWZ599hn79+uHzzz8HoLp/YR65XI7q1atj/fr1qFmzJsaNG4d+/fqhW7ducHZ25iwuIiOU97u5dOnS2LRpE65evYoJEyZg2bJlmDFjBkxMTHj2qZAkSQIARERECE5CmmD0Y+z27t2Ltm3b4v79+yhRooToOEYnKioKt27dyh8jA6gGQQcFBWHo0KEwNTVF//79YW5uLjAlEYn2zz//oH///rhz5w4CAwOxdu1aAMDdu3dhZWWFYsWKCU6oP5RKJVxdXTFw4EBMmTJFdBxSM6NfwdHT0xOAaskTFjvtUiqVWLBgAaKjoxEYGJg/zq569epwcHCAmZkZhgwZIjglEemCSpUqwdnZGcnJyZg5cyYA1e+QvMWJqeBkMhn8/f0RGhoqOgppgNFfii1btiwArmUngkwmQ8+ePREZGYmuXbsiJiYGgOqMXWxsLIs2kZHLuwybd2Fp9erV+PXXX/OHcDx/q0IqHEmSEBkZiezsbNFRSM2MvthZW1ujePHinEAhSM2aNfH7778jOjoaLVq0QJMmTeDt7Y0aNWrwkziREYmNjcW5c+fw+++/49q1awBU426fHy1UpEiR/FJn5KOI3pskSUhJScFff/0lOgqpmdFfigW45IloDg4OOHXqFNavX4/k5GR07NgR7dq14xk7IiMRExODVq1aISkpCTdv3kTdunVRo0YNjBo1ClWqVHnhdQkJCahQoQLP1r2nOnXqwMzMDGFhYahVq5boOKRGRj95AgB69uyJGzducGYVEZEAAQEBcHNzw5QpU2Bra4uVK1ciJCQET58+xahRo9CjRw8AwNChQ/H7778jODgYNWrUEJxa//n5+cHDwwMbN24UHYXUiGfsoJpAcejQIdEx6A3yFjgmIsNy48YNJCcnY+LEifln57755hucPHkSa9euxaJFi2BqaoquXbvC29sbqampLHVq4u/vj23btomOQWpm9GPsANWl2MePHyMlJUV0FHqF7OxsXLp0CefPnxcdhYjUzMnJCU+fPsW+ffteeDwwMBBjx45FsWLFsGDBAiiVSvTs2ZO3wVIjSZJw584dPHjwQHQUUiMWO6iKHcCZsbpKLpdj4sSJqF+/fv7Nv4nIMDg6OuLjjz/G0aNHcfHixReeq1ixIhYtWoS//voLx44dA4D8O9XQ+/Pz8wMAhIeHC05C6sRiBxY7XSeXy7Fp0yY0a9YMbdu2xeLFi0VHIiI1kclkGDJkCB4/foxOnTrh+PHjLyzBYW9vDw8PD97+SgOKFy8ODw8Pji83MCx2ANzc3GBlZcVip8Osra2xbds2DBs2DEOGDMEXX3zB28ARGQgPDw9cuHAB1apVQ4sWLTBu3DgcP34cFy5cwLJly3D//n00b95cdEyDJEkSFyo2MDynDdUnRi55ovtMTEzw448/wtPTE8OHD0dUVBTWrVsHa2tr0dGI6D1ZWFhgx44dWLNmDSZPnoxDhw7h1q1bqFatGtasWQM7OzvREQ2Sv78/fvnlF6SlpcHKykp0HFIDLnfyr7Zt2yInJ4djuPTE3r170aVLF1SrVg179uyBq6ur6EhEpCYpKSn4+++/YWJiAjc3N5QsWVJ0JIN18eJFeHl54dSpU6hfv77oOKQGvBT7L4VCwbtP6JEPP/wQp06dwt27d+Hr64srV66IjkREamJjYwMfHx/UrVuXpU7DqlWrBltbW46zMyAsdv9SKBS4ffs2x23pkTp16iAiIgI2NjaQJAknTpwQHYmISK+YmJjA19eXxc6AsNj9S6FQIDMzEw8fPhQdhQqhTJkyCA0NRd26ddG8eXOsX79edCQiKqRnz56JjmDUJElCWFgY779rIFjs/uXp6QmAS57oI3t7e+zfvx89evRAjx49MGXKFP6CItIT2dnZaNKkCb7//nv+3Ari7++P2NhYXL9+XXQUUgMWu3+VLVsWAIudvjIzM8Py5csxbdo0fP311/jss8+QmZkpOhYRvcW8efPw+++/o2HDhrxtoCA+Pj6QyWS8HGsgWOz+ZWVlBXd3d06g0GMymQwTJ07Exo0bsWnTJrRs2ZKLmhLpsJs3b2Ly5MkYNmwYfH19RccxWvb29qhWrRqLnYFgsXsO17IzDF27dsWRI0dw4cIFSJKEqKgo0ZGI6D+USiX69+8PFxcXTJs2TXQco5c3zo70H4vdc1jsDEf9+vURHh6OjIwM+Pj44OzZs6IjEdFzVq1ahWPHjiE4OBi2trai4xg9SZJw6dIlxMfHi45C74nF7jmenp4sdgakYsWKiIiIgEKhQGBgIHbv3i06EhEBePToEUaNGoVPP/2UtwrTEf7+/gCAiIgIwUnofbHYPUehUCAmJgbJycmio5CaFCtWDMeOHUPr1q0RFBSEefPmiY5EZPSGDh0KCwsLzJ07V3QU+pdCoYCLiwsvxxoAFrvnKBQKAJwZa2isrKzwyy+/YMyYMRgxYgSGDRuGnJwc0bGIjNKOHTuwY8cOLFiwAE5OTqLj0L9kMhnH2RkIFrvnsNgZLrlcjpkzZ2Lp0qVYvHgxgoKCkJKSIjoWkVGJj4/HkCFD0LZtW3Tq1El0HPoPSZIQGRmJ7Oxs0VHoPbDYPcfV1RXW1tYsdgZswIAB2Lt3L44fP47AwEA8evRIdCQiozF69GikpqZi8eLFXLNOB/n7+yMlJQV//vmn6Cj0HljsniOTyTgz1gi0atUKISEhiI6Ohq+vLy5duiQ6EpHBO3r0KFauXInZs2ejRIkSouPQK9SuXRvm5ua8HKvnWOz+g8XOONSsWRMRERFwcHCAJEk4cuSI6EhEBis1NRX9+/dHYGAg+vbtKzoOvYalpSXq1KnDYqfnWOz+Q6FQ8O4TRqJkyZI4ffo0JElCq1atsGrVKtGRiAzSV199hYcPH2LZsmWQy3nY0WWcQKH/+BP2HwqFAlFRUZw1aSSKFCmCvXv3ok+fPujduzcmT57MG5ETqdHZs2fx448/4ttvv0X58uVFx6G3kCQJd+7cwYMHD0RHoXfEYvcfCoUCmZmZePjwoegopCWmpqZYsmQJZs2ahWnTpqF79+7IyMgQHYtI72VmZqJPnz7w8vLCqFGjRMehApAkCQB41k6Psdj9h6enJwAueWJsZDIZxowZgy1btmD79u1o1qwZnj59KjoWkV6bNWsWLl++jBUrVsDU1FR0HCoANzc3KBQKFjs9xmL3H2XLlgXAYmesOnXqhGPHjuHKlSuQJInjLYne0ZUrVzB16lSMGTMGXl5eouNQIXCcnX5jsfsPS0tLlChRggd0IyZJEsLDw6FUKuHr64vw8HDRkYj0Sm5uLvr27YuyZcviq6++Eh2HCkmSJJw7dw5paWmio9A7YLF7BS55QuXKlUN4eDgqVaqExo0bY9u2baIjEemNxYsXIywsDMuWLYOVlZXoOFRIkiQhOzsbZ8+eFR2F3gGL3Suw2BEAFC1aFIcPH0ZQUBA6deqE2bNnc8Ys0VvcvXsXEyZMwMCBA9GgQQPRcegdVKtWDXZ2drwcq6c4mvUVPD09sX//ftExSAdYWlpi/fr1UCgUGDt2LG7duoUFCxZwIDjRKyiVSgwcOBD29vaYOXOm6Dj0jkxMTODr68tip6d4xu4VFAoFnjx5gmfPnomOQjpALpdj2rRpWLFiBZYvX462bdvyvUH0Chs2bMCBAwewZMkSFClSRHQceg95Eyh4lUL/sNi9gkKhAMCZsfSi3r1748CBAwgNDUX9+vW5gCfRc548eYIRI0agS5cu+PDDD0XHofckSRKePn2K69evi45ChcRi9wosdvQ6TZs2RWhoKOLi4uDj44OLFy+KjkSkE4YPHw6lUol58+aJjkJq4OPjA5lMhtDQUNFRqJBY7F7BxcUFNjY2LHb0StWqVUNERARcXV0REBCA3377TXQkIqH27duHTZs24aeffoKLi4voOKQG9vb2qF69OsfZ6SEWu1eQyWScGUtv5O7ujpMnT6Jhw4Zo06YNgoODRUciEiIpKQmDBg1Cy5Yt0b17d9FxSI24ULF+YrF7DRY7ehtbW1vs2rULgwYNwoABAzBu3Djk5uaKjkWkVePHj0d8fDyWLl0KmUwmOg6pkSRJuHz5MuLj40VHoUJgsXsNhULBu0/QW5mYmGD+/Pn48ccfMXv2bHTp0oWrtZPROH36NJYsWYIZM2agTJkyouOQmkmSBACIiIgQnIQKg8XuNRQKBaKiopCTkyM6Cuk4mUyGESNGYPv27di3bx+aNGmCJ0+eiI5FpFHp6eno27cv/Pz8MHjwYNFxSAMUCgVcXFw4gULPsNi9hkKhQFZWFpe0oAILCgrCiRMncPPmTfj5+eHatWuiIxFpzJQpUxAVFYXly5fDxMREdBzSAJlMBn9/f46z0zMsdq/h6ekJgEueUOF4e3sjIiIC5ubm8PPzQ0hIiOhIRGp34cIFzJo1C5MmTUKVKlVExyENkiQJkZGRyM7OFh2FCojF7jXKlCkDmUzGYkeF5uHhgdDQUNSoUQNNmjTBpk2bREciUpvs7Gz06dMHlStXxrhx40THIQ2TJAmpqan4888/RUehAmKxew1LS0uUKFGCEyjonTg6OuLgwYP4+OOP8cknn2D69Om8NQ8ZhLlz5+LChQtYsWIFzM3NRcchDatduzbMzc05zk6PsNi9AZc8ofdhbm6ONWvW4JtvvsHEiRPRr18/ZGVliY5F9M6uX7+Or7/+GiNGjIC3t7foOKQFlpaWqFu3LsfZ6REWuzdgsaP3JZPJ8PXXX2PNmjVYu3YtWrdujcTERNGxiApNqVSif//+KF68OKZMmSI6DmkRFyrWLyx2b+Dp6cliR2rRs2dPHDp0CGfPnkVAQADu3r0rOhJRoSxfvhwnTpxAcHAwbGxsRMchLZIkCXfv3sX9+/dFR6ECYLF7A4VCgdjYWCQlJYmOQgagYcOGCAsLQ3JyMnx8fHDu3DnRkYgK5MGDBxg9ejQ+++wzNG3aVHQc0jI/Pz8AQHh4uOAkVBAsdm+gUCgAcMkTUp/KlSsjIiICpUqVQoMGDbBv3z7RkYjeSKlUYsiQIbC2tsacOXNExyEB3NzcoFAoOIFCT7DYvQGLHWmCq6srTpw4gebNm6Ndu3ZYtGiR6EhEr7Vt2zbs3r0bCxcuhKOjo+g4JAgXKtYfLHZvUKxYMdjY2LDYkdpZW1tj69atGD58OIYOHYpRo0bx9nWkc+Li4jB06FAEBQWhY8eOouOQQJIk4fz580hNTRUdhd6Cxe4NZDIZJ1CQxpiYmGDu3LlYuHAh5s2bh06dOvGXJumUUaNGISMjAwsXLhQdhQSTJAnZ2dn4/fffRUeht2CxewsueUKaNmTIEOzevRsHDx5Eo0aN8PjxY9GRiHDo0CGsWbMGc+bMgbu7u+g4JFjVqlVhZ2fHy7F6gMXuLRQKBe8+QRrXpk0bnD59Gvfu3YOvry+uXLkiOhIZseTkZAwYMACNGzdG7969RcchHWBiYgJfX19OoNADLHZvoVAoEBUVxfFPpHG1a9dGREQEbG1tIUkSTpw4IToSGanJkyfj8ePHCA4OhkwmEx2HdETeBAreHlG3sdi9hUKhQHZ2NhdmJK0oXbo0QkJCULduXTRv3hzr1q0THYmMTEREBObNm4cpU6bA09NTdBzSIZIkIS4uDteuXRMdhd6Axe4t8n6xcZwdaYu9vT3279+Pnj17omfPnvj222/5CZm0IjMzE3379kWdOnUwYsQI0XFIx/j4+EAmk3GcnY5jsXuLMmXKQCaTsdiRVpmZmWHZsmX47rvv8M0336BXr17IzMwUHYsM3IwZM3D16lWsWLECpqamouOQjilSpAiqV6/OYqfj+JP7FhYWFihZsiQnUJDWyWQyfPnll/Dw8ECvXr1w7949bN++/b0Wic1VAs+ygPgsID4TSMwCsnKBXKg+5ZnJAXszwNEccDQD7MwAOYdYGYVLly7hu+++w7hx41CjRg3RcUhHSZKEkydPio5BbyBT8hrPWzVs2BBubm7YvHmz6ChkpE6fPo327dvD1dUV+/fvR9myZQv19cnZwK1k4HYKkP3vT7wMwKt++J9/3FQGeNgAClvAlh8DDVZOTg78/f2RkJCACxcuwNLSUnQk0lHr169Hjx498PTpUzg5OYmOQ6/AS7EFwLXsSLT69esjPDwcmZmZ8PHxwZkzZwr0dXEZwOknwMFo4Eby/0sd8OpS99/Hs5WqrzsYrdpOHK8GG6SFCxfizJkzWLFiBUsdvZEkSQBUk2xIN7HYFQDvPkG6oEKFCggPD4enpycaNmyIXbt2vfa1OUrgrwTg+BPgSYbqsXc9NZ/3dU8ygOMxqu3m8Dy/wYiKisKXX36JwYMHw9/fX3Qc0nEeHh5wdXXlODsdxmJXAAqFAk+fPkViYqLoKGTkihUrhqNHj6JNmzbo0KEDfvrpp5dmzMZnAoejgWvJqj+rq4PlbedaMnDksWo/pN+USiUGDBiAokWLYsaMGaLjkB6QyWSQJInFToex2BWAQqEAwCVPSDdYWVlh8+bNGDt2LEaOHIlhw4blL6D9OB04EQOkang97ZRs1X4ep2t2P6RZa9euxaFDh7B06VLY2dmJjkN6wt/fH5GRkcjKyhIdhV6Bxa4AWOxI18jlcnz//ff4+eefsWTJErRv3x534tMQGqua4arpK6VKqPYTGstyp68eP36MkSNHolu3bvjggw9ExyE9IkkSUlNT8eeff4qOQq/AYlcAzs7OsLW1ZbEjndO/f3/s27cPt2MSEB4ng1Ljle5FSgBhsbwsq4+GDRsGExMT/PTTT6KjkJ6pXbs2zM3NeTlWR7HYFYBMJuMECtJZzVq0xPQtRyA3MYVqsRLtygVwJo4TKvTJ7t27sWXLFsybNw/Ozs6i45CesbCwQN26dVnsdBTXsSugDh06ICUlBQcPHhQdhegFfyX8f6KESBXsgOr2olMYNnUsMJ2YmIgqVarAy8sL+/btg0zGFaip8MLCwuDu7l7oNTVJ87jkaAEpFIo3Li9BJEJchm6UOgC49gwoYQU4mYtOYngKs8B0XCZwK0X1/1+1wPTYsWORlJSEpUuXstTRO/P19YVczot+uojFroAUCgXu3LmD7Oxs3kORdMalpNcf4LVNBuBSIlC/mOgkhiMuQ/VvHJPx8r9zYRaYvp4MuFgAGTfPITg4GIsWLUKpUqU0F5wMHkud7uK/TAEpFApkZ2fj/v37oqMQAVCdxYnJADIzMrBu+jj0q+OOT8pZYfyHPrh46vBbvz7iwA7MHfQxBvsr8El5awwLrIg1U75ASmLCG78uOuomupazxEelZLhx8ff8x5VQ5UnOfs9vjDS0wLQS8e5eGL9oPfoNGKiGlESkizjGroASEhJw9uxZ1K9fn7fcIZ3wZ4LqbMzcIV0RsX8bWvcZgeIe5XF862rcvHgW3/xyHJW9A1779Z/VcIajqzu8W7SHc4nSuPvPXzi0filcSyswa/85WFhZvfLrvv+sLf4OO4b01BR8v+8sytWsm/+cDEA5W6CGg3q/V2MSnwlEPgVSNLUWoVIJWzMZvJ1UY/GINEWpVPJyvwAsdgWU99fENynpglwlsPchcOXcGUxo64MeE2ej3cDRAIDM9HSMaloNRZxdMH3X62et/R1+AtX8Gr7w2Ilta7Fw5KcYOGsZmnbt+9LXXDhxEN/3aYt2A8di+/xpLxU7QDWu60P3lwft09s9TlctH6OEZi+vy/79T3IGXPk5ldQsPj4eFhYWsLa2Fh3FKPFSbAHJZDKWOtIZz7JU46ci9m+D3MQEzbr1z3/O3NISjbv0wbU/whH78N5rt/HfUgcAPi2DAAAPrl956bnsrCys/GY4WvceDrcynq/dbrYSeMbLsYX2OB1cYJr00t27dzFr1iw0btwYxYoVg7e3N3r27ImdO3ciIyNDdDyjw2JHpIfi/72Tz+1L5+GuqABruyIvPF/OyxsAEHXpQqG2m/AkGgBg5/Ty2ma/rvgJKYnx6Dhs0tvzccHiQonP/P+ZOm3iAtP0PuLj4zFw4EBUrFgRS5YsQalSpfD1119j/PjxSE5Oxtdff43169eLjml0OL2TSA/FZ6oupcU/fgQHl+IvPe/472Nxjx8Waru7Fs+E3MQEfq0/enF/MdHYNm8qek764aUS+V8yAAmZAGwKtWujlaNUjakTNSYmb4Hppq6ACS9KUAEplUp89913OHToEJYtW4bmzZujWLFi+Ve2+vTpg1mzZmHhwoXo06eP4LTGhWfs1IjDFUlbErNURSAzPQ1m5hYvPW9uoRo4lZmeVuBtnt65EUc3r8CH/b9AcY/yLzy3fsY4uJZWoMkrxt39lxJAAu8NXmCXE1UTJUT+9kjOBi4nCQxAeufGjRs4fvw4Jk+ejO7du8PFxeWl4Uqurq549uyZoITGi2fs3kNCQgJSUlIQHx+PEiVKwNHRUXQkMhJZuar/Nbe0Qlbmy2NYMjPS858viMuRp7FkTB94BbbAJ2O/e+G5a+cicGr7Ony9+WiB167Ky0dvxgWmSV85OTnh8uXLaNGixSufv3XrFmbOnIlPPvmEs2O1jMWuENLS0vDLL79g48aNuHjxIuLi4pCTk4MyZcqgUqVKGD58OJo3b86FG0nj8nqTo2txxEU/eOn5+JhHAAAnV/e3bivq8kXM7NMWpSpWwxc/b4PJfxbgXvfdWFT2rg+XUh6IuRcFAEiKiwUAJMQ8wpMHd1GsROlX5qM34wLTpK+KFi0KDw8PTJkyBVOmTIFMJkNUVBRu3bqFc+fOYc+ePShatCh69uzJUqdlLHaFMHv2bGzduhVVqlTB5MmTUblyZRQpUgSPHz/G4sWL8eWXX8LGxgb169cXHZUMXN5Hh7JVvPB32HGkPkt6Yezb9fORquerer1xO9FRNzGtR0vYF3XBl2v3w8rG9qXXxD68iyf372Cw5PHSc9/3bgvrIvZYeynhlfno9fIWmAaArIwMbJ7zFU5tX4eUxHiUrlwDXcdMQ80Gzd64jYgDOxC25xfc+PMsEmKi4exeCnWatMFHwyfDxt7hhdeu+mYkLkeexJN7UcjMSEexkmUgffgx2g4YDSsb2xcWmLblkYEKYP78+Zg6dSqKFy+O6tWro0iRIoiLi4ONjQ3atWuHIUOG8A4nAnAduwI6dOgQhgwZgr59+2Lw4MGwtbV96VNI+/bt4enpiTlz5ghKScbiRAzwNBO4dj4SX7b1fWEdu6yMDIxsWg12jkUxY08EAODJg7vITEtFiXKV8rcRHxONSUH+yMpIx7SdoXApVfaV+7pw8hAy01JfeOyvsGM4sGoBek76ASXKVUKdJq1feL6oOdDQRY3fsAHKW2BaCeBHLSwyPalDABTV68CtbDmYWVgi6u/zOLZlJTxr1MWUbacgl8u5wDQV2t27d/PP0gFAtWrVUK9ePQ5NEoifywro7NmzKFu2LMaNGwfg1RMlbGxsEBMTo+1oZITszVQ3e69Qywd+bTph48wJSHoaA7ey5XBi2xo8uR+FwbNX5L9+wYieuBxxEtvu/f99+12Plnh89xbaDRqLf86G4J+zIf/fvrNr/tkir8DmL+0/JSkBAFDFN/ClBYplABzM1PjNGqBcJXA7RVXqrp8/g9A9m18o54Ede2JU02pYN33sGxeZ/uLnbS+tR6ioXgcLR36K07s2vLDI9LQdIfgv1zKeWDttNG5cOIMKtX2hhCpXNXsuME0FU7p0aZQuXRoNGzZ86TmOrRODxa6AKlWqhBUrVuDevXsoVapU/ps1OzsbCQkJ2LhxI8LCwrBkyRLBSckYOJoDt1JU///zH9dic4nJOLlDdRmvTKUamLBqH6r4NnjjNqIuXwQA7F4y66XnqvgGvvUy4OsoAThwAP4b5S0wDbx5kemNM79E7MN7cHZ/9eWs1y0yvXDkp69cZPq/8s7SPn9/4LwFpu1ZzqkAli9fjmPHjmH69OkoW7YssrKyYGamevOw1InBYldAAQEBqFq1Kpo3b4527drBxcUFWVlZePToES5fvowrV67g008/RbNm73YwJCoMx+cOuuaWlug5aTZ6Tpr92tdP2XripceeP3tXWI0690Kjzr1en4/F7o3in1sOpiCLTL+u2L3KmxaZzsnORkpSArIzM3H36t/YNHsSrGzt8veVny+TxY4K5unTp7h58yaio6NRtmxZmJqa8kydYCx2BeTq6orFixfj22+/RUREBDIzM5GamgpbW1vUqFEDX3zxxWunfROpm52Z6p6s2To4QtZUBtjxN8sb5S0wrYT2FpkGgJt//o4v2/nl/9ndsyLGrdwDO0en/Me4wDQVRr9+/dC9e3eUKFECwMtn6XJycmBiYiIimtHir99CKFWqFJYvX47o6GgkJSXB2dkZTk5Ob/9CIjWTywAPm/8PvtcVMqhycXzWm+UtMA1oZpHpdoPGvrTINACULF8FX208jPTUFFz9Iwx/hRxBesqLC+lxgWkqjOePgUlJSZgwYQL+/PNPfPXVV6hSpUp+4SPtYbErhJs3b+LixYto3Lgx3Nzc8h/Pm0jBU8+kTQpb4LqOLG6bRwlVLnqz5xdw1sYi03ms7YqgRv2mAADvFu1weudGzOrTDrMOnEPZKjVfmY/obfIuvcpkMuzZswf16tXDkiVL8ODBAzRq1Agffvgh/P39Rcc0GlxuqhA2bdqEoUOH4uzZswBUp5gB5L+hibTJ1hRwsVCdJdMFMqjycA20t3u+Nzm6FkfCvwtKP0+di0y/jk+rDgCA0D2bX5uP6G3yjn92dnYICAiAvb09duzYgZ9//hlKpRJLlixBkyZNcOjQIcFJjQOLXSG0adMGU6ZMQaVKqrXAOG6ARKtqrzuXYpVQ5aG3e/4Xb9kqXnh46xpSn714s1Z1LjL9OlmZGcjNzUVqUuJr8xEVRuvWrXHs2DEAgEKhwKBBg1C+fHkkJCSgZcuWvKe6FvCzdSF4eXnBy8vrtc8rlUo8ffoU5ubmKFKkyGtfR6QuTuZABVvduN9oBTveZ7SgzJ5rTr6tP8Ken3/A4Q3BLywyfXzLKpSv5ZM/I/Z1i0xP7dYccpkck9YfhH3RV98PLCUxARbWNjA1e3Gq69FNywEAihovrkVoxmZH7yA5ORnW1tZ48OABhg8fjujoaNy7dw9yuRwuLi5o27YtYmJi4OrqKjqqQWOxU6OsrCysXr0aSUlJmDJliug4ZCSq2AMP0oDUHDFn72QAbEyBKvwsU2B5C0wroZ1Fpi+Fn8DKr4fB94OPUNyjPLKzMnHlzGlEHtgBzxp10aBD9/yv4wLT9C5+/PFHHD9+HElJSbCyssLRo0fh7e2NVq1aoXbt2vDy8uJECi1hsSukefPm4cMPP0SZMmUgk8kgl///o625uTk8PT0xceJEDB06FC4uvKcSaZ6JDPApqrrNmKhi5+2kykEF8/wC04DmF5kuXak6qkqNcPbQbtXYPaUSrmU88dGIr9Bu4BiYmf//VCsXmKZ3YWpqiuzsbLRs2RJJSUlwcnLCypUrX3od17jTPN4rtpDkcjl27NiB9u3b5z+WmJiImzdv4tatWzh9+jQWLFiA48ePIzAwUFxQMjqP04HQWCA3NxcyuXaupckABDgDLpZa2Z3BSMwEjujw3QebunKBYiqc9PR0WFqqfhFcuHAB9+/fR5s2bQSnMk4sdoWUV9YqVaqE69ev49GjR0hOVg1wsrGxQfHixWFmZoZvv/0Wfn5+b9oUkdrtPBqKtDK1YW5uofFyJwfgz1L3TnKVwN6HurvA9IfuXIuQ3l9sbCzOnz+P8PBwPHv2DN26dUOFChVgbW0tOppB46XYQqpbty5+/PFHFC1aFBUqVECjRo3g7u4OV1dXODs7o2jRorCxsYGz88u38yHSpCtXruDToFb4uPdAdBw3Eyk5mtuXranq8itvHfZuuMA0GbLDhw9j1qxZOH36NDIzM2FnZ4eWLVuiTZs2aNKkCaZMmYIyZcqIjmmweMaukBYsWIC5c+fi1KlTcHBwgJWVFUwLuGYUkaYkJibCx8cHJiYmiIiIgLWtHS4nqmbL5t266n3lbaeCnWqiBMfUvZ/kbOBgtOgUL2vhxrUI6d2Fh4djyJAhsLe3R/Xq1XH9+nUolUp89NFHaN68OSZMmIDU1FTs3LlTdFSDxR/fQqpRowZycnLg6uoKc/MXT1fwDhQkQm5uLnr27Ino6GicPXsWdnZ2AIDqDkAJK+BSEhCT8e4FL+/rilmo1qnjkibqkbfA9JMM3ThrJ4Pq35iljt5VSkoKFi5cCFtbW6xcuRKlS5eGiYkJ1qxZg1mzZqFv374YPXo0AgICkJ2dzZMiGsLVigqpbt26+Oabb/LvOvE83oGCRJg2bRr27t2LDRs2oHz5F+8P6mQB1C+mOgtTzlY1firP696pzz9uKlN9XQs31XZY6tSLC0yTITExMcHJkyfxww8/wMPDI38R/wYNGiApKQk3b95ErVq14ODggJCQkLdsjd4V63Ih2djYoHfv3qJjEAEA9u3bh6+//hpTpkxB69atX/s6W1OghgNQzR54lg3EZwIJmaqbvWflqm4hJYdqYVoHM9VyF47mgJ0px1tpEheYJkNiaWkJKysr/PXXX/D29s5/fMWKFVAoFLCzs8OTJ0/Qo0cPmJlx2rWmcIwdkZ66evUqvL290bhxY2zfvv2FNRVJf+QogcPR4heYburKcZP0/n744Qfs2LEDHh4e8PHxwY0bN7B7924MHjwY48aNQ1ZWFrKysjgzVoNY7Ij0UFJSEnx8fAAAkZGRvIWdnovPVC0wnavl/ebk5ECmzEVTdzPOcCa1yMjIwJYtW7B69WqkpqbCzMwMHTp0wOeff877q2sJi917ys3N5ZkS0qrc3Fx07NgRR48exdmzZ1GxYkXRkUgN8haY1t4vZCVyc3IxtVtztPCrjZkzZ/J3GalNRkYGHjx4AA8PD4491zL+FL8jpVKJ0NBQXLt2TXQUMjIzZszArl27sH79epY6A+JqqVrwWY7XT2xRJzlkCHQ1Qd/O7TBnzhz06tULWVlZWtgzGQMLCwsoFAqWOgFY7N6RTCZD9+7dsWrVKtFRyIjs378fkydPxtdff422bduKjkNq5moJNHQBrDV8xcrWVLUfF0tg2LBh2LRpEzZv3ox27dohJSXl7RsgIp3FS7HvoUmTJnBycsLWrVtFRyEjcOPGDdStWxf169fH7t27ednMgOUoofUFpo8cOYKgoCBUqVIFv/76K++eQ6SneGR4DwqFArdu3RIdg4zAs2fP0L59e7i6umL9+vUsdQbORKZaYLpRMdWiwcC7X57N+7piFkAjF6C6/atnvzZt2hQnTpxAVFQUAgICcOfOnXfcI9H/vWrNV9IsHh3eg6enJ4sdaZxSqcRnn32GO3fuYNeuXbC35yqyxkLbC0zXqVMHoaGhyMrKgiRJ+Ouvv973WyAjlpCQgKNHj4qOYXRY7N6DQqFAQkIC4uPjRUchAzZz5kxs374da9euReXKlUXHIQHyFpj+0F213lwdR0BhAxQ1B4qYqp4vYqr6s8JG9XxTV9XrazgU7jZh5cqVQ2hoKFxcXFC/fn2cPn1aU98WGbiVK1eiffv2nJSjZSx270GhUAAAbt68KTgJGarffvsNX375JSZNmoSgoCDRcUgwuQywNwPK2gBejqoJEM3cVGfkmrmp/uzlqHre3uzd7xri5uaGkydPok6dOmjWrBl27dql1u+DjIMkSUhLS8PFixdFRzEqLHbvIa/Y8XIsacLNmzfRtWtXtGrVCt98843oOGRkihQpgv3796Nt27bo2LEjgoODRUciPVOrVi1YWFggLCxMdBSjwmL3HhwdHWFvb89iR2qXkpKCoKAgODs7Y8OGDVyxnYSwsLDApk2bMGjQIAwYMABTp04FF1KggrKwsEDdunVZ7LSsECMv6L9kMhknUJDaKZVK9O7dG7du3UJERAQcHBxERyIjZmJiggULFqB48eKYNGkSoqOjMX/+fH7YoALx9/fHxo0bRccwKjxj95645Amp2w8//IAtW7ZgzZo1qFatmug4RJDJZJg4cSKWLVuGpUuXokuXLkhPTxcdi/SAJEm4f/8+7t27JzqK0WCxe08KhYKTJ0htDh8+jPHjx2PChAno2LGj6DhEL+jbty927NiBffv2oVWrVkhMTBQdiXScn58fAPByrBax2L0nhUKBu3fvcjo3vbfbt2+jS5cuaNasGaZOnSo6DtErtWvXDocPH8aFCxcQGBiIR48eiY5EOszFxQXlypVjsdMiFrv3pFAokJubi7t374qOQnosNTUVQUFBcHBwwMaNGzl+iXRaQEAATp8+jdjYWPj7++P69euiI5EOkyQJoaGhomMYDRa79+Tp6QmAS57Qu1Mqlejbty+uX7+OnTt3wsnJSXQkoreqVq0awsLCYGFhAX9/f/z++++iI5GO8vf3x4ULF5CSkiI6ilFgsXtPpUqVgomJCYsdvbMff/wRmzZtwqpVq1CjRg3RcYgKrHTp0ggJCYFCoUDDhg1x+PBh0ZFIB0mShJycHJw9e1Z0FKPAYveezMzMULp0aU6goHdy7NgxjBkzBmPHjkXnzp1FxyEqtKJFi+Lo0aMIDAxE69atsWnTJtGRSMdUqVIFRYoU4Tg7LWGxUwMueULv4s6dO+jcuTOaNGmC6dOni45D9M5sbGywa9cufPLJJ/jkk08wb9480ZFIh8jlcvj5+bHYaQmLnRqw2FFhpaWlISgoCHZ2dti0aRMnS5DeMzMzw6pVqzBu3DiMGDECEyZM4F0qKJ8kSQgLC0Nubq7oKAaPxU4NPD09cfPmTf4SowJRKpXo378//vnnH+zcuRNFixYVHYlILWQyGb7//nvMnTsX33//PXr37s2loAiAagJFfHw8rl69KjqKwWOxUwOFQoGkpCTEx8eLjkJ6YP78+Vi/fj1WrFgBLy8v0XGI1G7kyJFYv3491q9fj6CgIKSmpoqORIJ5e3tDLpfzcqwWsNipgUKhAABOoKC3OnHiBL744gt88cUX6Nq1q+g4RBrTrVs3/Prrrzhx4gSaNm2Kp0+fio5EAtnZ2aFGjRosdlrAYqcGecWO4+zoTe7evYvOnTsjMDAQ33//veg4RBrXvHlzHD9+HNevX0f9+vV5v1AjlzfOjjSLxU4NHB0d4eDgwGJHr5WWloYOHTrA2toav/zyC0xNTUVHItKKevXqITQ0FGlpafDz88OlS5dERyJBJEnCP//8w7O3GsZipyaenp4sdvRKSqUSgwYNwqVLl7Bjxw44OzuLjkSkVRUqVEBYWBiKFi2KgIAA3l7KSPn7+wMAwsPDBScxbCx2asIlT+h1Fi9ejDVr1iA4OBi1a9cWHYdIiOLFi+PUqVOoWbMmmjZtir1794qORFpWpkwZFC9enJdjNYzFTk0UCgUnT9BLTp06hREjRmD48OHo0aOH6DhEQtnb2+O3335D69atERQUhJUrV4qORFokk8k4zk4LWOzURKFQ4N69e8jMzBQdhXTE/fv30alTJwQEBGD27Nmi4xDpBEtLS/zyyy/o378/+vTpg+nTp3MNUCMiSRLOnDnD9Q01iMVOTRQKBXJzc3H37l3RUUgHpKeno2PHjrCwsMAvv/wCMzMz0ZGIdIaJiQkWLVqEb7/9FhMnTsTw4cN5RwIjIUkS0tLScOHCBdFRDBaLnZp4enoC4JInpJosMWTIEFy8eBE7duyAi4uL6EhEOkcmk+Grr77C0qVLsWjRInTt2hUZGRmiY5GG1a5dGxYWFrwcq0EsdmpSqlQpmJiYsNgRfv75Z6xcuRJLly5F3bp1Rcch0mkDBgzAtm3bsHv3brRu3RpJSUmiI5EGmZubo169eix2GsRipyampqYoU6YMJ1AYudDQUAwbNgxDhw5Fr169RMch0gtBQUE4dOgQfv/9dzRs2BCPHz8WHYk0iBMoNIvFTo245Ilxe/jwIT766CP4+vpi7ty5ouMQ6ZUGDRrg1KlTiI6Ohr+/Pz8kGzBJknD//n2OSdcQFjs1YrEzXhkZGejYsSNMTEywdetWTpYgegd59xI1MTGBJEk4f/686EikAZIkAQDP2mkIi50a5d19glP3jc+wYcNw7tw57NixA66urqLjEOmtsmXLIiQkBGXLlkVgYCCOHTsmOhKpWbFixVC+fHkWOw1hsVMjhUKBpKQkxMXFiY5CWhQcHIzg4GAsWbIE3t7eouMQ6b1ixYrh6NGjkCQJLVu2xJYtW0RHIjXjODvNYbFTI4VCAQAcG2JEwsPDMXToUAwaNAi9e/cWHYfIYNja2mLv3r34+OOP0aVLFyxYsEB0JFIjSZJw4cIFpKSkiI5icFjs1Civ2HGcnXF49OgROnbsiHr16uGnn34SHYfI4JiZmWHNmjUYNWoUhg0bhkmTJnGoi4GQJAk5OTk4c+aM6CgGx1R0AEPi4OAAR0dHFjsjkJmZiY8++ggymQzbtm2Dubm56EhEBkkul+OHH36Am5sbxowZg+joaCxduhSmpjx86bMqVarA3t4eYWFhaNSokeg4BoU/GWqWN4GCDNuIESNw9uxZnDp1CsWLFxcdh8jgjR49Gq6urujduzeePHmCTZs2wdraWnQsekdyuRx+fn4cZ6cBvBSrZlzyxPCtWLECS5YswaJFi+Dr6ys6DpHR6NGjB/bs2YMjR46gefPmnKim5yRJQnh4OO8TrGYsdmqmUCg4ecKAnTlzBoMHD0b//v3Rr18/0XGIjE6rVq1w7Ngx/PPPP2jQoAHu378vOhK9I0mSEB8fj6tXr4qOYlBY7NRMoVDg3r17yMzMFB2F1Ozx48fo0KEDateujfnz54uOQ2S0fHx8EBoaimfPnkGSJFy5ckV0JHoH3t7ekMvlCA0NFR3FoLDYqZlCoYBSqcSdO3dERyE1yszMRKdOnZCTk4Pt27fDwsJCdCQio1axYkWEhYXB3t4eAQEBCA8PFx2JCsnOzg41a9bkODs1Y7FTM09PTwBc8sTQfPHFF4iIiMC2bdvg7u4uOg4RAShRogROnz6NqlWrokmTJvj1119FR6JC4kLF6sdip2YlS5aEqakpi50BWb16NRYuXIj58+fD399fdBwieo6DgwMOHjyIFi1aoF27dlizZo3oSFQIkiTh6tWriI2NFR3FYLDYqZmpqSnKlCnDCRQG4vfff8fAgQPRp08fDBgwQHQcInoFKysrbN26FX369EGvXr0wa9YsLmSsJyRJAgBEREQITmI4WOw0gEueGIaYmBh06NABNWvWxMKFCyGTyURHIqLXMDU1xdKlS/HVV19h3LhxGDVqFJfR0ANlypRB8eLFOYFCjbhAsQYoFAp++tBzWVlZ6Ny5MzIyMrB9+3ZYWlqKjkREbyGTyfDtt9/Czc0NQ4YMwePHj7F69WreGUaHyWQy+Pv7c5ydGvGMnQbk3X2ClwL015gxYxAaGopt27ahZMmSouMQUSEMGjQIW7Zswfbt29GmTRs8e/ZMdCR6A0mScObMGWRlZYmOYhBY7DRAoVDg2bNnePr0qego9A7WrVuHefPm4aeffkL9+vVFxyGid/DRRx/ht99+Q2RkJBo3boyYmBjRkeg1JElCeno6Lly4IDqKQWCx0wCFQgEAnEChh86dO4f+/fujV69eGDx4sOg4RPQeGjVqhJMnT+L+/fvw9/fH7du3RUeiV6hVqxYsLS15OVZNWOw0IK/YcQKFfomNjUVQUBCqVauGJUuWcLIEkQHw8vLKLwySJPGskA4yNzdHvXr1OIFCTVjsNMDe3h5OTk4sdnokOzsbH3/8MdLS0rBjxw5OliAyIB4eHggNDUWJEiUQGBiIEydOiI5E/yFJEkJDQzk2XQ1Y7DQkbwIF6Yfx48fj5MmT2LJlC0qVKiU6DhGpmYuLC44fPw4fHx+0aNEC27ZtEx2JniNJEh4+fIh79+6JjqL3WOw0hGvZ6Y+NGzdizpw5mDNnDho2bCg6DhFpiJ2dHfbt24eOHTuic+fOWLJkiehI9C8/Pz8A4Dg7NWCx0xCFQsHJE3rgwoUL6Nu3L3r06IFhw4aJjkNEGmZubo7169dj+PDhGDx4ML7++mte/tMBxYoVQ/ny5TnOTg24QLGGKBQK3L9/HxkZGbCwsBAdh15BqVRi48aNqFSpEn7++WdOliAyEnK5HHPnzoWbmxvGjx+P6OhoLFq0CKamPCSKxIWK1YPvYg1RKBRQKpW4c+cOKlSoIDoOvcasWbOQkJAAKysr0VGISItkMhnGjRsHV1dX9O3bFzExMdi0aRMnTgkkSRLWrVuH5ORk2Nraio6jt3gpVkM8PT0BcMkTXZZ3hs7BwUFsECISplevXti9ezcOHjyI5s2bIyEhQXQkoyVJEnJycnD27FnRUfQai52GlCxZEqampix2gnGGFRG9TevWrXH06FFcunQJDRo0wMOHD0VHMkqVK1eGvb09L8e+JxY7DTExMUHZsmU5gUKgn376Cd26dcOlS5eQm5srOg4R6TA/Pz+EhIQgISEBkiTh6tWroiMZHblcDj8/P06geE8sdhrEJU/E2bJlCyZNmoRBgwbBw8MDcjnf6kT0ZpUrV0ZYWBhsbGzg7++PM2fOiI5kdPz9/REeHs4P4++BRzsNYrETIy4uDnPmzME333yDrl274tGjR9iwYQO+/vpr7Nq1C4mJiaIjEpGOKlmyJE6fPo1KlSqhUaNG+O2330RHMiqSJCEhIQH//POP6Ch6i8VOg/LuPsE1krTLzMwMubm56NixIx4+fIimTZti3bp1WLVqFb777jv06NEDUVFRomMSkY5ycnLCoUOH0KRJE3z44YdYt26d6EhGw9vbG3K5nOPs3gOLnQYpFAokJycjNjZWdBSjkpOTg4SEBERGRmLChAn5tw+6c+cORo4ciWfPnmH16tWiYxKRDrO2tsaOHTvw6aefomfPnvjhhx9ERzIKtra2qFmzJovde2Cx0yCFQgEAnEChRdnZ2ShSpAh8fHywd+9eJCcno3nz5rC1tYVMJsMnn3yCOnXqYMOGDUhJSREdl4h0mKmpKZYtW4aJEydizJgxGD16NMd+aYEkSZxA8R5Y7DTIw8MDANey04br168DUP0ilsvlGDlyJPbv34+dO3fi3LlzL7y2WbNmKFu2LHJyckREJSI9IpPJMG3aNMyfPx83btzgRCwt8Pf3x7Vr13i16x3xHapB9vb2KFq0KIudhvXr1w+tW7fG9u3b8x+rU6cODh06hDJlymD58uVYtWoVHj16hISEBMybNw82NjYoUqSIwNREpE8+//xzbNu27Y1n7K5evYpNmzZh9uzZ2LBhgxbTGRZJkgAA4eHhgpPoJ5mSI/s1ysfHB1WrVsXKlStFRzFIaWlpCAwMhKWlJSwsLNC5c2f069cv//m7d++iS5cuePLkCZ48eYJKlSohJSUFf/zxB8zNzQUmJyJDcvDgQQwfPhxpaWmoUKECLl26hICAAGzZskV0NL2jVCpRsmRJ9OzZEzNmzBAdR+/wXrEaxiVPNMvKygqenp7593pdtmwZYmNjMWHCBFy9ehUVK1ZEWFgYjh49ikePHsHZ2Rl+fn4sdUSkNuHh4WjXrh169uyJzz//HNWrV8fVq1fRpk0b7NmzB23bthUdUa/IZDJIksQJFO+Il2I1TKFQcPKEhuSdbK5Tpw7Kly+Pn376CXXr1sWBAwcQFBSEypUr48qVKwCAJk2aoHv37mjZsiXs7e1FxiYiA5KcnIxOnTqhffv2mDlzJqpXrw4AqFixImxsbHDx4kXBCfWTJEk4c+YMMjMzRUfROyx2GqZQKPDgwQOkp6eLjmJwZDIZACAgIACHDh1CkSJFsHjxYpQrVw4HDhxA3bp14ezsDACcyUZEGtGrVy/Y29tj9uzZcHR0zH/81q1buH//PqpUqSIwnf7y9/dHeno6Lly4IDqK3mGx0zCFQgGlUok7d+6IjmKwXF1dERUVhYSEBKSkpGDXrl2oV68eLC0t8fnnn+PKlSucyUZEanf16lVcv34dY8eORYkSJfIfT01NxcqVK1GhQgWULl1aYEL95eXlBUtLS16OfQc82mmYp6cnAC55okkeHh5o3rw5IiMjUatWLXzwwQc4evQounXrhitXruRfjiUiUqfMzEzcuHEDZcqUeeHD4+bNm3HgwAEEBASgXr16AhPqL3Nzc9SrV4/F7h2w2GlYiRIlYGZmxmKnJq+bxG1iYoJWrVqhTJkyWLBgAczNzTFgwACsWrUKHTp00HJKIjIG1tbWqFixYv6wEAAIDg7G2rVrUapUKUydOhXAy0NBnj59ioMHD+Lhw4dazatv8hYq5uIdhcNip2EmJiYoW7YsJ1CoSd4v0P/+oE+fPh2zZs3CypUr4ejomP+LtHbt2lrPSETGwdPTEwEBAQgKCsLw4cPRpEkTTJkyBR4eHli4cCEsLCyQk5Pz0lCQS5cuYcGCBWjVqhX27NkjKL3u8/f3x8OHD3H37l3RUfQK17HTgpYtW8LS0hK7du0SHUUvbdiwAdevX0dsbCw++OAD1K1bFy4uLlAqlZDJZC/9LxGRNgUHByMiIgLJycno06cPatWqBRcXF2RlZcHMzOyl1+fm5uL27dsYOHAgTp48idDQUF6yfYXY2FgUK1YMGzduRNeuXUXH0Rtcx04LFAoFQkJCRMfQSzNmzMDs2bPRuHFjXL58GceOHUOFChXw5ZdfwtvbG7m5ufmfhvNK3fOPERFpWv/+/dG3b1/k5ubC1NQUN2/eRG5uLtzc3F56bWZmJszNzREXF4dbt25hwIAB+bP36UXOzs6oUKECwsLCWOwKgUc/LfD09MStW7c4TqCQrl69iiVLlmDjxo3Ytm0bLl++jHHjxiE7OxsDBw7EwYMH8wvc6tWrMWPGDGRmZrLUEZHWyeVymJqaIi4uDl26dMH48eMRHx//wmtycnJgbm6Ox48fo3fv3qhduzb69++ff19xehkXKi48HgG1QKFQICUlBU+ePBEdRa+kpKQgMzPzhU+9n376KcaOHYvy5ctj1qxZOHPmDNLT07Fv3z788ssv/DsmIqGcnJzQqlUreHl5vbCuXW5uLkxMTACofo85ODhgyJAh+Qsa06tJkoSLFy8iOTlZdBS9wWKnBQqFAgA4gaKQXF1d4eLigsjIyBdmlTVo0ACDBg3Co0ePcPDgQVhaWmLFihVYs2bNC2tJERGJMGXKFIwYMSL/z89PoBg0aBDu3r2L4cOHo0GDBgBeP9ufVBMocnJycObMGdFR9AaLnRbknWbnkieF4+bmBi8vL/zwww84f/78C881bNgQnTp1wvLlyxEXFwd7e3vUrFlTUFIiolcLDQ3FyJEjAQDz58/H/v37MWTIELRq1QpyuZyTvt6iUqVKcHBw4OXYQmCx04IiRYrA2dmZxa6QTExMsHbtWri6uuKjjz7C6dOnX7hvoKenJzw8PGBubi4wJRHR6xUtWhSLFi1C1apVMXPmTPTq1QudOnWCjY0NS10ByOVy+Pn5sdgVAoudluRNoKDCO3z4MGrUqIFWrVph7ty5+O2333Dx4kXMmTMHHh4esLW1FR2RiOiVKlWqhGfPnqFUqVJ49OgRqlSpAhcXFwBgqSsgSZIQHh7Oe34XENex05JPPvkEDx48wMmTJ0VH0VtTpkzBrl27cPv2bZQuXRqlSpXCvn37RMciIiqQPn36YMuWLdi6dStatmwpOo7eOHbsGJo0aYK///4bVatWFR1H53EdOy1RKBQ4deqU6Bh67auvvkKvXr2QmpoKmUyGChUqiI5ERFRgK1asgCRJyMrKEh1Fr3h7e8PExARhYWEsdgXAM3ZasnLlSvTp0wdpaWmwtLQUHYeIiEhv1KlTBzVq1MCqVatER9F5HGOnJXlLnkRFRYkNoieUSiWXACAio6FUKrFy5Uo8ffpUdBSdxIWKC47FTks8PT0BcMmTgpo9ezZmz54tOgYRkVYkJCRgwoQJCAgI4E3vX0GSJFy7dg2xsbGio+g8FjstcXd3h7m5OYtdARw6dAgTJkxAYmKi6ChERFrh6OiIkJAQZGRkQJIk/P3336Ij6RRJkgCAZ+0KgMVOS0xMTFC2bFnefeItbt26hS5duqBFixaYMmWK6DhERFpTvnx5hIWFwdnZGfXr10dISIjoSDqjdOnSKFGiBItdAbDYaZFCoeAZuzdISUlBUFAQnJycsGHDhvz7KhIRGQs3NzecPHkSXl5eaNasGfbs2SM6kk6QyWQcZ1dALHZaxGL3ekqlEn379sXNmzexa9euF26eTURkTOzt7XHgwAG0adMGQUFBWLFihehIOkGSJJw9e/aFOxDRy1jstCjv7hOc7fmyuXPnYvPmzVi1ahWqVasmOg4RkVCWlpbYvHkzBg4ciL59++K7774z+mOHJElIT0/HhQsXREfRaSx2WqRQKJCamoqYmBjRUXTKkSNHMHbsWIwbNw6dOnUSHYeISCeYmJhg4cKFmDJlCiZNmoRhw4YhJydHdCxhvLy8YGlpidDQUNFRdBqLnRblrWXHCRT/FxUVhS5duqBp06b47rvvRMchItIpMpkMkydPRnBwMBYvXoxPPvkEGRkZomMJYW5uDm9vb46zewsWOy3y8PAAwLXs8qSmpiIoKAhFihTBpk2bOFmCiOg1+vXrh+3bt2P37t344IMPkJSUJDqSEHkTKIz9svSbsNhpkZ2dHYoVK8ZiB9Vkif79++PatWvYtWsXnJycREciItJp7du3x6FDh/DHH3+gYcOGiI6OFh1J6yRJwsOHD7mI8xuw2GlZ3gQKYzdv3jxs2LABK1asQI0aNUTHISLSCw0aNMDp06fx+PFj+Pv748aNG6IjaZWfnx8ALlT8Jix2WsYlT4Djx49j9OjRGD16NLp06SI6DhGRXqlevTrCwsJgZmYGf39/nDt3TnQkrXF2dkbFihU5geINWOy0TKFQGPXkiTt37qBz585o2LAhZsyYIToOEZFeKlOmDEJCQlC2bFkEBgbi6NGjoiNpDRcqfjMWOy1TKBR4+PAh0tLSREfRurS0NHTo0AE2NjbYvHkzTE1NRUciItJbzs7OOHbsGAICAtCqVSv88ssvoiNphSRJuHjxIpKTk0VH0UksdlqWt+RJVFSU2CBaplQqMXDgQFy5cgW7du2Cs7Oz6EhERHrPxsYGe/bsQZcuXdC1a1csWLBAdCSNkyQJubm5OHPmjOgoOonFTss8PT0BGN+SJwsXLsTatWuxfPlyeHl5iY5DRGQwzMzMsHr1anzxxRcYNmwYJk6caNDLgVSqVAkODg4cZ/cavBamZe7u7jA3NzeqYnfy5EmMHDkSI0eOxCeffCI6DhGRwZHL5Zg9ezbc3NwwevRoREdH4+effzbIIS9yuZzj7N6AZ+y0TC6Xw8PDw2gmUNy7dw+dOnVC/fr1MWvWLNFxiIgM2hdffIF169Zh7dq16NChA1JTU0VH0ghJkhAeHo7c3FzRUXQOi50AxrLkSXp6Ojp27AgrKyts2bLFID85EhHpmu7du2Pv3r04duwYmjVrhri4ONGR1E6SJCQmJuLKlSuio+gcFjsBjKHYKZVKDBo0CH/99Rd27tyJYsWKiY5ERGQ0WrZsiWPHjuHatWuoX78+7t+/LzqSWtWrVw8mJia8HPsKLHYC5N19wpAHty5ZsgSrV69GcHAwateuLToOEZHR8fb2RkhICFJSUiBJkkGd3bK1tUXNmjU5geIVWOwEUCgUSEtLw+PHj0VH0YiQkBAMHz4cw4YNQ48ePUTHISIyWhUrVkRYWBgcHBwQEBCA8PBw0ZHUxt/fn2fsXoHFToC8tewMcQLFgwcP8NFHH0GSJPzwww+i4xARGT13d3ecOnUK1apVQ5MmTbBv3z7RkdRCkiRcv34dT548ER1Fp7DYCeDh4QHA8Nayy8jIQMeOHWFmZoYtW7bAzMxMdCQiIgLg4OCAgwcPomXLlmjfvj1Wr14tOtJ7kyQJAAzqLKQ6sNgJYGtrCxcXF4MqdkqlEkOHDsWFCxewY8cOuLq6io5ERETPsbS0xNatW9GnTx989tlnmDlzpl6P9S5VqhRKlCjBy7H/wfUnBMmbQGEogoODsXz5cqxatQr16tUTHYeIiF7BxMQES5cuRfHixTF+/Hg8evQIc+fOhVyuf+d5ZDIZJEniBIr/0L9/SQNhSEuehIWF4fPPP8eQIUPQq1cv0XGIiOgNZDIZvvnmGyxZsgTz589H9+7dkZmZKTrWO/H398fZs2f1Nr8msNgJolAoDGLyxMOHD9GxY0f4+Phg7ty5ouMQEVEBDRw4EFu3bsX27dvRunVrPHv2THSkQpMkCRkZGTh//rzoKDqDxU4QhUKBR48e6fXtXjIzM/HRRx9BLpdj69atMDc3Fx2JiIgKoWPHjjh48CDOnDmDRo0aISYmRnSkQvHy8oKVlRXH2T2HxU6QvCVPoqKixAZ5D8OHD8cff/yB7du3w83NTXQcIiJ6Bw0bNsSpU6fw4MED+Pv769UwITMzM9SrV4/F7jksdoJ4enoC0N8lT5YvX46lS5di0aJF8PX1FR2HiIjeQ82aNREWFpY/IeHChQuiIxWYv78/QkND9XqGrzqx2AlSvHhxWFhY6GWxi4iIwJAhQzBw4ED07dtXdBwiIlIDDw8PhIaGolSpUmjQoAGOHz8uOlKBSJKER48e4c6dO6Kj6AQWO0Hkcjk8PDz0bgJFdHQ0OnbsiLp162LevHmi4xARkRoVK1YMx48fh5+fH1q2bIlt27aJjvRWeVeNeDlWhcVOIH1b8iQzMxOdOnWCUqnEtm3bOFmCiMgA2draYu/evfjoo4/QuXNnLF68WHSkN3J2ds6/Jy5xgWKhFAoFjh07JjpGgY0aNQqRkZE4ceIEihcvLjoOERFpiLm5OdatWwdXV1cMGTIE0dHR+PbbbyGTyURHeyUuVPx/PGMnUN7dJ/RhwOeqVauwaNEiLFiwIP/+fEREZLjkcjnmzJmDWbNmYerUqRgwYACys7NFx3olf39//Pnnn3q5Fp+6sdgJpFAokJ6ejujoaNFR3ujs2bMYNGgQ+vbti/79+4uOQ0REWiKTyTBmzBisWbMGK1euRKdOnZCWliY61kskSUJubi7OnDkjOopwLHYC5a1lp8sTKB4/foygoCB4eXlh4cKFOnsanoiINKdnz57Ys2cPDh48iBYtWiAhIUF0pBdUrFgRjo6OHGcHFjuhPDw8AOjuWnZZWVno3LkzsrOzsX37dlhYWIiOREREgnzwwQc4duwYLl26hPr16+PBgweiI+WTy+Xw8/NjsQOLnVA2NjZwdXXV2WI3evRohIWFYdu2bShRooToOEREJJivry9CQkKQmJgISZLwzz//iI6UT5IkhIeHIzc3V3QUoVjsBMubQKFr1q5di/nz52PevHkICAgQHYeIiHRE5cqVERYWBjs7OwQEBCAyMlJ0JACqCRSJiYm4fPmy6ChCsdgJpotr2f3xxx8YMGAAPvvsMwwaNEh0HCIi0jElS5bE6dOnUalSJTRu3BgHDhwQHQn16tWDiYmJ0V+OZbETTKFQ6NTkiSdPniAoKAjVq1fH4sWLOVmCiIheydHREYcPH0bTpk3Rtm1brF27VmgeGxsbeHl5sdiJDmDsFAoFoqOjkZqaKjoKsrOz0blzZ2RkZGD79u2wtLQUHYmIiHSYlZUVtm/fjl69euHTTz/FDz/8IDSPJEksdqIDGLu8JU9u374tOAkwduxYhISEYOvWrShVqpToOEREpAdMTU0RHByMSZMmYcyYMRg9erSwCQySJOH69euIiYkRsn9dwGInmKenJwDxS55s2LABP/74I+bOnYsGDRoIzUJERPpFJpNh6tSpWLBgAebOnYtPP/0UWVlZWs/h7+8PAAgPD9f6vnUFi51gbm5usLS0FFrszp8/j379+qFnz54YOnSosBxERKTfhg4dis2bN2PLli348MMPkZycrNX9lypVCiVLljTqy7EsdoLJ5XJ4eHgIm0ARGxuLoKAgVK5cGUuXLuVkCSIiei+dO3fGgQMHEBYWhsaNG+PJkyda3b+xj7NjsdMBopY8yc7ORpcuXZCSkoKdO3fCyspK6xmIiMjwNG7cGCdPnsTdu3cREBCAqKgore1bkiScPXsWmZmZWtunLmGx0wGiit2ECRNw4sQJbNmyBaVLl9b6/omIyHDVqlULYWFhyMnJgSRJ+PPPP7WyX0mSkJGRgXPnzmllf7qGxU4HeHp64vbt21qdRbR582b88MMP+OGHH9CoUSOt7ZeIiIyHQqFAaGgoihcvjgYNGuDkyZMa36eXlxesrKyM9nIsi50OUCgUSE9PR3R0tFb2d/HiRfTu3RvdunXD8OHDtbJPIiIyTq6urjhx4gTq1q2LFi1aYMeOHRrdn5mZGby9vVnsSJy8tey0MYEiLi4OQUFBqFixIoKDgzlZgoiINM7Ozg6//vor2rdvj06dOuHnn3/W6P4kSUJoaCiUSqVG96OLWOx0gIeHBwDNr2WXk5ODrl27IikpCTt37oS1tbVG90dERJTHwsICGzduxNChQzFw4EBMmTJFY8VLkiRER0fjzp07Gtm+LjMVHYAAa2truLm5abzYTZw4EUeOHMGhQ4dQtmxZje6LiIjov+RyOX766ScUL14cEyZMwKNHj7Bw4UKYmJiodT9+fn4AgNDQUKM73vGMnY7w9PTUaLHbsmULZs6ciVmzZqFJkyYa2w8REdGbyGQyjB8/HitWrMCyZcvQuXNnpKenq3UfRYsWRaVKlYxynB2LnY7Q5JInf/31Fz777DN06dIFo0aN0sg+iIiICqN3797YuXMn9u/fj5YtWyIhIUGt2zfWhYpZ7HSEQqHQyOSJ+Ph4BAUFoVy5cli+fDknSxARkc748MMPcfToUfz5558IDAzEo0eP1LbtvLXznj17prZt6gMWOx2hUCjw+PFjpKSkqG2bOTk56NatG+Li4rBz507Y2NiobdtERETqIEkSQkJCEBcXB0mScO3aNbVtNzc3F5GRkWrZnr5gsdMReUue3L59W23b/Oqrr3Dw4EFs3rw5f/tERES6pkqVKggLC4OVlRX8/f1x9uzZ995mxYoV4eTkZHSXY1nsdISnpycA9S15sn37dkyfPh0zZsxA8+bN1bJNIiIiTSlVqhRCQkJQvnx5NGrUCAcPHnyv7cnlcvj5+bHYkRhubm6wtLRUS7G7dOkSPv30U3Tq1AljxoxRQzoiIiLNc3JywpEjR9CoUSO0adMGGzZseK/tSZKE8PBwrd6yUzSuYydYrhJ4lgXEZ8nw+ZwVKFLbB4ejgVyoWreZHLA3AxzNAUczwM4MkL9h/kNCQgKCgoLg4eGBlStXcrIEERHpFWtra+zcuRP9+/dH9+7dERMTg5EjR77Ttvwkfzi6l0H4jYewLlYSiVlAVu67H2P1gUxpjPfb0AHJ2cCtZOB2CpD9779ATnY2TExf7toyAHn/SKYywMMGUNgCtv95aW5uLtq2bYvQ0FCcPXsW5cqV0+j3QEREpClKpRITJ07EjBkzMHbsWHz//fcFPlmRd4y9laxEDmRQKpWQy2R4VeEp6DFWX+hpbP0VlwFcSgJiMl58MwF4ZanDf16TrQRuJAPXkwEXC6CqPeBkrnru22+/xf79+/Hrr7+y1BERkV6TyWSYPn06XF1dMWLECERHR2P58uUwMzN77de8fIyV5W/rdWexCnqM1Rc8Y6clOUrgciJwLfnlQveu8rZTwRa4cXIPOrRvh++++w5ffvmlGrZORESkGzZv3oyePXuiWbNm2LJly0vLd2n6GFvFHjDRk0u0LHZaEJ8JRD4FUnI0tAOlEtF3buLCtmAE/ziT4+qIiMjgHDlyBEFBQahatSp+/fVXFC1aFIAWjrFQXZb1dlKNxdN1LHYa9jgdCItVtX5N/kXn5GTDzMQEkrMMrpYa3BEREZEgf/zxB1q1aoWiRYvi4MGDsHAprZVjrOzf/yRn6PwxlsVOgx6nA6Gxmn2z/ZcMgL8evPGIiIjexfXr19GiRQuUqeGNoQs2AVq8SqUPx1gWOw2JzwROxKimVGubHEBDF/04ZUxERFRYNx7F4vdUW5iYmkFuYqLVfev6MZYLFGtAjlJ1vV9UY84FcCZOlYOIiMiQ5CiBG3CGmYWF1ksdoPvHWBY7DbicqBrEKfLfPDkbuJwkMAAREZEG5B1jAXETBXX5GMtip2ZxGarp1rrg2jMgLlN0CiIiIvXgMfbtWOzU7FKSyM8QL5IBuJQoOgUREZF68Bj7drzzhBolZ6tWuwaArIwMbJ7zFU5tX4eUxHiUrlwDXcdMQ80Gzd64jUF+ZfHk/p1XPudWthwWnr6e/+eDa5fgr7BjuHE+ErEP76HhR59i6I+r859XQpUnOVt/b41CREQE8BhbUDoURf/dem7F64WjeiFi/za07jMCxT3K4/jW1Zj+6Qf45pfjqOwd8NptfPb1T0hPffE885P7d7Bp9iTUbND8hcd3LZmJtORnKOfljfiYR6/cnuzfXDUc3u97IyIiEonH2IJhsVOTXCVwO0X1hrt+/gxC92xGj4mz0W7gaABAYMeeGNW0GtZNH4vpu8Jeux3vlu1femzbvGkAgPpB3V54fMrWk3AuURoymQzdK9q+cntKqHJVswfkunL+moiIqBB4jC04jrFTk2dZqpsHA0DE/m2Qm5igWbf++c+bW1qicZc+uPZHOGIf3ivUtkN2b4RLaQ9Uqiu98HixkmUKdPuwbCXwLLtQuyQiItIZPMYWHIudmsRn/f//3750Hu6KCrC2K/LCa8p5eQMAoi5dKPB2b/19HvevX0H9dp+8Xz4dnLlDRERUEDzGFhyLnZrEZ/5/pk7840dwcCn+0msc/30s7vHDAm/39M4NAF4+RVwYMgAJOvSmIyIiKgweYwuOxU5NErP+vyBxZnoazMwtXnqNuYVl/vMFkZubi9A9m+FRrRZKlq/8ztmUABKy3voyIiIincRjbMGx2KlJ1nM3hTW3tEJWZsZLr8nMSM9/viAuR5xEXPQD1G//7p8kXpWPiIhIn/AYW3Asdmry/L+po2txJLxianTedGknV/cCbfP0zg2Qy+UIaNdVrfmIiIj0CY+xBcdipybP/0WWreKFh7euIfXZizeSu34+UvV8Va+3bi8rIwMRB7ajil9DOLkV7E1a0HxERET6hMfYgtOlLHrN7Lm/Sd/WHyE3JweHNwTnP5aVkYHjW1ahfC0fOLuXAgA8eXAXD27888rtnTu2HymJCWo5RfzffERERPqEx9iC4wLFamJvproZsBJAhVo+8GvTCRtnTkDS0xi4lS2HE9vW4Mn9KAyevSL/axaM6InLESex7Z7ype2d3rUBZhYW8P2g42v3+fvhvYi6fBEAkJ2dhTv//Jm/0GLd5m1RtnINAKoZOw5m6vteiYiItInH2IJjsVMTR3PgVsr///z5j2uxucRknNyhuo9dmUo1MGHVPlTxbfDWbaU+S8K5o7+iduPWsCli/9rXRezfjhPb1uT/+fbf53H77/MAgKLFS+a/6ZQAHMzf7fsiIiISjcfYgpMplcqXqywVWmImcCRGdIrXa+qq+sRDRESkb3iMLTgduiqs3+zMAFMduU/cf5nKADuemyUiIj3FY2zBsdipiVwGeNj8f2VsXSGDKpeu3JyYiIiosHiMLTgWOzVS2P5/ZWxdoYQqFxERkT7jMbZgWOzUyNYUcLHQnU8UMqjy2OrQKWIiIqJ3wWNswbDYqVlVe935RKGEKg8REZEh4DH27Vjs1MzJHKigI6dlK9ip8hARERkCHmPfjsVOA6rYAzYm4k4Xy6A6NVyliKAAREREGsJj7Jux2GmAiQzwKSr2TeftpMpBRERkSHiMfTMWOw1xNAckZ+2/8WQA/J1V+yciIjJEPMa+Hu88oWGP04GwWNUgS03/RcuhesO5WGp4R0RERDqAx9iXsdhpQXwmEPkUSMnR3D5sTVWnhnX5UwQREZG68Rj7IhY7LclRApcTgWvJqlO56vhLz9tOBTvVIE5dvd5PRESkSTzG/h+LnZbFZQCXkoCYjHd/8+V9nYuFag0dXZxuTUREpG08xrLYCZOcDdxKBm6nANn//gu87k34/OOm/94vT2Gre6tdExER6QJjPsay2AmWqwSeZavGCCRkAglZQFYukAvVQE0zOeBgBjiYq67t25nq1s2GiYiIdJUxHmNZ7IiIiIgMBNexIyIiIjIQLHZEREREBoLFjoiIiMhAsNgRERERGQgWOyIiIiIDwWJHREREZCBY7IiIiIgMBIsdERERkYFgsSMiIiIyECx2RERERAaCxY6IiIjIQLDYERERERkIFjsiIiIiA8FiR0RERGQgWOyIiIiIDASLHREREZGBYLEjIiIiMhAsdkREREQGgsWOiIiIyECw2BEREREZCBY7IiIiIgPBYkdERERkIFjsiIiIiAwEix0RERGRgWCxIyIiIjIQLHZEREREBoLFjoiIiMhA/A9nthgKqbdizgAAAABJRU5ErkJggg==\n" |
||
| 248 | }, |
||
| 249 | "metadata": {} |
||
| 250 | } |
||
| 251 | ], |
||
| 252 | "source": [ |
||
| 253 | "fig, (ax1, ax2) = plt.subplots(1, 2)\n", |
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| 254 | "\n", |
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| 255 | "# interpret diagonal of matrix as node attributes\n", |
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| 256 | "node_labels = {n: A[n,n] for n in range(len(A))}\n", |
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| 257 | "np.fill_diagonal(A, np.zeros(len(A)))\n", |
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| 258 | "\n", |
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| 259 | "G1 = nx.Graph(A)\n", |
||
| 260 | "pos1=nx.spring_layout(G1)\n", |
||
| 261 | "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n", |
||
| 262 | "edge_labels = nx.get_edge_attributes(G1,'weight')\n", |
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| 263 | "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n", |
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| 264 | "\n", |
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| 265 | "# interpret diagonal of permuted matrix as node attributes\n", |
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| 266 | "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n", |
||
| 267 | "np.fill_diagonal(A_perm, np.zeros(len(A)))\n", |
||
| 268 | "\n", |
||
| 269 | "G2 = nx.Graph(A_perm)\n", |
||
| 270 | "pos2=nx.spring_layout(G2)\n", |
||
| 271 | "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n", |
||
| 272 | "edge_labels = nx.get_edge_attributes(G2,'weight')\n", |
||
| 273 | "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n", |
||
| 274 | "\n", |
||
| 275 | "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n", |
||
| 276 | "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n", |
||
| 277 | "plt.tight_layout()\n", |
||
| 278 | "plt.show()" |
||
| 279 | ] |
||
| 280 | }, |
||
| 281 | { |
||
| 282 | "cell_type": "markdown", |
||
| 283 | "metadata": { |
||
| 284 | "id": "gttt4AcTNVp2" |
||
| 285 | }, |
||
| 286 | "source": [ |
||
| 287 | "::: {.note}\n", |
||
| 288 | "::: {.title}\n", |
||
| 289 | "Note\n", |
||
| 290 | ":::\n", |
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| 291 | "\n", |
||
| 292 | "The issue of non-unique numerical representations of graphs ultimately\n", |
||
| 293 | "stems from the fact that the nodes in a graph do not have an intrinsic\n", |
||
| 294 | "order, and by labelling them in a numerical data structure like a matrix\n", |
||
| 295 | "we therefore impose an arbitrary order.\n", |
||
| 296 | ":::\n", |
||
| 297 | "\n", |
||
| 298 | "Permutation equivariant embeddings\n", |
||
| 299 | "==================================\n", |
||
| 300 | "\n", |
||
| 301 | "When we design a machine learning model that takes graph data, the first\n", |
||
| 302 | "step is to encode the adjacency matrix into a quantum state using an\n", |
||
| 303 | "embedding or [quantum feature\n", |
||
| 304 | "map](https://pennylane.ai/qml/glossary/quantum_feature_map.html) $\\phi$:\n", |
||
| 305 | "\n", |
||
| 306 | "$$A \\rightarrow |\\phi(A)\\rangle .$$\n", |
||
| 307 | "\n", |
||
| 308 | "We may want the resulting quantum state to be the same for all adjacency\n", |
||
| 309 | "matrices describing the same graph. In mathematical terms, this means\n", |
||
| 310 | "that $\\phi$ is an *invariant* embedding with respect to simultaneous row\n", |
||
| 311 | "and column permutations $\\pi(A)$ of the adjacency matrix:\n", |
||
| 312 | "\n", |
||
| 313 | "$$|\\phi(A) \\rangle = |\\phi(\\pi(A))\\rangle \\;\\; \\text{ for all } \\pi .$$\n", |
||
| 314 | "\n", |
||
| 315 | "However, invariance is often too strong a constraint. Think for example\n", |
||
| 316 | "of an encoding that associates each node in the graph with a qubit. We\n", |
||
| 317 | "might want permutations of the adjacency matrix to lead to the same\n", |
||
| 318 | "state *up to an equivalent permutation of the qubits* $P_{\\pi}$, where\n", |
||
| 319 | "\n", |
||
| 320 | "$$P_{\\pi} |q_1,...,q_n \\rangle = |q_{\\textit{perm}_{\\pi}(1)}, ... q_{\\textit{perm}_{\\pi}(n)} \\rangle .$$\n", |
||
| 321 | "\n", |
||
| 322 | "The function $\\text{perm}_{\\pi}$ maps each index to the permuted index\n", |
||
| 323 | "according to $\\pi$.\n", |
||
| 324 | "\n", |
||
| 325 | "::: {.note}\n", |
||
| 326 | "::: {.title}\n", |
||
| 327 | "Note\n", |
||
| 328 | ":::\n", |
||
| 329 | "\n", |
||
| 330 | "The operator $P_{\\pi}$ is implemented by PennyLane\\'s\n", |
||
| 331 | "`~pennylane.Permute`{.interpreted-text role=\"class\"}.\n", |
||
| 332 | ":::\n", |
||
| 333 | "\n", |
||
| 334 | "This results in an *equivariant* embedding with respect to permutations\n", |
||
| 335 | "of the adjacency matrix:\n", |
||
| 336 | "\n", |
||
| 337 | "$$|\\phi(A) \\rangle = P_{\\pi}|\\phi(\\pi(A))\\rangle \\;\\; \\text{ for all } \\pi .$$\n", |
||
| 338 | "\n", |
||
| 339 | "This is exactly what the following quantum embedding is aiming to do!\n", |
||
| 340 | "The mathematical details behind these concepts use group theory and are\n", |
||
| 341 | "beautiful, but can be a bit daunting. Have a look at [this\n", |
||
| 342 | "paper](https://arxiv.org/abs/2210.08566) if you want to learn more.\n", |
||
| 343 | "\n", |
||
| 344 | "Implementation in PennyLane\n", |
||
| 345 | "===========================\n", |
||
| 346 | "\n", |
||
| 347 | "Let\\'s get our hands dirty with an example. As mentioned, we will\n", |
||
| 348 | "implement the permutation-equivariant embedding suggested in [Skolik et\n", |
||
| 349 | "al. (2022)](https://arxiv.org/pdf/2205.06109.pdf) which has this\n", |
||
| 350 | "structure:\n", |
||
| 351 | "\n", |
||
| 352 | "{.align-center\n", |
||
| 353 | "width=\"70.0%\"}\n", |
||
| 354 | "\n", |
||
| 355 | "The image can be found in [Skolik et al.\n", |
||
| 356 | "(2022)](https://arxiv.org/pdf/2205.06109.pdf) and shows one layer of the\n", |
||
| 357 | "circuit. The $\\epsilon$ are our edge weights while $\\alpha$ describe the\n", |
||
| 358 | "node weights, and the $\\beta$, $\\gamma$ are variational parameters.\n", |
||
| 359 | "\n", |
||
| 360 | "In PennyLane this looks as follows:\n" |
||
| 361 | ] |
||
| 362 | }, |
||
| 363 | { |
||
| 364 | "cell_type": "code", |
||
| 365 | "execution_count": 171, |
||
| 366 | "metadata": { |
||
| 367 | "id": "TIDSojceNVp3" |
||
| 368 | }, |
||
| 369 | "outputs": [], |
||
| 370 | "source": [ |
||
| 371 | "import pennylane as qml\n", |
||
| 372 | "\n", |
||
| 373 | "def perm_equivariant_embedding(A, betas, gammas):\n", |
||
| 374 | " \"\"\"\n", |
||
| 375 | " Ansatz to embedd a graph with node and edge weights into a quantum state.\n", |
||
| 376 | "\n", |
||
| 377 | " The adjacency matrix A contains the edge weights on the off-diagonal,\n", |
||
| 378 | " as well as the node attributes on the diagonal.\n", |
||
| 379 | "\n", |
||
| 380 | " The embedding contains trainable weights 'betas' and 'gammas'.\n", |
||
| 381 | " \"\"\"\n", |
||
| 382 | " n_nodes = len(A)\n", |
||
| 383 | " n_layers = len(betas) # infer the number of layers from the parameters\n", |
||
| 384 | "\n", |
||
| 385 | " # initialise in the plus state\n", |
||
| 386 | " for i in range(n_nodes):\n", |
||
| 387 | " qml.Hadamard(i)\n", |
||
| 388 | "\n", |
||
| 389 | " for l in range(n_layers):\n", |
||
| 390 | "\n", |
||
| 391 | " for i in range(n_nodes):\n", |
||
| 392 | " for j in range(i):\n", |
||
| 393 | " \t# factor of 2 due to definition of gate\n", |
||
| 394 | " qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n", |
||
| 395 | "\n", |
||
| 396 | " for i in range(n_nodes):\n", |
||
| 397 | " qml.RX(A[i,i]*betas[l], wires=i)" |
||
| 398 | ] |
||
| 399 | }, |
||
| 400 | { |
||
| 401 | "cell_type": "markdown", |
||
| 402 | "metadata": { |
||
| 403 | "id": "fBNWZT2LNVp3" |
||
| 404 | }, |
||
| 405 | "source": [ |
||
| 406 | "We can use this ansatz in a circuit.\n" |
||
| 407 | ] |
||
| 408 | }, |
||
| 409 | { |
||
| 410 | "cell_type": "code", |
||
| 411 | "execution_count": 172, |
||
| 412 | "metadata": { |
||
| 413 | "colab": { |
||
| 414 | "base_uri": "https://localhost:8080/", |
||
| 415 | "height": 264 |
||
| 416 | }, |
||
| 417 | "id": "wk7UvVY-NVp3", |
||
| 418 | "outputId": "7933a912-6f3b-49d5-c601-0f88a376aa54" |
||
| 419 | }, |
||
| 420 | "outputs": [ |
||
| 421 | { |
||
| 422 | "output_type": "display_data", |
||
| 423 | "data": { |
||
| 424 | "text/plain": [ |
||
| 425 | "<Figure size 2400x600 with 1 Axes>" |
||
| 426 | ], |
||
| 427 | "image/png": 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WLauLFy+6OwyXe/3115nVb6d+/fppxowZDt0m/WG/ovYHn7X7OWMMwTEYH+7H+ABsQ75yP67BXIdzg/djfNiPXOR5yGnGxfhwP8YHYBvylftxDeY6nBsAlGTFOX/cfIerwMBANWzY0O5YQkJCrNrCw8MVFhZm9zb/7s4771T58uUt5q3s2bNHXbt2dcj28RevntDVrl07TZkyRV9//bUiIyMtXtu4cWPuOp7EZDKpXLly7g7D5fz9/d0dgsfy9/d3+N8M/WG/ovYHn7X7OWMMwTEYH+7H+ABsQ75yP67BXIdzg/djfNiPXOR5yGnGxfhwP8YHYBvylftxDeY6nBsAlGTFOX8cOHDAYvmee+6Rr6+vXdvavXu3zpw5Y9V+8yMdi8PX11f33HOPvv3229y2/fv3M6HLCbz6kYsPPfSQ6tevr3//+9/av39/bvv58+c1efJklSpVSlFRUe4LEAAAAADgNcxms5o3b65OnTq5OxS7xMbGytfXV4mJie4OBQAAAAA8iqfXg5s3b5bJZNJXX33l7lAAoMRJT0+3WK5bt65d2zGbzWrVqpVV+8yZM1WqVCm7tpmfm2MsiU+ZcwWvntDl5+en2NhY5eTkqG3bturfv7+GDBmipk2b6pdfftHkyZMVHBzs7jABAAAAAF5g8eLFSkhI0MSJEy3as7KyNHHiRIWGhqp06dKqXbu2+vfvr9OnT9u87cuXL+uNN95Q27ZtVbt2bZUuXVo1a9ZU69attWDBAmVnZ+f5vuTkZPXp00ehoaEqU6aMbr31VnXs2FFffvml1brR0dEKCgrSm2++WbQDBwAAAIASzpn1oCQtXbpUAwYMUIsWLRQQECCTyaSFCxfmu35MTIxMJlO+/9LS0izWj4iIUJs2bTRs2DBdu3atSLEBAIqnadOmioyMVLdu3dSpUyc1btzYru2MHj06z/bBgwcXJ7w8NWnSRJ06dVK3bt0UGRmppk2bOnwf8PJHLkrSgw8+qJ07d2r8+PH69NNPlZ2drcaNG2vatGn6xz/+4e7wAAAAAABeICcnRzExMXrggQd03333WbR369ZNGzdu1H333acePXooOTlZsbGx2rJli+Lj41WtWrVCt3/x4kV9+OGHuvfee/XYY4+pWrVq+vPPP7V+/Xo9//zz+uSTT7R+/Xr5+Pz1u609e/bowQcfVHZ2trp27aoePXro9OnTWr16tbp166aYmBiNHz8+d31/f3+9/vrrGjx4sOLi4tS6dWvHfkgAAAAA4IWcXQ9K0pgxY3T06FFVrVpVtWrV0tGjR216X3R0dJ43t6hUqZJV27Bhw9S1a1d98sknevbZZ23aPgCg+Hr16qVevXoVaxvp6emaMmWKVXtSUlKxtpufIUOGaMiQIU7ZNv7i9RO6JOnee+/V+vXr3R0GvERwcLDMZnOB67Rv377QdQAAAAB4j/Xr1ystLc3ql3CLFi3Sxo0b1bNnTy1btkwmk0mSNGfOHL344osaM2aM5s6dW+j2b7nlFp0/f97q9uhXr15Vx44d9fXXX2v9+vV67LHHcl+bMGGCLl26pM8//1zdunXLbR8/fnzuD51GjBihgICA3NciIyP1xhtvaM6cOUzoAgAAAAAbOLselKTY2FiFhoYqKChIU6dO1ciRI216X+/evdW+fXub1n344YdVtWpVzZkzhwldAOBhQkJCrNrCw8MVFhbmhmjgKF79yEUAAAAAAFxhwYIFMplM6tGjh0X7/PnzJUlTpkzJ/fJekgYMGKD69etr2bJlunTpUqHb9/HxsZrMJUl+fn7q3r27JCklJcXitcOHD8tkMumRRx6xaA8KClLjxo116dIlXbx40eK1atWqqX379lq5cqXVawAAAAAAa86uB6Xrj0QMCgpyXNB58Pf31+OPP66dO3da1ZcAAOPavXu3zpw5Y9UeHx/vhmjgSEzoAgAAAACgGMxms7799lvdcccdqly5cm775cuXtWfPHt1xxx1WX7ybTCZ17NhRGRkZ+v777+3ed05OjjZs2CBJatSokcVrjRo1ktlstrpj9bFjx5SYmKimTZuqSpUqVtu8//77dfnyZe3atcvuuAAAAACgJHBnPWiL7du3a9q0aZo+fbo+//zzQn+4c//990uSvvnmG6fGBQBwDLPZrFatWlm1z5w5M88fh8KzlIhHLgIAAAAA4CxJSUk6d+6c1Z2wUlNTlZOTo9DQ0Dzfd6M9OTlZDzzwgE37unLliiZPniyz2ayzZ89qy5Yt+umnn9SnTx899NBDFutOmjRJcXFxevLJJ9W1a1fdfvvtOn36tFavXq2QkBB9+umnee6jRYsWkqS4uDh16tTJprgAAAAAoCRyZT1oj/Hjx1ssV6pUSTNnzlRUVFSe6/+9Huzfv7/T4gIAOMbNj/u9YfDgwS6OBM7AhC4AAAAAAIrhxIkTkqQaNWpYtJ8/f16SVLFixTzfV6FCBYv1bHHlyhVNmDAhd9lkMmno0KGaMmWK1bphYWGKj4/XU089pdWrV+e2V6lSRX369FFISEie+7hxHDeOCwAAAACQN1fWg0XRtGlTffzxx2rfvr1q1aqlkydPau3atRo3bpx69+6tSpUqqWvXrlbvox4EAM+Rnp6e53eCSUlJbogGzsAjFwEAAAAAKIazZ89Kuv5LZ2crX768zGazrl27puPHj2v27NmKjY1V+/btdeHCBYt19+7dq/vvv1+VK1fWvn37lJGRodTUVEVFRenVV19Vz54989zHLbfcIkn6448/nH48AAAAAODJXFkPFkX37t3Vp08f1atXT6VLl1ZwcLBefvllrVixQpI0ZsyYPN9HPQgAniOvH2uGh4crLCzMDdHAGZjQBQAGZjKZLJavXbvmpkhKjqtXr1os39wHMA7Gh+sxPgD7kK9cz9X5qkyZMpKky5cvW7Tf+CV2fr+4vjEBK79fbBfEx8dHderU0Ysvvqh58+YpLi5O//znP3Nfz87OVmRkpHx8fPTZZ5/p7rvvVtmyZVW/fn299957evzxx7VixQrFxcVZbfvSpUuSpLJlyxY5LgCOw/nD9bje9RyMD9djfAD2IV+5XkmoB4vjoYceUkhIiBITE61+FCRRDwKAp9i9e7fOnDlj1R4fH++GaOAsTOgCAAO7cdvlG1JTU90USclx+PBhi2VXF9SwHePD9RgfgH3IV67n6nxVrVo1SdK5c+cs2uvXry8fHx8lJyfn+b4b7aGhocXaf6dOnSRJW7duzW376aefdOTIEbVs2TLPL+IffPBBSdJ///tfq9duHMeN4wLgHpw/XI/rXc/B+HA9xgdgH/KV65W0etAeVatWlSRlZmZavUY9CADGZzab1apVK6v2mTNnqlSpUm6ICM7ChC4AMLDGjRtbLG/evFm7du1yUzTeb9euXdq8ebNF2819AONgfLgW4wOwH/nKtdyRr+666y75+Pjo559/tmgvU6aM7r33Xv388886evSoxWtms1mbNm1SuXLl1KJFi2Lt/7fffpMk+fv757ZduXJFkvL8pd7f2wMCAqxeu3Ec5HnAvTh/uBbXu56F8eFajA/AfuQr1yqJ9WBRZWRk6NChQypXrlzuxK6/ox4EAOMbPXp0nu2DBw92cSRwNj93BwAAyF+XLl1UunRpi9s1t27dWhEREapfv778/Py0fft2N0bo2bZv365Bgwbp6tWrOnz4sFWxX7p0aXXp0sVN0aEwjA/nYnwAjkO+ci4j5KtKlSqpSZMm+v7775WTkyMfn79+O9W/f3/Fx8dr5MiRWrZsWe7jPubOnavDhw+rf//+uY/okK4/KjE1NVX+/v4KCQnJbf/xxx8VHBxsdbetzMxMvfHGG5KkRx99NLe9UaNGqlChguLi4vT111/n3sVLko4fP665c+fKZDKpXbt2VsezZ88eScrzNQCuw/nDuYxw/oD9GB/OxfgAHId85VxGyFeuqAeLKj09Xb///rtuv/12i/ZLly6pX79+Sk9PV58+feTnZ/2/iakHAcDY0tPTNWXKFKv2pKQkN0QDZ2NCFwAYWGBgoHr06KFly5ZZtN9cmMI+Bw8e1MGDB/N9vUePHipfvrwLI0JRMD6ci/EBOA75yrmMkq+6d++u8ePHKz4+3uKW59HR0fr000/1n//8R0eOHFG7du2UkpKi1atXq169epo0aZLFdn799Vc1bNhQQUFBSktLy21fvny53nvvPbVp00bBwcGqUKGCfv31V61fv15nz57VAw88oNdffz13/YCAAE2fPl0DBgzQI488oi5duigsLEwnT57U6tWrdfHiRQ0ZMsTqC36z2awtW7aoYcOGVq8BcC3OH85llPMH7MP4cC7GB+A45CvnMkq+cnY9KEmxsbHauXOnJCkxMTG3bevWrZKkNm3aqG/fvpKks2fPKiwsTPfcc48aNmyomjVr6tSpU9q8ebNOnDihxo0ba/r06Xkey6ZNm1S5cmW1bdvWER8NAMDB8prwGx4errCwMDdEA2fjkYvwSDk5Oe4OwbD4bLzP3Llz+TWMG7Rr105z5851dxgoBOPDPRgfQNGRr9zDUfnKlmvsvn37ys/PT0uXLrVo9/Hx0RdffKGYmBidOXNGM2bMUFxcnF544QXt3r1b1apVsymGLl26KDIyUseOHdN//vMfvfvuu1q/fr2aNGmiuXPn6ptvvrH4Zbd0/dfgX3/9tR555BHt2rVL7777rr744gvdfffdWrp0qd555x2r/Wzfvl3Hjh3TgAEDbIqL+gNwLs4f7sH1rmdgfLgH4wMoOvKVe3hTPShJO3fu1KJFi7Ro0SIlJCRIkuLi4nLbbkz2kqRbbrlFL730ksxms7766iu9++67WrVqlWrXrq23335be/bsUZUqVaz2kZaWpri4OEVHR6t06dKFxkQ9CAD5c0aO/Omnn3TmzBmr9vj4eIfvy5k4f9iOCV3wCAEBARbLV65ccVMkxpeVlWWxbMtFtxFMnDhRK1eutHn9RYsWqUOHDk6MyDjKlSundevW6dlnn/WY/vRkpUuX1rPPPqt169apXLly7g4HhWB8uBbjA7Af+cq1ipuv7Kk/ateurcjISH3yySdKT0+32t748eOVkpKirKws/f7775o/f75q1KhhtZ3g4GCZzWarX2O3aNFC8+bN08GDB/Xnn38qOztbf/zxh7755hv1798/z0dlSFLHjh21du1anTlzRlevXtX//vc/bdu2Tc8++2ye68+fP1+33HKLoqOjCz1myXPrDxgL9WD+OH+4Fte7noXx4VqMD8B+5CvX8sZ6UJIWLlwos9mc77+FCxfmrluhQgV98MEH2rt3r06fPq3s7GxduHBBe/bs0Ztvvmn1Y6AbYmNj5efnp5dffrnQY5aoBwHg75w9n8FsNuu1116zap85c6ZKlSrl0H05G+cP2/HIRXiEmwdxZmammyIxvps/G09JgDExMTKZTBo0aJBmzJghX1/fAtdPS0vTtm3bXBSd+5UrV05Lly7VnDlztHbtWiUmJur8+fMym83avn17gbeVRv4aNWqktm3bymQyqWLFimrcuLG6dOnCYwM8DOPDORgfgOORr5zDGfnK3vpj0qRJWrlypWbNmqVRo0bZvX93+eWXX/TJJ59o+vTpqlSpkk3v8dT6A8ZCPVgwzh/OwfWud2B8OAfjA3A88pVzUA86zp9//qlZs2bpxRdfzPNxXnmhHgSAvzh7PsPp06f1888/W7RVrlxZgwcPduh+XIHzh+2Y0AWPULVqVYvl48ePuykS4ztx4oTFcl63zTWy2bNnKzExUStWrLDqd0jly5dXZGSkIiMjc9sGDRpEwW+ntm3bavbs2e4OAw7C+HAsxgfgPOQrx3JGvrK3/ggKCtKiRYt06tQph8bjKidOnND48eM1aNCgIr3n7zyt/oCxUA8WjPOHY3G9610YH47F+ACch3zlWNSDjnPkyBG9/vrreuWVV2x+D/UgAPzF2fMZatSooR9//FFTp07VtGnT5Ofnpx9++MGh+3AVzh+2Y0IXPEKDBg0sllNSUtwUifElJydbLIeGhropkqJ744039Msvv2jNmjVq0aKFPvvsM4WHh7s7LAAAAJQwxak/nn76aUeH4zIdOnQo8mPsPLn+gLFQDwIAAMAISmo9ePfdd+vuu+8u0nuoBwHgL66Yz1CmTBlNmDBBUVFROnDggOrUqePwfbgC5w/b+bg7AMAWNw/iU6dO6cKFC26KxrguXLig06dPW7R5UgIMDAzUF198obFjx+r48eNq06aNli1b5u6wAAAAUMJQf9jG0+sPGAv1IAAAAIyAetA21IMAYMmV54+QkBA98cQTTtm2s3H+KBomdMEj1K9fXyaTyaLt5pmbsP5MfHx8VK9ePTdFY78JEyZo5cqV8vHxUVRUlIYMGaKcnBx3hwUAAIASgvrDNt5Sf8BYqAcBAADgTtSDtqEeBABLnD9sw/mjaJjQBY8QEBCgoKAgi7bNmze7KRrj2rRpk8VyUFCQAgIC3BRN8XTv3l3x8fGqX7++3n//fXXu3Fnnzp1zd1gAAAAoAag/bONN9QeMhXoQAAAA7kI9aBvqQQCwxPnDNpw/ioYJXfAYnTt3tlhesWKFmyIxrps/k5s/M09z11136bvvvlPHjh21ZcsW3XPPPfrhhx/cHRYAAABKAOqPwnlb/QFjoR4EAACAu1APFo56EACscf4oHOePomFCFzzGU089ZbG8b98+HT582E3RGE9qaqoSEhIs2m7+zDxRpUqVtH79er355ps6cuSIWrdureXLl9u9vcOHDys2NlZ9+vRRx44dFR4ertatW+vxxx/X2LFjtXnzZl25csWBRwAAAABPRP1RMG+tP2As1IMAAABwB+rBglEPAkDeOH8UjPNH0fm5OwDAVu3atVO1atV05syZ3LZZs2ZpxowZbozKOD744AOL5erVq6tt27ZuisaxTCaTpk2bpvDwcPXt21c9e/ZUcHCwze83m8365JNPNGfOHO3cuTO37WZffvmlJk+erMqVK6t3794aNGgQz+wFAAAooag/CubN9QeMhXoQAAAArkY9WDDqQQDIG+ePgnH+KDru0AWP4efnpx49eli0zZo1SwcPHnRTRMaRmJioWbNmWbQ98cQT8vPzrjmbkZGR2rlzp+rWrasjR47Y9J4NGzaoadOmevbZZ5WUlKQXXnhBsbGxOnDggE6ePKkrV67o/PnzOnLkiDZs2KCYmBg1bNhQM2bMUMOGDfXGG2/ozz//dPKRAQAAwGioP/JXUuoPGAv1IAAAAFyFejB/1IMAkD/OH/nj/GEfJnTBowwdOlQBAQG5y9euXdOgQYOUk5PjxqjcKycnR4MGDdK1a9dy2wICAjR06FA3RlV00dHRatasWaHrNWvWTPv27dMjjzyi2267rdD1H330UVWqVElffvmlfvvtN82bN099+vRR48aNVb16dfn5+SkwMFBBQUHq1KmTxo4dqx07dujw4cMaOnSoPv74Y6uTCwAAAEoG6g9r3lJ/wFioBwEAAGA01IPWqAcBoHCcP6xx/rAfE7rgUUJCQjRs2DCLtu3bt2vgwIElMgnm5ORo4MCB2rFjh0X78OHDFRIS4qao7LNgwQJ17drVpnWrVKmidevW2fSr7E2bNmn79u3q0qVLkWb4BgUFadKkSUpLS9P/+3//z+b3AQAAwHtQf1jypvoDxkI9CAAAAKOhHrREPQgAtuH8YYnzR/EwoQseZ8SIEQoKCrJomz9/folLgjeS3/z58y3ag4ODNWLECDdFZb9jx47p4sWLNq//ww8/aPHixYWu99BDDxUnLFWqVEnh4eHF2gYAAAA8F/XHdd5Wf8BYqAcBAABgRNSD11EPAkDRcP64jvNH8TGhCx6nbNmymjdvntWva+fPn6/27dsrMTHRTZG5TmJiotq3b2+V/Pz8/DR37lyVKVPGTZHZLzg4WGFhYYqPj7dp/c8++0x9+vRxclQAAAAo6ag/vLP+gLFQDwIAAMCIqAepBwHAHpw/OH84ChO64JE6deqk5cuXWyXBHTt2KDw8XK+//rpSU1PdFJ3zpKam6vXXX1d4eLjVbQn9/Py0fPlyderUyU3RFd9vv/2mBx98ULGxsS7d78WLF3X69OkSNSMaAAAAtqP+8M76A8ZCPQgAAAAjoh6kHgQAe3D+4PzhCEzogsfq3r17nknw2rVrev/999WgQQM1b95cU6dO1b59+3ThwgU3RWq/CxcuaN++fZo6daqaN2+uBg0a6P3339e1a9cs1ruR/Lp37+6mSB3joYceUtmyZTVgwAC99NJLunr1qkO2e+zYsTz7f+3atWrWrJkqVqyoWrVqqVKlSurXr5/+/PNPh+wXAAAA3oP64y/eUn/AWKgHAQAAYFTUg3+hHgQA23H++AvnD/v4Fb4KYFzdu3fXunXrNGDAAKWlpVm9npCQoISEBI0cOVKSVL16dYWGhqpOnToqW7asAgIC5ONjjHmNOTk5ysrKUmZmpk6cOKHk5GSdPn260PcFBwdr7ty5XjGT9YEHHtDcuXPVtWtXzZ07VwcPHtTKlStVvXr1Ym23Xr16iomJ0dixY3PblixZoj59+shsNiskJERVq1bVoUOH9NFHH+n7779XfHy8AgICintIAAAA8CLUH95Vf8BYqAcBAABgZNSD1IMAYA/OH5w/ioMJXfB4nTp10o8//qipU6dq2rRpysrKynfd06dP25RUPEFAQICGDx+uESNGeNUzZuvXr689e/boueee0+eff64WLVpo9erVatGihd3bNJvNMpvNucsZGRl69dVXValSJS1fvlwdOnSQJGVmZqpv37769NNPNXv2bL3xxhvFPh4AAAB4F+oP76o/YCzUgwAAADAy6kHqQQCwB+cPzh/2MsZUPqCYypQpowkTJujQoUMaOHCgqlWr5u6QnKZ69eoaOHCgDh06pAkTJnhl8itXrpxWr16tmJgY/frrr2rbtq0WLVrksO1v3rxZ//vf/zRx4sTcL+8lqWzZsvr444916623asWKFQ7bHwAAALwL9QfgPNSDAAAAMDLqQQCAPTh/wB5M6IJXCQkJ0YcffqjffvtNW7Zs0cCBA1WvXj2ZTCZ3h2Y3k8mkevXqaeDAgdqyZYt+/fVXffjhhwoJCXF3aE43btw4ffbZZ/L399fzzz+vwYMHWz1v1x7JyckymUzq0qWL1WulS5dWRESEkpKSir0fAAAAeDfqD8B5qAcBAABgZNSDAAB7cP5AUfDIRXglPz8/dejQIffXtllZWTpy5IiSk5OVnJyss2fP6vLly7p8+bKbI7VUunRplS5dWlWqVFFoaKhCQ0NVr149BQQEuDs0t+natav27Nmjbt26afbs2UpMTCz2r6VzcnIkSTVr1szz9Ro1aujSpUvF2gcAAABKDuoPwDmoBwEAAGB01IMAAHtw/oAtmNCFEiEgIEBhYWEKCwtzdyiwQ1hYmL777jv17NlT69evV4sWLdS8efMibSMtLU3bt2+XpNznEv/+++8KCgqyWvfkyZOqXLly8QMHAABAiUT9ATgO9SAAAAA8CfUgAMAenD+QFyZ0AfAIFSpU0Nq1azV69GhNnTpVx48fL9L7Fy1apEWLFkmSzGazTCaTtm7dqujoaKt1k5KSFBwc7IiwAQAAAADFRD0IAAAAAACAkoYJXQA8hslk0uTJkxUeHq4+ffrY/BiM8ePH59leqVIlq7bk5GR99913GjRoUHFCBQAAAAA4EPUgAAAAAAAAShImdAEwhJycHJvXfeqpp3TvvfcqLS3NpvXz+wI/L7Vq1dLhw4d1yy232PweAAAAAID9qAcBAAAAAAAAS0zoAuCRgoKCFBQU5PDtli9fXuXLl3f4dgEAAAAAjkE9CAAAAAAAAG/HhC4AhnPs2LFC1/Hx8VGFChVUoUIFh+zzyy+/VHBwsJo0aeKQ7QEAAAAAis4d9SAAAAAAAABgNEzoAmA4wcHBMplMNq1bvXp1de/eXePHj1eNGjXs3ufjjz+ufv36ae7cuXZvAwAAAABQPM6qB7Ozs5WYmCg/Pz81btw433388MMP2r9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|
||
| 428 | }, |
||
| 429 | "metadata": {} |
||
| 430 | } |
||
| 431 | ], |
||
| 432 | "source": [ |
||
| 433 | "n_qubits = 5\n", |
||
| 434 | "n_layers = 2\n", |
||
| 435 | "\n", |
||
| 436 | "dev = qml.device(\"lightning.qubit\", wires=n_qubits)\n", |
||
| 437 | "\n", |
||
| 438 | "@qml.qnode(dev, diff_method=\"adjoint\")\n", |
||
| 439 | "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n", |
||
| 440 | " \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n", |
||
| 441 | "\n", |
||
| 442 | " perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n", |
||
| 443 | " return qml.expval(observable)\n", |
||
| 444 | "\n", |
||
| 445 | "\n", |
||
| 446 | "A = create_data_point(n_qubits)\n", |
||
| 447 | "betas = np.random.rand(n_layers)\n", |
||
| 448 | "gammas = np.random.rand(n_layers)\n", |
||
| 449 | "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n", |
||
| 450 | "\n", |
||
| 451 | "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n", |
||
| 452 | "plt.show()" |
||
| 453 | ] |
||
| 454 | }, |
||
| 455 | { |
||
| 456 | "cell_type": "markdown", |
||
| 457 | "metadata": { |
||
| 458 | "id": "ctJwGkJ3NVp3" |
||
| 459 | }, |
||
| 460 | "source": [ |
||
| 461 | "Validating the equivariance\n", |
||
| 462 | "===========================\n", |
||
| 463 | "\n", |
||
| 464 | "Let\\'s now check if the circuit is really equivariant!\n", |
||
| 465 | "\n", |
||
| 466 | "This is the expectation value we get using the original adjacency matrix\n", |
||
| 467 | "as an input:\n" |
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| 468 | ] |
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| 469 | }, |
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| 470 | { |
||
| 471 | "cell_type": "code", |
||
| 472 | "execution_count": 173, |
||
| 473 | "metadata": { |
||
| 474 | "colab": { |
||
| 475 | "base_uri": "https://localhost:8080/", |
||
| 476 | "height": 0 |
||
| 477 | }, |
||
| 478 | "id": "EDqMgzZ7NVp3", |
||
| 479 | "outputId": "d7ad1c5e-5ba0-44ec-86a9-957f4127a073" |
||
| 480 | }, |
||
| 481 | "outputs": [ |
||
| 482 | { |
||
| 483 | "output_type": "stream", |
||
| 484 | "name": "stdout", |
||
| 485 | "text": [ |
||
| 486 | "Model output for A: 0.3630430013602127\n" |
||
| 487 | ] |
||
| 488 | } |
||
| 489 | ], |
||
| 490 | "source": [ |
||
| 491 | "result_A = eqc(A, observable, betas, gammas)\n", |
||
| 492 | "print(\"Model output for A:\", result_A)" |
||
| 493 | ] |
||
| 494 | }, |
||
| 495 | { |
||
| 496 | "cell_type": "markdown", |
||
| 497 | "metadata": { |
||
| 498 | "id": "DEkoYys7NVp3" |
||
| 499 | }, |
||
| 500 | "source": [ |
||
| 501 | "If we permute the adjacency matrix, this is what we get:\n" |
||
| 502 | ] |
||
| 503 | }, |
||
| 504 | { |
||
| 505 | "cell_type": "code", |
||
| 506 | "execution_count": 174, |
||
| 507 | "metadata": { |
||
| 508 | "colab": { |
||
| 509 | "base_uri": "https://localhost:8080/", |
||
| 510 | "height": 0 |
||
| 511 | }, |
||
| 512 | "id": "qWDQi1aRNVp3", |
||
| 513 | "outputId": "96314ec2-d253-4979-91ef-dc45154a6d52" |
||
| 514 | }, |
||
| 515 | "outputs": [ |
||
| 516 | { |
||
| 517 | "output_type": "stream", |
||
| 518 | "name": "stdout", |
||
| 519 | "text": [ |
||
| 520 | "Model output for permutation of A: 0.3741504926751962\n" |
||
| 521 | ] |
||
| 522 | } |
||
| 523 | ], |
||
| 524 | "source": [ |
||
| 525 | "perm = [2, 3, 0, 1, 4]\n", |
||
| 526 | "A_perm = permute(A, perm)\n", |
||
| 527 | "result_Aperm = eqc(A_perm, observable, betas, gammas)\n", |
||
| 528 | "print(\"Model output for permutation of A: \", result_Aperm)" |
||
| 529 | ] |
||
| 530 | }, |
||
| 531 | { |
||
| 532 | "cell_type": "markdown", |
||
| 533 | "metadata": { |
||
| 534 | "id": "0MuYtWbFNVp3" |
||
| 535 | }, |
||
| 536 | "source": [ |
||
| 537 | "Why are the two values different? Well, we constructed an *equivariant*\n", |
||
| 538 | "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n", |
||
| 539 | "that embedding a permutation of the adjacency matrix leads to the same\n", |
||
| 540 | "state as an embedding of the original matrix. An *equivariant* ansatz\n", |
||
| 541 | "embeds the permuted adjacency matrix into a state where the qubits are\n", |
||
| 542 | "permuted as well.\n", |
||
| 543 | "\n", |
||
| 544 | "As a result, the final state before measurement is only the same if we\n", |
||
| 545 | "permute the qubits in the same manner that we permute the input\n", |
||
| 546 | "adjacency matrix. We could insert a permutation operator\n", |
||
| 547 | "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n", |
||
| 548 | "the observables!\n" |
||
| 549 | ] |
||
| 550 | }, |
||
| 551 | { |
||
| 552 | "cell_type": "code", |
||
| 553 | "execution_count": 175, |
||
| 554 | "metadata": { |
||
| 555 | "id": "cQLZbuBENVp4" |
||
| 556 | }, |
||
| 557 | "outputs": [], |
||
| 558 | "source": [ |
||
| 559 | "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])" |
||
| 560 | ] |
||
| 561 | }, |
||
| 562 | { |
||
| 563 | "cell_type": "markdown", |
||
| 564 | "metadata": { |
||
| 565 | "id": "2e8FSH7dNVp4" |
||
| 566 | }, |
||
| 567 | "source": [ |
||
| 568 | "Now everything should work out!\n" |
||
| 569 | ] |
||
| 570 | }, |
||
| 571 | { |
||
| 572 | "cell_type": "code", |
||
| 573 | "execution_count": 176, |
||
| 574 | "metadata": { |
||
| 575 | "colab": { |
||
| 576 | "base_uri": "https://localhost:8080/", |
||
| 577 | "height": 0 |
||
| 578 | }, |
||
| 579 | "id": "fJ6p7TLFNVp4", |
||
| 580 | "outputId": "2929b94c-aff7-4bae-8273-520d121612c5" |
||
| 581 | }, |
||
| 582 | "outputs": [ |
||
| 583 | { |
||
| 584 | "output_type": "stream", |
||
| 585 | "name": "stdout", |
||
| 586 | "text": [ |
||
| 587 | "Model output for permutation of A, and with permuted observable: 0.3630430013602128\n" |
||
| 588 | ] |
||
| 589 | } |
||
| 590 | ], |
||
| 591 | "source": [ |
||
| 592 | "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n", |
||
| 593 | "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)" |
||
| 594 | ] |
||
| 595 | }, |
||
| 596 | { |
||
| 597 | "cell_type": "markdown", |
||
| 598 | "metadata": { |
||
| 599 | "id": "g-F-D4kNNVp4" |
||
| 600 | }, |
||
| 601 | "source": [ |
||
| 602 | "Et voilà!\n", |
||
| 603 | "\n", |
||
| 604 | "Conclusion\n", |
||
| 605 | "==========\n", |
||
| 606 | "\n", |
||
| 607 | "Equivariant graph embeddings can be combined with other equivariant\n", |
||
| 608 | "parts of a quantum machine learning pipeline (like measurements and the\n", |
||
| 609 | "cost function). [Skolik et al.\n", |
||
| 610 | "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n", |
||
| 611 | "pipeline as part of a reinforcement learning scheme that finds heuristic\n", |
||
| 612 | "solutions for the traveling salesman problem. Their simulations compare\n", |
||
| 613 | "a fully equivariant model to circuits that break permutation\n", |
||
| 614 | "equivariance and show that it performs better, confirming that if we\n", |
||
| 615 | "know about structure in our data, we should try to use this knowledge in\n", |
||
| 616 | "machine learning.\n", |
||
| 617 | "\n", |
||
| 618 | "References\n", |
||
| 619 | "==========\n", |
||
| 620 | "\n", |
||
| 621 | "1. Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n", |
||
| 622 | " Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n", |
||
| 623 | " weighted graphs.\n", |
||
| 624 | " [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n", |
||
| 625 | "2. Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n", |
||
| 626 | " Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n", |
||
| 627 | " (2022). Theory for Equivariant Quantum Neural Networks.\n", |
||
| 628 | " [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n", |
||
| 629 | "\n", |
||
| 630 | "About the author\n", |
||
| 631 | "================\n" |
||
| 632 | ] |
||
| 633 | }, |
||
| 634 | { |
||
| 635 | "cell_type": "code", |
||
| 636 | "source": [ |
||
| 637 | "seconds = time.time()\n", |
||
| 638 | "print(\"Time in seconds since end of run:\", seconds)\n", |
||
| 639 | "local_time = time.ctime(seconds)\n", |
||
| 640 | "print(local_time)" |
||
| 641 | ], |
||
| 642 | "metadata": { |
||
| 643 | "colab": { |
||
| 644 | "base_uri": "https://localhost:8080/", |
||
| 645 | "height": 0 |
||
| 646 | }, |
||
| 647 | "id": "DAMWWXsOTLna", |
||
| 648 | "outputId": "ce8e4005-6f88-4457-bb8e-f920938309be" |
||
| 649 | }, |
||
| 650 | "execution_count": 177, |
||
| 651 | "outputs": [ |
||
| 652 | { |
||
| 653 | "output_type": "stream", |
||
| 654 | "name": "stdout", |
||
| 655 | "text": [ |
||
| 656 | "Time in seconds since end of run: 1693414140.4222758\n", |
||
| 657 | "Wed Aug 30 16:49:00 2023\n" |
||
| 658 | ] |
||
| 659 | } |
||
| 660 | ] |
||
| 661 | } |
||
| 662 | ], |
||
| 663 | "metadata": { |
||
| 664 | "kernelspec": { |
||
| 665 | "display_name": "Python 3", |
||
| 666 | "language": "python", |
||
| 667 | "name": "python3" |
||
| 668 | }, |
||
| 669 | "language_info": { |
||
| 670 | "codemirror_mode": { |
||
| 671 | "name": "ipython", |
||
| 672 | "version": 3 |
||
| 673 | }, |
||
| 674 | "file_extension": ".py", |
||
| 675 | "mimetype": "text/x-python", |
||
| 676 | "name": "python", |
||
| 677 | "nbconvert_exporter": "python", |
||
| 678 | "pygments_lexer": "ipython3", |
||
| 679 | "version": "3.9.17" |
||
| 680 | }, |
||
| 681 | "colab": { |
||
| 682 | "provenance": [] |
||
| 683 | } |
||
| 684 | }, |
||
| 685 | "nbformat": 4, |
||
| 686 | "nbformat_minor": 0 |
||
| 687 | } |