LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qulacs.simulator 25 qubit V100 319.98s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qulacs.simulator 25 qubit V100 319.98s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "7139cf83-e109-40d5-a21d-a53eab91ea1c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695112650.7796192\n",
            "Tue Sep 19 08:37:30 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-gpu\n",
        "# !pip install pennylane pennylane-qulacs --upgrade\n",
        "\n",
        "import time\n",
        "seconds = time.time()\n",
        "print(\"Time in seconds since beginning of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5b957375-4b8a-4533-d4e7-337f76e304b3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.23 0.16 0.55]\n",
            " [0.16 0.23 0.43]\n",
            " [0.55 0.43 0.39]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def create_data_point(n):\n",
        "    \"\"\"\n",
        "    Returns a random undirected adjacency matrix of dimension (n,n).\n",
        "    The diagonal elements are interpreted as node attributes.\n",
        "    \"\"\"\n",
        "    mat = np.random.rand(n, n)\n",
        "    A = (mat + np.transpose(mat))/2\n",
        "    return np.round(A, decimals=2)\n",
        "\n",
        "A = create_data_point(3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZNWu6j_jAmh"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "7ecd511c-6bc4-4d77-a1ce-9d7b1b157a8b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.23 0.43 0.16]\n",
            " [0.43 0.39 0.55]\n",
            " [0.16 0.55 0.23]]\n"
          ]
        }
      ],
      "source": [
        "def permute(A, permutation):\n",
        "    \"\"\"\n",
        "    Returns a copy of A with rows and columns swapped according to permutation.\n",
        "    For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n",
        "    \"\"\"\n",
        "\n",
        "    P = np.zeros((len(A), len(A)))\n",
        "    for i,j in enumerate(permutation):\n",
        "        P[i,j] = 1\n",
        "\n",
        "    return P @ A @ np.transpose(P)\n",
        "\n",
        "A_perm = permute(A, [1, 2, 0])\n",
        "print(A_perm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9CqRTZjAmi"
      },
      "source": [
        "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n",
        "and plot them, we see that they are identical as claimed.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "7fb565aa-c7a4-4128-e315-9a151fcbf977"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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BP/74IyIiIvDRRx9hwIAB8PHxwb59+ziDlug9sbCTiA+ZOPGiLl26wM7ODkuWLPnwUESkUypUqAB7e3ud6I59FRcXF/z66684c+YMbG1t0bJlSzRt2hQhISGioxHpDBZ2EqBWqwussDM3N0f//v2xcuVKpKamfng4ItIZMplMZ8bZvYmfnx+OHTuGXbt24f79+6hZsyb69OmDO3fuiI5GJHks7CQgKioKiYmJBVLYAYC/vz/i4uKwZcuWAjkeEemOnB0odL0LUyaToV27drh8+TKCgoJw4MABVKpUCePGjUN8fLzoeESSxcJOApRKJYD330rsdVxdXdGsWTPuREFkgBQKBZ48eaI3rVvGxsYYOnQobty4gQkTJuCXX36Bi4sLfvzxR6Snp4uORyQ5LOwkQKlUwtHREaVKlSqwYwYEBODs2bOSW4WeiLTL19cXAHS+O/a/rK2tMWXKFNy8eRMdO3bE6NGjUaVKFWzevFnnWyeJChILOwkoqPF1L2rTpg3Kli3LVjsiA1OiRAk4OTnpXWGXo1SpUli6dCkuX76MatWqoXv37vDz88Px48dFRyOSBBZ2EqCNws7Y2BhDhgzBxo0bkZCQUKDHJiJpyxlnp888PDzw+++/48iRI1Cr1WjQoAHatWuHiIgI0dGIhGJhJ9izZ88QHR1d4IUdAAwaNAgZGRlYu3ZtgR+biKRLoVAgODjYILYXbNiwIc6ePYtNmzYhLCwM1apVw9ChQ/Ho0SPR0YiEYGEnWGhoKICCmzjxolKlSqFDhw4ICgriGBQiA6JQKJCSkmIwrVdyuRzdunVDREQEvv/+e2zduhWurq6YMmUKkpKSRMcjKlQs7AQLCQmBhYUF3NzctHL8wMBARERE4NixY1o5PhFJT40aNSCXy/W+O/a/zMzMMGrUKERGRiIwMBCzZs2Cq6srlixZYhCtl0QACzvhlEolvLy8YGRkpJXjN2zYEJUrV+YkCiIDYmVlBQ8PD4Mr7HIUK1YMc+bMwbVr19C0aVP4+/vD09MTv//+O3svSO+xsBNMGxMnXiSTyeDv74/t27dzzAmRATGECRRv4+TkhHXr1iE4OBilS5dG+/bt0bBhQ4P/dyH9xsJOoLS0NERERGi1sAOAvn37wsTEBMuXL9fqeYhIOhQKBS5fvsytBaHpmj548CD27t2LZ8+ewc/PD926dcOtW7dERyMqcCzsBAoPD0dWVpbWCztbW1v06NEDS5cuhUql0uq5iEgaFAoFVCoVQkJCREeRBJlMhpYtW0KpVGLFihU4ceIEKleujFGjRuHp06ei4xEVGBZ2AimVSshkMnh6emr9XAEBAbh79y727Nmj9XMRkXjVqlWDubk5ux3/w8jICAMGDMCNGzfwzTffYMWKFXBxccGcOXPe+sVXrVYjNDQUW7duRUxMTCElJno/LOwEUiqVcHd3h6WlpdbPVbNmTfj6+mLRokVaPxcRiWdiYgIfHx8Wdq9RpEgRfP3117h58yZ69eqFLVu2vHES2/379zFq1Ch8/PHHmDt3LpycnDBmzBhkZGQUYmqit2NhJ5C2J078V2BgIPbv34/IyMhCOycRiaNQKHD+/HnRMSStRIkS+Pnnn3HkyJE3LokSGBiIs2fPYv78+fj777+xbds27Nu3D5cuXSrEtERvx8JOkOzs7EIv7Lp27YpixYphyZIlhXZOIhJHoVDg5s2bePbsmegokmdtbQ1jY+NXPrd//37s3r0bX3/9NQYNGgRTU1O0adMGGRkZ+O233wo5KdGbsbATJCoqCs+fP4ePj0+hndPCwgL9+vXDypUrkZaWVmjnJSIxfH19AYCtdh/o22+/RceOHdGsWbPcxzIyMmBmZgY7OzuByYhexsJOEKVSCUA7W4m9ib+/P54+fYqtW7cW6nmJqPC5urrC1taW4+w+QFhYGM6cOYNhw4bB1NQ09/HDhw/D2toa1tbWr3xfbGws/vzzTzx8+LCwohIBYGEnjFKpRMmSJeHo6Fio53V3d0eTJk24EwWRAZDJZBxn94H27NkDhUIBV1fX3MfS0tJw9OhRpKSkoGXLlgCQZ0eLrKwsnD9/Ht9//z3q1q2LXr16sTucCg0LO0EKe3zdiwICAnD69OncVkMi0l85O1BwK638KVWqFO7duwczM7Pcx/bv34+///4bTZs2hZOTE9RqNWQyWe7zxsbGqF27Nn755Rc0a9YMu3bt4n7dVGhY2AkSEhIirLBr164dSpcuzVY7IgPg6+uLmJgY3L17V3QUnVS1alXY2toiLCwMKpUK165dw5QpU2BnZ4fhw4cDwEtFs1qthp2dHSpXroyQkBD07NkTderUeeVriQoaCzsBnjx5gnv37gkr7IyNjTFkyBBs2LABiYmJQjIQUeHImUDBcXb54+npiVatWqFFixaoW7cuGjRoAFtbW3z77bcoX748AEAuz/tRmp2dDQBYt24dnjx5gpYtW6JkyZIANN3jLxZ3mZmZhfSTkKFgYSdAaGgogMKfOPGiQYMGIS0tDevWrROWgYi0r1SpUihXrhzH2eWTqakp5syZg4iICHTr1g1bt27Frl274OPjg0OHDuHRo0cvvSdnoeOffvoJDRs2hJ+fHwDkrpMnk8lw69YtTJgwAYMGDUKvXr1w+fLlwvuhSK+xsBNAqVSiSJEieQbjFrYyZcqgffv2WLRoEbsGiPRczjg7yr+KFSti1KhRqFevHooWLYobN25gwIABmDt3bp6tyHL+vGHDBsTGxqJt27a5rXU5LXs//vgjevTogQsXLsDDwwMymQy1a9fG559/jtTU1ML/4UivsLATQKlUwsvL643b1xSGwMBAhIeH48SJE0JzEJF2KRQKXLhw4a17odK7K1myJPz9/VGvXr3ce7larc7988KFC9GgQYPc1rrMzEzI5XJcuXIFc+fORYMGDbBo0SKMHz8e69atw759++Di4sI1RumDvXqZbdIqpVKJjz/+WHQMNGrUCO7u7ggKCkL9+vVFxyEiLfH19UVSUhKuXr2KqlWrio6jF6ytrTFx4sTcv6vVakyZMgWtWrXCrVu38OTJE7Rv3x6lS5cG8G/37NSpU/Hw4UOcOXMGhw8fRlZWFn7++WfUq1cPHh4esLGxEfLzkP5gi10hS0tLQ0REhNDxdTlkMhn8/f3x22+/ISYmRnQcItKSmjVrQiaTcZydFmVlZSEiIgJ16tRBz5494eTkhJo1a+Y+J5fLcfXqVfz222+oU6cOJk+ejPXr16NJkyb47rvvEBcXB3t7+5cmYhC9L15BhezKlStQqVSSKOwAoF+/fjA2NsaKFStERyEiLSlatCiqVKnCcXZaZGJigi1btuDhw4cYPnw4jh49ij59+uDcuXO5rXU7duyAi4sLvv76azRp0gSVKlVCt27dcPjwYVy8eFHwT0D6goVdIVMqlZDL5fD09BQdBQBQrFgxdOvWDUuWLOH4GyI9xgkUhcPR0RELFizAw4cP4e7ujnPnzuUuXly0aFEAyLPnrImJCapWrYr79+8LyUv6h4VdIVMqlahUqRKKFCkiOkqugIAAREdH488//xQdhYi0xNfXF6GhoRycX0gcHR2xdOlSfP7557mPFStWDOnp6YiNjQWgWe/u+PHjuHv3LurWrSsqKukZFnaFTORWYq/j6+uLmjVrYtGiRaKjEJGWKBQKZGVlcStBgZo3b47y5cujW7du+P3339GrVy8sX74cXbt2haura+7CxkQfgoVdIcrOzkZoaKjkCjtAs/TJvn37cPv2bdFRiEgLvLy8YGpqygkUAtnb22P37t3w8PDAjBkzkJqaivHjx2P69OkAkGe/WaL8kqm5Om2hiYyMhKurK/bv359njIUUpKSkoEyZMhg6dChmzZolOg4RaUHt2rXh5ubGHWckICMjA4BmZ4v/yszMxOXLl2Fubg4PD4/CjkY6ji12hSgkJAQAUL16dcFJXlakSBH07dsXK1asQHp6uug4RKQFvr6+nEAhEaampq8s6gDNhIrp06fD09MTQ4YMwcOHDws5HekyFnaFSKlUolSpUnB0dBQd5ZUCAgLw5MkTbNu2TXQUItIChUKB69evIz4+XnQUeotNmzbhhx9+wG+//QZXV1d88803eP78uehYpANY2BUiKU6ceFGlSpXQqFEjBAUFiY5CRFqgUCgAABcuXBCchN7GzMwMI0aMQGRkJD7//HPMnj0bbm5uWLx4MTIzM0XHIwljYVeIpF7YAZpWu5MnT+LSpUuioxBRAXNzc4ONjQ27Y3WIra0tZs+ejevXr6N58+YIDAyEp6cndu3aBQ6Rp1dhYVdIYmNjcf/+fckXdu3bt0epUqXYakekh+RyOWrVqsXCTgeVL18ea9asQXBwMMqVK4cOHTqgQYMGOHv2rOhoJDEs7ApJaGgoAEi+sDMxMcHgwYOxfv16jucg0kPcgUK3+fj44MCBA9i3bx/i4+NRu3ZtdOnSBZGRkaKjkUSwsCskSqUSlpaWcHFxER3lrQYPHozU1FSsX79edBQiKmAKhQIPHz7kFlY6TCaToXnz5ggJCcGqVatw6tQpVKlSBSNGjMCTJ09ExyPBWNgVEqVSCS8vr9zNoKWsbNmyaNu2LRYtWsQxHER6JmcCBVvtdJ+RkRH69euH69ev49tvv8WqVavg4uKCWbNmITU1VXQ8EoSFXSHRhYkTLwoMDERYWBhOnjwpOgoRFaDSpUujTJkyLOz0SJEiRTBx4kRERkaib9++mDx5Mtzd3bFmzRqoVCrR8aiQsbArBKmpqbh69Sp8fHxER3lnjRs3hqurKydREOkhLlSsn4oXL46FCxciPDwctWvXRr9+/VCzZk389ddfoqNRIWJhVwiuXLkClUqlUy12crkc/v7+2LZtGx4/fiw6DhEVIIVCgQsXLnDTeT3l5uaGrVu34tSpU7C0tESzZs3QvHnz3El8pN9Y2BUCpVIJuVyOatWqiY7yXvr16we5XI6VK1eKjkJEBUihUCAxMRHXr18XHYW0qE6dOvj777+xfft2REVFwcfHB/369cPdu3dFRyMtYmFXCEJCQlC5cmVYWFiIjvJe7O3t0bVrVyxZsoTjNIj0SK1atQBwAoUhkMlk+PTTTxEWFoaff/4Ze/fuhbu7OyZOnIiEhATR8UgLWNgVAl2bOPGigIAAREVFYf/+/aKjEFEBsbGxQaVKlVjYGRATExMEBgbi5s2bGDNmDBYsWAAXFxcsXLgQGRkZouNRAWJhp2XZ2dkIDQ3V2cJOoVDAx8cHixYtEh2FiAqQQqHA+fPnRcegQla0aFFMmzYNN27cQIcOHTBq1Ch4eHhg69atXN5KT7Cw07LIyEgkJyfrbGEnk8kQGBiIvXv3IioqSnQcIiogCoUCSqUS6enpoqOQAGXKlMHy5csRGhqKSpUqoUuXLrlj8ki3sbDTMqVSCQCoXr262CAfoHv37ihatCiWLl0qOgoRFRCFQoGMjAxcunRJdBQSqFq1atizZw8OHTqEzMxM1KtXDx06dMC1a9dER6N8YmGnZUqlEqVLl0aJEiVER8k3S0tL9OnTB8uXL+e3eyI9Ub16dZiYmHCcHQEAGjVqhPPnz2PDhg1QKpWoWrUqAgMDERMTIzoavScWdlqmyxMnXhQQEIDY2Fhs375ddBQiKgBmZmaoXr06x9lRLrlcjh49euDq1auYNWsWNm3aBFdXV0ybNg3Jycmi49E7YmGnZfpS2FWpUgUNGzbkThREekShULDFjl5ibm6OMWPGIDIyEkOGDMH06dPh5uaG5cuXIysrS3Q8egsWdlr0+PFjPHjwQC8KO0DTanfixAmEhYWJjkJEBUChUODq1atcz4xeyc7ODvPmzcPVq1fRsGFDDB48GN7e3tizZw9n0EoYCzstytm+RV8Kuw4dOsDR0ZGtdkR6wtfXF2q1GsHBwaKjkIRVqFABGzduxPnz51G8eHG0adMGjRo1woULF0RHo1dgYadFSqUSVlZWcHFxER2lQJiammLw4MFYt24dkpKSRMchog9UqVIlWFtbszuW3kmtWrVw+PBh/PHHH3j8+DF8fX3Ro0cPLoUlMSzstEipVKJ69eqQy/Xnn3nIkCFITk7Ghg0bREchog9kZGSEWrVqcQIFvTOZTIbWrVsjNDQUy5Ytw9GjR1GpUiWMGTMGz549Ex2PwMJOq/Rl4sSLypUrhzZt2mDRokUcY0GkBziBgvLD2NgYgwYNwo0bNzBp0iQsWbIELi4u+P7775GWliY6nkFjYaclKSkpuHr1qt4VdgAQGBiIS5cu4fTp06KjENEHUigUuHfvHh48eCA6CukgS0tLTJ48GTdv3kT37t0xYcIEVK5cGRs2bEB2drboeAaJhZ2WhIWFITs7Wy8Lu6ZNm8LFxYWTKIj0gK+vLwCwO5Y+iKOjIxYtWoSwsDB4e3ujV69e8PX1xeHDh0VHMzgs7LREqVTCyMgIVatWFR2lwMnlcgwdOhRbtmzBkydPRMchog9QtmxZlCxZkoUdFYjKlStj586dOH78OExMTNC4cWO0bt0aV65cKbQM2WogIQOISgZC4oCjj4G/HgH7H2n+/+hjzeNRyZrXZevZqCIWdlqiVCpRuXJlWFhYiI6iFf3794dMJsPKlStFRyGiDyCTyTjOjgpcvXr1cPr0aWzZsgXXrl2Dl5cXBg0apNUu/6Qs4FI8sPsBcPAxEBwH3E4GnmYAiVma5xOzNH+/nax5/uBjzesvxWue1wcs7LREHydOvMjBwQFdunTBkiVLOI6CSMcpFAqcP3+ev8tUoGQyGTp37ozw8HDMnz8fO3fuhKurKyZPnoznz58X2HmepQMnYjUtcjeTgKwXWuBe1xj34uNZas379j/SHOdZRoFFE4KFnRaoVCpcunRJrws7QLMTxa1bt3DgwAHRUYjoA/j6+iI+Ph43b94UHYX0kKmpKb744gtERkZixIgR+P777+Hi4oJFixYhMzMz38dVqYHL8cCRWCA2XfNYfntVc94Xmw4ceaw5rkpHu2hZ2GlBZGQkkpOT9b6wq127NqpXr45FixaJjkJEH6BWrVoAOIGCtMvGxgbfffcdrl+/jlatWuHzzz9HtWrVsGPHjvdePisuQzNe7vo/a+UXVA2Wc5zrScDBGM15dA0LOy1QKpUAgOrVq4sNomUymQyBgYHYs2cPoqOjRcchonyys7ODm5sbx9lRoShXrhxWr16NixcvwtnZGZ999lnumLx3EZOmmQCRotJuzuQszXlidGxZPhZ2WqBUKlGmTBkUL15cdBSt69GjBywtLbF06VLRUYjoA3ACBRU2b29v7N+/H/v378fz589Rt25ddO7cGTdu3Hjte2LSgJNPgGwUXCvd66ihOc/JJ7pV3LGw0wJ9nzjxIisrK/Tp0wfLly9HRoYOtlkTEQDNOLuQkBD+HlOha9asGS5evIjVq1fjzJkz8PDwwBdffIHY2Ng8r4vLAE490X5B919qaM6rK92yLOy0QKlUwsfHR3SMQhMQEICYmBjs2LFDdBQiyieFQoH09HSEhYWJjkIGyMjICH379sX169cxbdo0rFmzBq6urvjuu++QmpoKlRo4+7Twi7oc2QDOPdONCRUs7ApYTEwMHj58aDAtdgBQtWpV1K9fnztREOkwb29vGBsbszuWhLKwsMCECRMQGRmJfv364X//+x/c3d3x68nLSFaphRV2gGadu/BEgQHeEQu7ApYzccKQCjtA02p37NgxhIeHi45CRPlgYWEBLy8vFnYkCQ4ODliwYAEiIiLQumtvmJSvCkAmOhauP5f+Oncs7AqYUqmEtbU1KlSoIDpKofrss89QokQJttoR6TBfX18WdiQprq6u6Dl+JuQy8UUdoCktrySITvFmLOwKmFKpRPXq1SGXG9Y/rampKQYNGoS1a9ciKSlJdBwiygeFQoHw8PAC3RWA6EMkZQGP0wHIZMhMT8e6meMxuGZp9HC1wIS2fgg9/tdbj3Hmz+34IaArAj+qiB5uRfBFg0pYM3U0khPiX3rtqimjMLZlDfSrZocebkUw4pMq+PWHKUhN1nyuqaHJI+Xtxwyr+igEhjQj9r+GDBmC58+fY9OmTaKjEFE+KBQKqNVqXLx4UXQUIgDAraR/O2B//rIf/lj2A+p92hP9v10AuZERZvZthYhzf7/xGEvGD8G9mxGo/2kvDJi6EN4NW+DPNT/jqw51kJ6amue1kZfOo4qiHrqM/hb9v12AanU+wc5FszCjd4vcLfdk/+SSKpn6fZd7ptdKTk6GtbU1li1bhoEDB4qOI0Tbtm1x7949XLx4ETKJNJ0T0btRqVSwsbHBN998g7Fjx4qOQwYuWw3sfqDZy/VGyDlMbOeH3l/PRXv/MQCAjLQ0fNmkGoo6lMDMnadee5yw00dRrU7DPI8d3bYWP4/qC/85y9Ck+6A35vh9yTysnT4GM3edhnuN2gAAYxnQtjQgl+DHHFvsClBYWBjUarXBttgBQGBgIJRKJc6ePSs6ChG9JyMjI9SsWZPj7EgSnmdqijoAOLN3G+RGRmjac0ju86bm5mjUbSCuB5/Gkwd3X3uc/xZ1AODX4lMAwP0bEW/NUaKcMwDk6brNUgPPJdody8KuACmVShgZGaFq1aqiowjTvHlzVKhQgZMoiHQUd6AgqYjL/PfPt6+EoHRFdxSxLprnNa7eCgBA1BXlex07PvYRAMDazuGl51RZWUh89gTPHj2A8tgBbJo7CRZW1rnnys0n0dmxLOwKkFKpRJUqVWBubi46ijByuRxDhw7Fr7/+iqdPn4qOQ0TvSaFQIDo6GjExMaKjkIGLy/h3fF1czEPYlij10muK/fPYs5gH73XsnYtmQ25khDqtO730XOSlCxhQvTiG+JbB9F7NoVarMX7l77AuZpf7GhmAeBZ2+s+QJ068aMCAAVCr1Vi1apXoKET0nhQKTavE+fPnBSchQ5eQ+e9OExlpqTAxNXvpNaZm5rnPv6sTOzbi0OYVaDtkNEpVcHvp+bJuHvjfxr8wbvlOtA8YB/MilkhLzjtbQg0gPvOlt0oCC7sColKpcOnSJRZ2AIoXL47OnTtj8eLFubOIiEg3lC9fHiVKlGB3LAmX+cLHh6m5BTIz0l96TUZ6Wu7z7yL87AkEjR0I7wbN0WPcjFe+poh1UXjVawJF8/bo/dVstB08GnMGtkdUeOhr80kJC7sCcvPmTaSkpLCw+0dAQAAiIyNx8OBB0VGI6D3IZDIuVEyS8GLdVMyxFOIfP3zpNXH/PGbnWPqtx4sKD8Xsge1QrlI1jF6yDUbGxu+Uw6/lZwCAk79vfm0+KWFhV0AMdSux16lbty48PT2xaNEi0VGI6D0pFAqcP38eXA2LRHqxQHH28MaDW9eR8jzvZq03QjQrMDhX9X7jsR5FRWJ67xawsS+Br9buhYWl1TvnyMxIR3Z2NlIS8245IdUCSqq5dI5SqUS5cuVgb28vOookyGQyBAYGYvfu3bh79/XT0IlIehQKBZ49e4Zbt26JjkIGzOSFCqV2607IVqnw14aluY9lpqfjyJZVcPPxg0PpcgCA2PvRuH/zap7jxD1+hGk9m0Euk2PS+v2wsS/+yvMlJ8QjK/PlgXOHNi0HAFT0qvXafFLybu2Q9FYhISFsrfuPnj17YuzYsVi2bBmmTp0qOg4RvSNfX18AwLlz5+Di4iI4DRkqGxPgWYZmooK7jx/qtOmMjbMnIvHpY5R0dsXRbWsQey8KgXNX5L7np5F9EH7mGLbd/be1eUbvFoiJvoX2AeNw9fzfuHr+350qbBwcUb1+UwDAldNHsfKbL1C7VSeUquCGrMwMRJw7gbN/boeLVy3U/6xX7vtkAGxNtP5PkC8s7AqIUqnEkCFD3v5CA2JtbY3evXtj2bJlmDx5MkxMJPpbQER52Nvbo2LFijh37hy6d+8uOg4ZqGKmwK3kf/8+fP5abC4zGce2r0NyQhycKnth4qo/4FG7/huPkzPpYVfQnJee86jdILewK1/ZE1XrfoLzB3Zpxu6p1XB0ckGnkf9De/+xMDE1zX2fGoCt6UuHkwRuKVYAMjIysHjxYtSpUyf3my5pXL58GV5eXtiyZQs6d+4sOg4RvaPu3bvj7t27+PvvN+/DSaQtCRnAwceiU7xeE0dNq6LUsLArIBkZGTA1lWj5Lli9evVgYmKCw4cPi45CRO9o/vz5+Prrr5GQkMDWdhLixb1ipYZ7xRoAFnWvFxAQgCNHjiAi4u178hGRNCgUCqSmpuLKlSuio5CBksuACpb/7j4hFTJockmxqANY2FEh6NixI4oXL47FixeLjkJE78jHxwdGRkZcz46Eqmj17+4TUqGGJpdUsbAjrTMzM8PAgQOxZs0aJCcnv/0NRCRckSJFUK1aNW4tRkJZGQMlzKTTaieDJo+VhKeesrB7TxySmD9Dhw5FYmIiNm/e/PYXE5EkKBQKttiRcFVtpNNqp4Ymj5SxsHtPMlne7w3cC/XdODs7o2XLlli0aBGLYyIdoVAoEBYWxpZ2EsrOFHCXSNenu7Umj5SxsHsPz58/x6ZNm/IUJnK5HKmpqYiPj2fB8haBgYG4ePEiu3aIdISvry+ys7Nx8eJF0VHIwHnYAJZG4rpkZdB0v3oUFRTgPbCwew/79u3D3Llzc1vtwsPD0aVLF7Ro0QIjRozAb7/9JjihtLVo0QJOTk4ICgoSHYWI3kHVqlVhYWHBL2MknJEM8LMXW9gp7DQ5pI6F3XvYv38/KlSoAAA4cuQI+vfvj6ioKFSvXh13795Fly5d8PXXXwPgWLxXMTIywtChQ7F582Y8e/ZMdBwiegtjY2PUrFmT4+xIEoqZAnUdCr+4kwH4yEFzfl3Awu49nD59Gu3atQMArFy5EpUrV8bWrVuxcOFCHD58GFOnTsXBgwdx69atl8bikcbAgQOhUqmwevVq0VGI6B1wAgVJiaO5psiSo3AKPDmAjx2AEuaFcLICwsLuPVy7dg0JCQmIi4vDqVOn0KVLFzg5OUGlUgEAevfujeTkZDx58kRwUukqUaIEOnXqhMWLF3PiCZEOUCgUuH37NmJjY0VHIQKgKe4algCKGGn3PFbGmvPoUlEHsLB7Z7GxsXBycsLmzZvRsmVLJCUlwdraGoCmixHQrNd269YtVKpUSWRUyQsICMCNGze4xRiRDsjZ/5rj7EhKipkCTUtqZsuq1WqosrIK5Lg5rYDu1pq9YHWl+/VFLOzeka2tLdavX4/hw4ejefPm6Nq1a25LHaBZ9uTIkSNwdHSEjY3EF7kR7OOPP0bVqlWxaNEi0VGI6C0qVKgAe3t7FnYkOUYywEmeiO96NUPC3RsA8t89m/O+4mbAJyUATxvdmCjxKhJeO1laTExMUKdOHdSpUyf3sbS0tNw/X716FatWrULbtm1FxNMpMpkMgYGB+OKLL3D//n2UKVNGdCQieg2ZTMZxdiRZixYtQtiZ42hVsShsHIFbScDtZCDrn/mLMrx6ceMXHzf+Z0/ailbS3lHiXcnUnL75XlQqFeRy+SsnRzx9+hQAYG9vX9ixdE5iYiJKly6NMWPGYMqUKaLjENEbTJkyBb/88gseP37MiWEkGcnJyXB2dkanTp3yLKOVrQaeZwFxGUB8BhCfCWRmA9nQdFOayAFbE8DWVNPVam0MyPXosmZh944++eQT/Pbbb7CzswMApKSk4NixY0hJSYGnpyfc3d0FJ9Q9/v7+2L17N6KiomBiYiI6DhG9xp49e9CmTRvcunUrd8knItF++OEHjB8/Hjdv3oSTk5PoOJLBMXbvQKlU4tixY7Czs0NWVhb27NmDsmXLIjAwEHPmzEFgYCBOnjwpOqbOCQgIwIMHD/D777+LjkJEb8AJFCQ1qampmDNnDvr06cOi7j9Y2L2DI0eOoEaNGgCAY8eOYcKECejevTt27dqFCRMmICMjAz179kRiYqLgpLqlevXqqFu3LneiIJK4EiVKwNnZmePsSDKWL1+OJ0+e4KuvvhIdRXJY2L2Dw4cPo1WrVrl/9vT0xKxZs+Dl5YVPP/0U69atg6OjI7Zv3y44qe4JCAjAoUOHcO3aNdFRiOgNOIGCpCI9PR2zZ89Gjx494OLiIjqO5LCwewdXrlzB1q1bsWrVKuzatQt+fn6wtrZGdnY2MjMz4eTkBAsLC2RmZoqOqnM6deoEe3t7LF68WHQUInoDX19fBAcHI6uA1gsjyq/Vq1fjwYMHbK17DRZ272Dw4MHw8vLC/Pnz8ezZM5iYmCA7OxtyuRwmJiZISkrC5cuXUbNmTdFRdY65uTkGDhyI1atXIyUlRXQcInoNhUKBlJQUREREiI5CBiwzMxOzZs1Cly5dULlyZdFxJEkPVmzRvi+//BIpKSl4+vQpHj58iKJFi0Iu19TE2dnZ2L59O2xsbHLH4dH7GTp0KObOnYtff/0V/fv3Fx2HiF6hRo0akMvlOHfuHDw9PUXHIQO1fv16REVFcdLdG3C5kw/07NkzLFiwAFZWVhg7dqzoODqrZcuWePLkCWfdEUmYl5cX6tSpgyVLloiOQgYoKysLVapUgaenJ8e0vwELu/egVqvzLM754t//+xy9n927d6Ndu3Y4f/48atWqJToOEb3CwIEDcfHiRYSEhIiOQgZow4YN6NWrF4KDg9lD9gYcY/eOXlX/ymQyPHz4EHFxcSzqPlCrVq1Qvnx5Ln1CJGEKhQKXL19Gamqq6ChkYFQqFWbMmIHWrVuzqHsLFnbvSCaT5SnecmaGzZw5E507d8azZ89ERdMLRkZGGDJkCDZt2oS4uDjRcYjoFRQKBVQqFVvsqND99ttviIiIwOTJk0VHkTwWdu8gMzMTp06dQnBwcG7RYWysmXfi4OAAOzu73K3GKP8GDhyIzMxMrFmzRnQUInqFatWqwdzcnOvZUaHKzs7G9OnT0axZM/j5+YmOI3kcY/cGz58/xw8//ICVK1fC1tYWxsbGyMrKQvny5dG0aVP06tWLBV0B69atG5RKJSIiIti9TSRBH330EZycnLBx40bRUchA7Ny5E59++ilOnDiBjz/+WHQcyWNh9wYBAQE4d+4cPvvsM1SsWBGpqal48OABrl+/juDgYLi6uuL777+Hm5ub6Kh649ixY2jYsCEOHTqERo0aiY5DRP8xcuRI7NmzBzdu3BAdhQyAWq1GrVq1ULRoURw5ckR0HJ3Awu4N7O3tsXLlSrRv3z7P43FxcQgLC0O/fv3Qvn17zJ07F0ZGRoJS6he1Wo1q1aqhSpUq2LZtm+g4RPQfGzduRM+ePfH06VP2WJDW7d27F61bt+aX/ffAMXavkZCQgKJFi77yxlWsWDHUq1cPCxcuxNatWxEfH1/4AfWUTCZDQEAAdu7ciQcPHoiOQ0T/oVAoAIBrTpLWqdVqTJs2DXXr1sUnn3wiOo7OYGH3GqampmjSpAn69OmDU6dOIS0t7aXXWFlZISEhAfb29gIS6q/evXvDzMwMy5cvFx2FiP7DxcUFxYoV4wQK0rpDhw7hzJkzmDx5Msdcvwd2xb7BnTt3MHLkSISHh8PPzw8NGzbM3Zvu8OHD2LNnD6pUqYKVK1cKTqp/hgwZgr179yIqKip3BjIRSUPz5s1hamqK3bt3i45CeqxBgwZISUnBuXPnWNi9BxZ2b3H//n1s27YN27dvR1hYGOLi4lC8eHGUKVMGjRs3xpdffolSpUqJjql3lEolfHx8sH37dnz66aei4xDRCyZPnoxly5bh4cOH/MAlrciZSLdr1y60a9dOdBydwsLuPWRlZSE+Ph63b9+Gra0tZ8NqWZ06dWBtbY0DBw6IjkJEL8jZAvDOnTsoX7686Dikh5o0aYInT54gJCSEXx7eE/u43oOxsTEcHBzg4OAAgPvDaltAQAD69u2LGzdusIgmkhBfX18AwLlz51jYUYE7ffo0Dh06hK1bt/IzNh84eeID8ILTri5dusDOzg6LFy8WHYWIXlCyZEmUK1eOEyhIK6ZNmwYPDw989tlnoqPoJBZ2JFnm5uYYMGAAVq1axU3HiSRGoVBwyRMqcBcuXMCff/6JSZMmQS5niZIf/Fd7RyqVCoCm+5UKz9ChQxEXF4ctW7aIjkJEL1AoFLhw4ULuvZGoIEyfPh3u7u7o0qWL6Cg6i4XdOxo2bBi6devG7tdC5urqimbNmmHRokWioxDRCxQKBZKSknD16lXRUUhPXLp0Cbt27cJXX33F3Zw+AAu7dxQcHAwLCwvRMQxSYGAgzp07h4sXL4qOQkT/qFmzJmQyGcfZUYGZPn06KlSogB49eoiOotNY2L2DrKwsXL58Gd7e3qKjGKTWrVujbNmyCAoKEh2FiP5hbW2NKlWqcJwdFYiIiAhs27YNEydOhImJieg4Oo2F3Tu4du0a0tPTWdgJYmxsjCFDhmDjxo3cl5dIQhQKBVvsqEDMmDEDZcuWRd++fUVH0Xks7N6BUqkEAFSvXl1sEAM2aNAgZGRkYO3ataKjENE/FAoFQkNDX7mXNtG7unHjBjZt2oTx48fD1NRUdBydx8LuHSiVSjg7O8PW1lZ0FINVqlQpfPrpp1i8eDFnJhNJhEKhQFZWVu6XX6L8mDlzJhwdHTFw4EDRUfQCC7t3oFQq2Q0rAQEBAYiIiMCxY8dERyEiAJ6enjA1NeU4O8q327dvY926dRg3bhzMzc1Fx9ELLOzeQq1Ws7CTiIYNG6Jy5cpc+oRIIkxNTeHj48NxdpRvs2bNgr29PYYMGSI6it7gXrFvcf/+fTx58oSFnQTIZDIEBARg9OjRiI2NRfHixUVHIjJ48+fPR9myZUXHIB109+5drFq1CtOnT0eRIkVEx9EbLOzeImfsiI+Pj9ggBAAYMGAAqlevzqKOSCL8/Py49RPly5w5c2BtbY2AgADRUfQKfxvfQqlUolixYihXrpzoKATAysoKH3/8segYRPQPFnWUHw8fPsSyZcswatQoWFtbi46jV/gb+RY54+u4lZh0cKsZIiLd9v3338Pc3BzDhw8XHUXvsLB7C06cICIiKjixsbFYvHgxvvjiC9jY2IiOo3dY2L1BYmIiIiMjWdgREeWTSqUSHYEk5ocffoBcLsfIkSNFR9FLnDzxBpcuXQIAFnY6QKVSYceOHQgNDYWrqytq166NSpUqiY5FZFCSk5Px+++/4+DBgwgJCYGxsTEaN26Mrl27onr16hzSQnj69Cl+/vlnDBs2DHZ2dqLj6CW22L2BUqmEqakpKleuLDoKvUZqairGjx+P4sWLY8CAATh79iy+/PJL9OzZE+vXrxcdj8ggxMfHY+TIkShevDgCAwMRFRWFhg0bomXLlti+fTsGDRqEv/76S3RMkoAFCxYgOzsbX375pegoekum5v5MrzVo0CBcvHgRFy9eFB2FXpBzya5fvx4jR46EtbU1hg8fjrZt28Le3h4AsGHDBsyaNQsPHjwQGZVI76nVaowfPx47duzA2LFj0bx5c5QuXRpGRkaQy+VIS0vD2LFjcf36dezfv190XBIoISEBTk5OGDhwIObNmyc6jt5ii90bcOKENMlkMty8eRMLFy5E7969cfToUYwePRru7u6wt7eHvb09WrduDZlMxhXxibTsypUr+OuvvzB+/HgMGTIETk5OMDExyV0GxdzcHDVq1MCtW7cEJyXRfvrpJ6SlpWHMmDGio+g1FnavkZmZibCwMBZ2EvXbb78hPj4eX375JZydnV96fv/+/bC1tYWLi0vhhyMyIBYWFoiMjESXLl1e+XxaWhpWrVqFDh06cCKFAXv+/Dnmz5+PwYMHo1SpUqLj6DUWdq9x7do1pKens7CTqLCwMLRs2RLly5fP8/idO3cwZ84cfPPNN2jXrl1u1ywRaYeLiwusrKzwww8/IDs7G8nJybh27Rr++usvzJo1C7Vq1cLdu3fRq1cvrkFpwIKCgvD8+XOMGzdOdBS9xzF2r7F+/Xr07t0b8fHxXGdHgrZs2YIvvvgCW7ZsQf369XH+/HmcP38ex48fR2RkJOrVq4epU6fCyspKdFQivbd582ZMnz4d0dHRqF69OooUKYLY2FjIZDL4+vpi3LhxqFixouiYJEhKSgoqVKiADh06YMmSJaLj6D0Wdq8xevRo7Nixg+NCJKxnz544d+4cYmJiUKFCBRgZGcHBwQF9+/ZF165dYWzM1XyICsulS5cQFhaGsLAwqNVqVK5cGX5+frmrCmRnZ3P7MQP1448/YsyYMbhx4wYqVKggOo7eY2H3Go0bN4aNjQ22b98uOgq9RkZGBk6dOoVHjx4hNTUVLi4uqF+/fu7zarWa62YREQmUlpaGihUronnz5li1apXoOAaBTRqvoFaroVQquSq2xJmamqJhw4YvPa5SqWBkZMSijqgQLViwANHR0fjuu+9gamoKlUoFuVye5/eQX7YMz4oVKxATE4OvvvpKdBSDwXbxV7h37x6ePXvGiRM64Pnz55g4cSIWLFgAQPPB8aoB2hkZGUhLSyvseEQGIzg4GMHBwXj48CEAvPLLFYs6w5KRkYHZs2ejW7ducHNzEx3HYLDF7hWUSiUAbiWmC4yNjbF//37UrFkTycnJsLS0fOk1aWlp+P333xEZGYmJEycKSEmk/yZPngyZTAYnJ6eXnlOpVEhOTkZMTAySkpLg4+MjICEVtjVr1uDevXv4+uuvRUcxKCzsXkGpVMLOzg5ly5YVHYXewsLCAitXrkT58uVfWdRlZ2fD3Nwc6enp2L59OxwcHDB48GABSYn026taZLKzs3Hx4kWcPHkSISEhuHTpEp4/f44bN24ISEiFKTMzE9999x06deoEDw8P0XEMCrtiXyFnxwl2G+gGb2/vlzaTVqlUeWbhNWvWDObm5vj2229FRCTSe9nZ2Vi2bBnmzJmT+5hcLsfdu3fx9ddfIzw8HF26dEFkZCTOnz8vMCkVho0bN+L27duYNGmS6CgGh4XdK3ArMd109+7d3JXtc/apvH//PiZMmICPPvoIz58/R7NmzRATEyM4KZH+kcvlr1xFoEGDBvD29sbUqVMxYcIENG7cGHv27BGQkAqLSqXCzJkz0b59e3h5eYmOY3BY2P1HQkICbt26xcJOx9y4cQNubm548uQJACA0NBQDBgxAnTp1cOjQIXTv3h0LFizA3Llz4ejoKDgtkX4qWrQooqKiAGg+3FUqFYoVKwY3Nzfs2rULAFCvXj389ddfAlOStm3ZsgXXr1/H5MmTRUcxSBxj9x+XLl0CwIkTusbNzQ3Ozs7w9/eHXC7H2bNn4erqii+++AINGjSAh4fHK8fgEVHBad68OZYsWYLExEQULVoUAJCamoqrV6+iXbt2AIBGjRpxSIQey87OxowZM9CyZUvUrFlTdByDxAWK/+Onn37CmDFjkJSUBBMTE9Fx6D38+eefaN26NZo3b45PP/0UH330Edzd3XP/O6rVaqjVaq5+T6Qljx49QqtWreDl5YURI0YgKioKa9euxf79+xEREQEnJydkZ2cjJiaGG8Hrqd9++w2dOnXCqVOnUKdOHdFxDBILu/8YOHAglEolgoODRUehfHByckLnzp3x/fff5z6WM5GChTqR9p09exZdunRBWloanJycYG1tjW+++Qb169dHdnb2a9eaJN2nVqvh4+MDBwcHHDx4UHQcg8Wu2P/gxAnd9uWXX2Lx4sWYOnUqzMzMcgu6nA+S8+fPo3Tp0rC2ts7tKiKiguPn55f75fjp06eoXr167n6xbC3Xb7t370ZoaCiOHj0qOopBY4vdCzIzM2FlZYXvv/8ew4cPFx2H8mn+/PkYPHgwrKysAGjGfCxduhQ///wzzMzMkJmZieTkZHz77bfo2LEjLCwsBCcm0n/p6emIjIxEREQELl26hPT0dMyaNUt0LCogarUaCoUCRYoUwbFjx0THMWhssXtBREQEMjIy2GKn40aNGgVAc6PZuHEjvv32W9y8eRMA8Pnnn6NFixaIi4vDwoULERERgRkzZoiMS6R3VCoVHj58iLJly0KtViM7OxubNm3C0qVLc9eXPHPmDL766iu2nOuJ/fv348KFC5zxLAFsF39BzlZi1atXFxuECkR4eDh++OEHuLm5YdasWZg1axbu3LmDI0eOoGfPnvjmm2/w008/ITs7W3RUIr3Su3dvfPfdd8jMzIRMJoORkRG8vLxw//59tGnTBrt370bp0qU5DktPqNVqTJs2DbVr10bjxo1FxzF4bLF7gVKphIuLC79B6ol58+YhPT0dy5cvz52BFxwcjObNmyMgIACtWrVC+fLlsW7dOvTt21dwWiL98fDhQ9SoUQMmJiZQq9WQyWTw8fFBtWrVYGtrC3t7e9SrVw9//PEHPvvsM9Fx6QMdOXIEp06dwp49e7hjkwSwxe4FnDihP1JSUnD9+nVMmDAhz7IKdnZ2cHNzw71796BSqTBt2jS20BIVMC8vL5w+fRoAcmfCJiUloWjRornDIpo2bYoTJ06IjEkFZNq0aahZsyZatmwpOgqBhV0utVrNwk6PFClSBEWLFs3zwRETE4Off/4ZDx48gLu7O4yMjNCsWTP+NycqYB06dMDVq1dx8OBBGBkZQSaT4dq1azh69CiaNGkCAGjZsiX8/PwEJ6UP9ffff+Po0aOYNGkSW+skgrNi/xEdHQ0nJyfs3r0bbdq0ER2HCkBwcDD69OmDChUqwNvbG1FRUTh79ixGjhyJYcOGiY5HpLcyMzMxfPhw7Nq1Cy1atMD9+/dx7NgxNGzYELt27YK5ubnoiFRAmjdvjocPH0KpVHI5G4ngGLt/5EycYOuN/qhZsyaWLFmClStXQqlUIiMjA7NmzULHjh1FRyPSayYmJggKCoKdnR3OnTsHR0dHLFq0CAMHDhQdjQrQ2bNnceDAAfz6668s6iSELXb/mDp1KhYuXIjY2Fg2J+uhhIQE2NjY5P49Z0A3EWlfQkICrK2tIZfL+bunR9q0aYPIyEiEhYVxNxEJYYvdP3LG1/GGo59yirqcNbT435mocKjV6jxfqvi7px8uXryIPXv2YP369SzqJIZtp//gxAnDwO4CosLFQk4/TZ8+Ha6urujatavoKPQfbLEDEB8fj9u3b7OwMxA5rXZERPT+Ll++jB07dmDlypUwNmYZITX8dAMQGhoKgBMn9J1arUZGRgb27dsnOgqRQeHuLvplxowZcHZ2Rq9evURHoVdgYQdNN6yZmRkqVaokOgppkUwmw5YtW9CmTRtERUWJjkNkEDIzM3Hw4EGkp6eLjkIF4OrVq9iyZQsmTJgAExMT0XHoFVjYQVPYVatWjRepAfj0009RtGhRLFmyRHQUIoNw7do1NG/eHGfOnBEdhQrAzJkzUaZMGfTr1090FHoNFnbQFHY+Pj6iY1AhsLS0RN++fbFixQq2IBAVgipVqsDS0hLnzp0THYU+UGRkJDZu3Ihx48bBzMxMdBx6DYMv7DIyMnDlyhWOrzMg/v7+iI2Nxfbt20VHIdJ7RkZGqFWrFgs7PfDdd9/BwcEBgwYNEh2F3sDgC7uIiAhkZmaysDMgVapUQcOGDbFo0SLRUYgMgkKhYGGn46KiorBmzRqMHTsWFhYWouPQGxh8YZezlZiXl5fYIFSoAgMD8ffff+Py5cuioxDpPV9fX0RHRyMmJkZ0FMqn2bNnw9bWFv7+/qKj0FuwsFMq4erqCmtra9FRqBB16NABJUuWxOLFi0VHIdJ7CoUCAHD+/HnBSSg/7t+/j5UrV2L06NGwtLQUHYfegoUdd5wwSCYmJhg0aBDWrVuH58+fi45DpNfKly+PEiVKsDtWR82ZMweWlpYYNmyY6Cj0Dgy6sFOr1SzsDNiQIUOQnJyMDRs2iI5CpNdkMhnH2emoR48eYenSpRg5ciR7tnSEQRd20dHRiI+PZ2FnoMqVK4e2bdsiKCgIarVadBwivebr64vz58/zd03HzJs3D6ampvjiiy9ER6F3ZNCFXc7ECRZ2hisgIACXLl3C6dOnRUch0msKhQLPnj3DrVu3REehd/TkyRMEBQVh+PDhsLW1FR2H3pHBF3YODg4oXbq06CgkSNOmTeHi4sKlT4i0zNfXFwDYHatD5s+fDwAYOXKk2CD0Xgy6sAsJCYG3tzdkMpnoKCSIXC6Hv78/tm7ditjYWNFxiPSWvb09XFxcWNjpiLi4OPz0008IDAyEg4OD6Dj0Hgy6sOPECQKA/v37QyaTYdWqVaKjEOk1TqDQHQsXLkRWVhZGjx4tOgq9J4Mt7OLi4nDnzh0WdgR7e3t06dIFixcvRnZ2tug4RHrL19cXISEhyMzMFB2F3iAxMRE//vgjhgwZAkdHR9Fx6D0ZbGEXGhoKAPDx8RGchKQgMDAQt2/fxv79+0VHIdJbCoUCqampuHLliugo9AY///wzUlNTMW7cONFRKB8MtrBTKpUwNzeHu7u76CgkAX5+fvD29kZQUJDoKER6y8fHB0ZGRuyOlbCkpCT88MMPGDhwICcW6iiDLuw8PT1hbGwsOgpJgEwmQ0BAAPbs2YM7d+6IjkOkl4oUKQJPT08WdhK2ePFiJCYmYvz48aKjUD4ZdGHH8XX0oh49esDS0hJLly4VHYVIb+UsVEzSk5mZiV9++QV9+/ZF+fLlRcehfDLIwi4jIwPh4eEs7CgPKysr9O3bF8uXL0dGRoboOER6SaFQICwsDMnJyaKj0H8YGxvjzJkzmDlzpugo9AEMsrALDw9HZmYmCzt6ib+/Px4/fowdO3aIjkKklxQKBbKzs3Hx4kXRUeg/ZDIZihcvjuLFi4uOQh/AIAs7pVIJmUwGT09P0VFIYqpWrYr69etzJwoiLfHw8ECRIkU4zk6i5HKDLAv0ikH+F1QqlXB1dYW1tbXoKCRBgYGBOH78OJdkINICY2Nj1KhRg+PsiLTEYAs7dsPS63z66adwdHTE4sWLRUch0kvcgYJIewyusFOr1Szs6I1MTU0xcOBArF27FklJSaLjEOkdhUKB27dvc39mAbKysqBUKvHgwQPuAKKnDK6wi4qKQkJCAgs7eqMhQ4bg+fPn2Lhxo+goRHpHoVAAALtjC1lMTAwGDhyIRo0aoWLFipz9qqcMrrBTKpUAwMKO3sjJyQlt2rRBUFAQ1Gq16DhEesXZ2Rn29vYs7ApZYGBg7qz/X375BWvWrEFMTAxOnjyJw4cPc3F2PSFTG9in1jfffIOgoCDExMRAJpOJjkMS9ueff6JVq1Y4ffo0ateuLToOkV5p1aoVZDIZ9uzZIzqKQVAqlahfvz4uX74MJycnAJqWUwsLC4SGhsLOzg5NmjTBwoULYW5uLjgtfQiDbLHz8fFhUUdv1bx5c1SoUIFLnxBpQc4ECgNrWxBm5cqV6Nq1K8qVKwcACA0NxcWLF9GjRw9ER0dj3rx5WL58OdavXy84KX0ogyzs2A1L70Iul8Pf3x9btmzB06dPRcch0isKhQJPnjxBVFSU6Ch6LyMjA15eXmjUqFFuo8ZPP/2Efv36YejQoShatCg+/fRTdOjQAc+ePROclj6UQRV2z549Q3R0NAs7emf9+/eHWq3GqlWrREch0iu+vr4AOIGiMJiammLQoEFo27YtZDIZsrKyMGLECMyfPx8AkJ2dDQBIS0tDenq6yKhUAAyqsAsNDQXAiRP07ooXL47OnTtj8eLFuTc/IvpwxYsXh7OzM9ezK0RFihQBoFkk2tPTE1ZWVgA0vRNHjx7F8ePH8fnnn4uMSAXAoAo7pVIJCwsLuLu7i45COiQwMBCRkZH466+/REch0itcqFj7vvvuO5w9exbAv9uFZWVlAUBut+zevXsxadIkDBs2DMWKFRMTlAqMwRV2np6eMDIyEh2FdEidOnXg5eWFoKAg0VGI9IpCoUBwcHBuoUEFa8WKFfj666/xv//9D+PHj8fVq1cBaFrsUlJSAGjG30VFRaFcuXKYNWuWyLhUQAyusGM3LL0vmUyGgIAA7N69G3fv3hUdh0hvKBQKpKSkIDw8XHQUveTq6opixYqhTJkyOH36NPz9/bFgwQIcOHAAjRo1QnJyMkxNTREYGIgVK1ZwtQg9YTCFXXp6OsLDw1nYUb707NkTRYoUwdKlS0VHIdIbNWrUgFwu5wQKLalXrx7atGmDzz77DN9//z3c3NywY8cO9OzZE4mJiVCpVLmvzRl/R7rPYAq78PBwZGVlsbCjfLG2tkafPn2wfPly7q9IVEAsLS1RtWpVjrPTErlcDoVCgVmzZsHHxwfLli1DgwYNEB8fDzMzM/Tv3x/Lly/nWoJ6xmAKu5CQEMhkMnh6eoqOQjoqICAAjx49ws6dO0VHIdIbnEChXcOGDUPJkiWxY8cOAMCuXbswYMAAjBw5Es+fP8epU6fYBatnjEUHKCxKpRJubm6507uJ3le1atXw8ccfY9GiRejcubPoOER6QaFQYPXq1UhJSWF3YAFTqVQwMjJCq1atsGfPHqSnpyM6OhoHDx6Eg4MDGjVqlDtTlvSHwfwX5cQJKgiBgYE4evQoIiIiREch0gu+vr5QqVRQKpWio+idnBUgunbtitDQUPTt2xdjxoyBg4MDAKBcuXIoU6aMyIikBQZR2GVnZ7OwowLx2WefoXjx4li8eLHoKER6oVq1ajA3N2d3rBZZWlpi9erVGDt2LAYNGiQ6DmmZQRR2UVFReP78OQs7+mBmZmYYOHAg1qxZg+TkZNFxiHSeiYkJatSowcKugOTskPPiTjlqtRre3t6YPn06SpQowckSes4gCrucJn4fHx+xQUgvDB06FImJidi0aZPoKER6gRMoCo5cLodarc4dO6dSqXKLvJyuWU6W0G8GU9g5OjqiZMmSoqOQHnB2dkarVq0QFBTEb75EBcDX1xeRkZF49uyZ6Cg6a//+/ejevTt69uyJ8ePHY/v27QA0xVxOQbd69WqsWLECGRkZIqOSlhlMYcduWCpIAQEBuHjxIhdWJSoACoUCAPj7lE9Lly7FoEGDkJKSgqSkJISEhODbb79Fq1atcPDgQQBAXFwc1q1bh2XLlrHFTs/J1AbQ5FC+fHn06NGD++BRgVGpVHBxcUHDhg2xevVq0XGIdJparYa9vT1GjRqFyZMni46jc0qXLo2pU6fmToy4ceMGjhw5gr179yI2NhYBAQHo1asXoqOjcf/+fdSpU0dwYtImvW+xe/r0Ke7evcsWOypQRkZG8Pf3x6+//sruI6IPJJPJOM4unyIjI1GyZEm4u7vnPubm5oYhQ4ZgypQpKFeuHCZNmoSIiAiUL1+eRZ0B0PvCLjQ0FABY2FGBGzBgAFQqFVvsiAqAQqHA+fPnOW71PZUrVw5FihTBwoULkZCQkOc5b29vbN68GRYWFti/f7+ghFTY9L6wUyqVsLCwgJubm+gopGdKlCiBTp06YfHixXmWFiCi9+fr64uYmBjcvXtXdBSdYmpqilGjRiE4OBjTpk3DgwcPXnqNQqHgAtAGxCAKOy8vr9xZQUQFKTAwEDdu3MChQ4dERyHSab6+vgDA7th86NixI6ZOnYoVK1agXr16+OWXXxAeHo579+5BqVRiz549aNu2reiYVEj0fvKEp6cnPvroI+4UQFqhVqvh5eUFNze33OUFiCh/nJyc0LVrV8yZM0d0FJ0UFxeHb7/9FkuWLEH58uWRnp4OExMT1K5dG+vWrRMdjwqJXhd2aWlpsLKyws8//wx/f3/RcUhPLVq0CF988QWioqJQtmxZ0XGIdFbnzp3x5MkTHDlyRHQUnZaWlobNmzfDysoKTk5O8PDwgKWlpehYVEh0urDLVgPPM4G4TCAuA0jIBDKzgWxo+pjTU55j58Y16N6uJWpVdoG1CSDn8j1UwBITE1G6dGmMHj0a3377reg4RDprzpw5mDZtGuLj4zl8hiifdLKwS8oCbiUBt5OBrH/SywC86gfJysyAsYkJABmMZUAFS6CiFWBlXIiBSe8FBARg165duHPnDkxMTETHIdJJR48exSeffIKwsDBUrVpVdBwinaRTkyeepQMnYoH9j4CbSf8WdcCrizoAMDYxhabs07z+ZpLm/SdigWfcVYUKSEBAAB4+fIjff/9ddBQinVWzZk3IZDJOoMinzMxM0RFIAnSisFOpgcvxwJFYIDZd81h+mxlz3hebDhx5rDmuSufaLElqvLy8ULduXSxatEh0FCKdZW1tDQ8PDxZ27+np06do0KAB7t27JzoKSYDkC7u4DOCvR8D1JM3fC6oGyznO9STgYIzmPEQfIjAwEIcPH8a1a9dERyHSWb6+vtwz9j39+OOPuHDhAqysrERHIQmQdGEXkwYcfQykqLR7nuQszXli0rR7HtJvnTp1goODA5fWIfoACoUCoaGhSEvjDfldxMfHY+HChQgICEDx4sVFxyEJkGxhF5MGnHyimeGq7Z5SNTTnOfmExR3ln5mZGQYMGIDVq1cjJSVFdBwinaRQKJCVlcWdEt7RTz/9hIyMDIwZM0Z0FJIISRZ2cRnAqSfaL+j+Sw3NedktS/k1dOhQJCQkYPPmzaKjEOkkT09PmJmZcZzdO3j+/Dnmz5+PwYMHo2TJkqLjkERIrrBTqYGzTwu/qMuRDeDcM06ooPypWLEiWrRogaCgINFRiHSSqakpvL29Oc7uHfzyyy9ITk7GuHHjREchCZFcYReeACSrxBV2gGadvPBEgQFIpwUEBODChQv8YCLKJ4VCwRa7t0hOTsa8efPQv39/7nhDeUiqsHuW/u/sV9GuP+c6d5Q/rVq1Qvny5dlqR5RPCoUC169fR1xcnOgokrVkyRLEx8djwoQJoqOQxEiqsLuSmLOUsHgyAFcSRKcgXWRkZIShQ4di8+bN/GAiygeFQgEAuHDhguAk0pSamoq5c+eiT58+cHZ2Fh2HJEYyhV1SFvA4XdMFm5mejnUzx2NwzdLo4WqBCW39EHr8r7ce4+yfOzCtZ3MMrlka3VzMMMS3LL4f2gnRV8Neem1qchJWTRmJIb5l0c3FDCM+qYL9a/9tYVFDkycpqwB/SDIYAwcORFZWFtasWSM6CpHOcXV1ha2tLYczvMaKFSvw+PFjTJw4UXQUkiDJ7BV7KV6z3ZcawPxh3XFm7za0HjgSpSq44cjW1YgMPY8pvx5BFcXHrz3G1h+n4u71cFSo5oOidg6If/wIh39dibjHDzFz12k4e1QHAKhUKvyvU31EXrqAFn2GoVQFNyiP7cf5A7vQfdwMdBz+FQBNq52rFeBlq/Ufn/RQt27dEBISgqtXr0Imk0pbNJFuaNq0KSwtLbFz507RUSQlPT0drq6uaNiwIdatWyc6DkmQJAq7bDWw+4FmL9cbIecwsZ0fen89F+39NevyZKSl4csm1VDUoQRm7jz1XseOj43BUEVZNOo2EEO/0ywce+qPrfghoAsC5q5A424Dcl/7/dBOuHhoD4LO3IGNQwkAgLEMaFsakPNzmd7T8ePH0aBBAxw8eBCNGzcWHYdIp3z99ddYuXIlHjx4wC9GL1i6dCn8/f0RHh6OypUri45DEiSJrtjnmZqiDgDO7N0GuZERmvYckvu8qbk5GnUbiOvBp/Hkwd33OraNQwmYWRRBckJ87mMR504AAD5u3y3Paz9q1w0Z6Wk4d2BX7mNZauA5u2MpH+rVq4eqVatyEgVRPigUCjx69Aj3798XHUUyMjMz8d1336Fz584s6ui1JFHYxWX+++fbV0JQuqI7ilgXzfMaV2/NYNqoK8q3Hi85IR4JT2NxJ+IygsYOQsrzRHh+/G+LSVZGOuRGRjA2Mc3zPjOLIgCAW5eD8+bj7FjKB5lMBn9/f+zcuRMPHjwQHYdIp+RMoOA4u39t2LABUVFRmDRpkugoJGHSKOwy/p0NGxfzELYlSr30mmL/PPYs5u0fkBPb18ZA7xIY3cwLp/7Ygo5fTELjbgNzny9dsRKyVSpcv3gmz/tyWvKePfr3G6IMQDwLO8qn3r17w8zMDMuWLRMdhUinlCpVCmXKlOF6dv/IysrCzJkz0aFDB3h6eoqOQxImicIuIfPfBYkz0lJhYmr20mtMzcxzn3+bYfNWYdK6fRg8YxHKulZBRloqslWq3Oc/7tADRYraYNGYAQg9/hce343CXxuWYv/aRS+dQw0gPvO/ZyB6NzY2NujVqxeWLVuGrCz26RO9Dy5U/K9ff/0VN27cYGsdvZUkCrvM7H//bGpugcyM9Jdek5Gelvv821SqWQfeDZujeZ8ATFq/Hyd2rMeGWf9OCy9WoiQmrPgdmRnpmNazGQLrVsC6GWMxYOpPAADzIlavzUf0vgICAnD//n3s3r1bdBQinaJQKHDhwgVkZxv2TTg7OxszZsxA69atUbNmTdFxSOIkUdi9+CtbzLEU4h8/fOk1cf88ZudY+r2ObWVbDNXqNsKJnRvyPO5Ruz5+OXkLc/eFYPr2v7Hk/H2416gNAChd0f21+Yjel7e3N2rXrs1JFETvSaFQIDExEdevXxcdRajffvsNERERmDx5sugopAMkUdi9GMLZwxsPbl1HyvO8m7XeCDmreb6q93sfPyMtFSmJL28jYWRkhApVvVHZ9yNYWFrh0omDAADPj5u8Nh9RfgQGBuKvv/7CjRs3REch0hk5rVOG3B2bnZ2N6dOno2nTpvDz8xMdh3SAJGoWkxdS1G7dCdkqFf7asDT3scz0dBzZsgpuPn5wKF0OABB7Pxr3b17Nc5yEJ49fOvbju1G4fPIQXLxqvTFDwtNY7AyaDacqXvCql7ewM5HEvxLpss6dO8Pe3h6LFy8WHYVIZ9jY2KBy5coGXdjt3r0bly5dYmsdvTNj0QEAwMYEeJahmajg7uOHOm06Y+PsiUh8+hglnV1xdNsaxN6LQuDcFbnv+WlkH4SfOYZtd/9dX/nLpp7w/KgxnKt6w9KmGB7dvoFDm1dAlZmJnhNn5Tnn/zo1gHvNOijp7Ir4x49wcONSpCUnYeKqPyCX/1vJyQDYmmj7X4D0nbm5Ofr3748VK1Zg+vTpsLB4+1hRIjLsCRRqtRrTpk1DgwYNUK9ePdFxSEdIorArZgrcSv7378Pnr8XmMpNxbPs6JCfEwamyFyau+gMeteu/8TjNegfg4qE9UB7dh9Tk57CxL4Hq9Zvhs8+/glOVvNPDK3rWxOk/tuJZzH1YWBWFV72m6D5mGhydKuZ5nRqAbd7l7ojyZejQofj+++/x66+/ol+/fqLjEOkEhUKBTZs2IT09HWZmL6+YoM/27duH4OBgHDx4UHQU0iGS2FIsIQM4+HIvqmQ0cdS0KhJ9qBYtWiAuLg5nz54VHYVIJ5w7dw5+fn44d+4cfH19RccpNGq1Gh999BEA4OTJk9xWjd6ZJEaPWZto9mSVImMZYC2Jdk3SBwEBATh37hyCg4Pf/mIiQvXq1WFiYmJw3bGHDx/G6dOnMXnyZBZ19F4kUdjJZUAFy393n5CK7GwVimXGQS61YKSzWrdujbJly3LpE6J3ZGZmBm9vb4Mr7KZOnYpatWqhRYsWoqOQjpFEYQcAFa3+3X1CKuRyI3T7RIGuXbvi4sWLouOQHjA2NsbQoUOxceNGxMfHi45DpBMMbQLF8ePHcfz4cbbWUb5IprCzMgZKmEmn1U4GwMFEhf+NH40LFy6gZs2aaNq0KQ4dOgQJDEskHTZo0CBkZmZi7dq1oqMQ6QSFQoFr164hIeHl9Uj10bRp01C9enW0bdtWdBTSQZIp7ACgqo10Wu3UADyLGcHf3x/Xrl3D5s2b8fTpUzRp0gS+vr7YunUrVC/sP0v0rkqWLIlPP/0UQUFB/JJA9A58fX2hVqsNYmzqmTNncPDgQUyaNImtdZQvkirs7EwBd6u3v64wuFtr8gCa7rOuXbsiODgYBw4cgK2tLbp06YLKlStj6dKlSEtLExuWdE5AQACuXr2Ko0ePio5CJHmVKlWCtbW1QXTHTps2DR4eHvjss89ERyEdJanCDgA8bABLI3FdsjJouoU9ir7iOZkMTZs2xcGDB3H+/Hl4e3vD398fzs7OmDVrlsF0E9CHa9iwISpXrsxJFETvQC6Xw9fXV+8Lu+DgYOzduxdff/11noXyid6H5K4cIxngZy+2sFPYaXK8Sa1atbB161Zcu3YN7du3xzfffINy5cph3LhxePDgQaFkJd0lk8kQEBCAHTt24OHDh6LjEEmeQqHA+fPnRcfQqunTp8PNzQ1du3YVHYV0mOQKO0CzE0Vdh8Iv7mQAPnLQnP9dubm5YcmSJYiKikJgYCCWLFmCChUqYPDgwbh+/brWspLu69OnD0xNTbF8+XLRUYgkz9fXF/fu3dPbL86XLl3Czp078dVXX8HIyEh0HNJhkizsAMDRXFNkyVE4BZ4cwMcOQAnz/L2/VKlSmDVrFqKjozFt2jT88ccfqFy5Mjp27Kj33QeUP7a2tujRoweWLl2KrKws0XGIJE2hUACA3rbazZgxA87OzujZs6foKKTjJFvYAZrirmEJoIiWv7xYGWvOk9+i7kU2NjYYN24cbt++jSVLluDy5cvw8/NDo0aNsH//fs6CpDwCAgJw79497NmzR3QUIkkrU6YMSpUqpZdflCMiIrB161ZMnDgRJibcv5I+jCT2in0blRoITwCuJ2la7woicM5x3K01EyXeNqYuv1QqFXbu3InZs2fnTrgYN24cOnfuDGNj7lVGgJ+fH4oVK4Z9+/aJjkIkaR06dEBKSgoOHDggOkqB6tWrF44dO4abN2/CzMxMdBzScZJuscthJAM8bYFPigPF/7nm81uH5byvuBnwSQnA00Z7RR0AGBkZoWPHjjh79iwOHTqEEiVKoEePHnB3d8eiRYuQmpqqvZOTTggMDMT+/ftx8+ZN0VGIJM3X1xfnz59Hdna26CgF5saNG9i0aRMmTJjAoo4KhE4UdjnszIB6xYHmJQFXK8D4hYLsdbXZi48byzTva15Scxy795gk8aFkMllud+zFixfh5+eH4cOHw8nJCdOnT0dcXFzhhSFJ6dKlC4oVK4YlS5aIjkIkaQqFAvHx8Xr1Jei7776Do6MjBg4cKDoK6Qmd6Ip9nWw18DwLiMsA4jOA+EwgMxvIhqZiNZEDtiaAralmpqu1MSCX0ELet27dwrx587By5UoYGRlh6NChGDVqFMqWLSs6GhWy0aNHY/Xq1bh37x4sLCxExyGSpLi4ONjZ2WHdunXo1auX6DgfLCoqCm5ubpgzZw5GjRolOg7pCZ0u7PTF48ePsXDhQvzyyy9ITk5Gz549MW7cOFSpUkV0NCokN27cgLu7O9asWYM+ffqIjkMkWZUqVUKLFi2wYMEC0VE+mL+/P7Zv346oqCgUKVJEdBzSEzrVFauvSpQogenTpyM6OhqzZs3CX3/9BQ8PD3To0AGnT58WHY8KgZubG5o2bcqdKIjeQl92oLh37x5WrVqF0aNHs6ijAsXCTkKsra3x5Zdf4tatW1i5ciWuXbuGunXron79+tizZw+XStFzAQEBOHPmDEJCQkRHIZIshUKBkJAQZGRkiI7yQebMmQMrKysEBgaKjkJ6hoWdBJmamqJ///64cuUKduzYgczMTLRp0wZeXl5Yt24dMjMzRUckLWjbti3KlCnDVjuiN1AoFEhPT8fly5dFR8m3R48eYdmyZRg5ciSsra1FxyE9w8JOwuRyOTp06IBTp07h2LFjKF++PPr06QNXV1csXLgQycnJoiNSATI2NsaQIUOwYcMGJCQkiI5DJEne3t4wNjbW6R0ovv/+e5iammL48OGio5AeYmGnA2QyWW537KVLl1C/fn18+eWXcHJywpQpU/DkyRPREamADBo0COnp6Vi3bp3oKESSZG5uDi8vL50dZxcbG4ugoCB88cUXsLW1FR2H9BALOx3j6emJdevW4ebNm+jRowfmzJkDJycnjBgxAnfu3BEdjz5Q6dKl0aFDBwQFBXFMJdFrKBQKnS3sfvjhB8jlcowcOVJ0FNJTLOx0lLOzMxYuXIjo6GiMHTsW69evh4uLC3r37q3TY09IM4kiPDwcx48fFx2FSJIUCgXCw8Px/Plz0VHey7Nnz/Dzzz9j2LBhsLe3Fx2H9BQLOx3n4OCAKVOmIDo6GvPmzcOxY8fg5eWFNm3a4MSJE2z10UGNGjVCpUqVOImC6DUUCgXUajWCg4NFR3kvCxYsgEqlwpdffik6CukxFnZ6wtLSEiNGjEBkZCTWrl2LqKgo1K9fHx999BF27dqlV3sr6juZTJa7cOmjR49ExyGSnMqVK8PKykqnJlAkJCRgwYIF8Pf3R4kSJUTHIT3Gwk7PmJiYoHfv3rh06RJ2794NIyMjdOjQAdWqVcPq1at1fu0nQ9G3b18YGxtjxYoVoqMQSY6RkRFq1qypU+Psfv75Z6SlpWHs2LGio5CeY2Gnp+RyeW537MmTJ+Hm5ob+/fvDxcUFP/zwg86NTTE0xYoVQ/fu3bF06VKoVCrRcYgkR5cmUCQlJWH+/PkYNGgQSpUqJToO6TkWdgagbt262LVrF65cuYLGjRtj/PjxcHJywuTJk/H48WPR8eg1AgICEB0djb1794qOQiQ5CoUC0dHRiImJER3lrYKCgpCYmIjx48eLjkIGQKbm6HqDc/fuXcyfPz+3NWjAgAEYPXo0KlasKDoa/Yevry+KFy/O4o7oP6Kjo+Hk5ITdu3ejTZs2ouO8VkpKCipUqID27dtj6dKlouOQAWCLnQEqV64cfvjhB0RHR+Orr77Cli1b4Obmhh49eiA0NFR0PHpBYGAg9u3bh1u3bomOQiQp5cqVQ4kSJSTfHbt06VI8ffoUEyZMEB2FDAQLOwNmZ2eHyZMn486dO1i4cCFOnz4Nb29vtGjRAkeOHHnvpVI4MaPgde3aFTY2NliyZInoKESSIpPJJD/OLi0tDXPmzEHv3r3ZI0KFhoUdoUiRIhg2bBhu3LiBjRs34uHDh2jUqBH8/Pywffv2ty6VkpKSgh07diAgIAAff/wxli9fXkjJ9V+RIkXQr18/rFy5EmlpaaLjEEmKQqHA+fPnJbte58qVKxETE4OvvvpKdBQyICzsKJexsTG6d+8OpVKJP//8E5aWlujYsSPu3LnzxhvnpEmTMHLkSCQlJaF169aYNm0aux0KkL+/P548eYJt27aJjkIkKQqFAs+ePZPkUIWMjAzMmjUL3bp1g5ubm+g4ZEA4eYLeKDw8HB4eHq99/uTJk2jSpAl++uknDBw4EDKZDFu2bMGIESNw/Phx3tAKSJMmTZCamoqTJ0+KjkIkGU+fPoWDgwM2btyI7t27i46Tx/LlyzFkyBCEhYW98R5KVNDYYkdv9LYb0pQpU9CoUSN06dIFMpkMgOZbdEJCAsfcFaCAgACcOnWKk1uIXmBvbw8XFxfJjbPLysrCd999h44dO7Koo0LHwo7yLTo6GocPH8awYcNQtGjR3MdPnz6NKlWq4MGDBwLT6Zd27dqhVKlS3D+W6D+kOIFi48aNuHXrFiZNmiQ6ChkgFnaUbxs2bICzszNq1qyZ+5hKpcLly5dhbGwMT09PAMgzPk+tVuf+PS0tDYcPH8bOnTsLNbcuMjExwZAhQ7B+/XokJiaKjkMkGQqFAiEhIcjMzBQdBYDmHjhjxgy0a9cO1atXFx2HDBALO8q3O3fuoFatWnla6y5evIizZ8/C29sbJUuWhFqtzu2iBTRLFMhkMpw9exbDhg1D586d8dlnn2HdunUifgSdMnjwYKSlpWH9+vWioxBJhq+vL1JTU3HlyhXRUQAAW7duxfXr1zF58mTRUchAsbCjfKtcuTL+/vvvPC1y69atQ3JyMvr37w8AL82mffToEX7++Wf0798fNWrUQOvWrdGsWTP4+fnlviYyMhI3btwonB9Ch5QpUwbt2rVDUFCQZJd3ICpsPj4+MDIykkR3bHZ2NqZPn44WLVqgVq1aouOQgWJhR/nWqFEjlCxZEr/88guCg4MxevRobNiwAZ07d0bt2rUB5C3sduzYgZ49e+Lw4cNYvXo12rRpgwcPHqBy5cpwd3fPfd3OnTvRrVs3eHl5cWHe/wgICEBYWBj+/vtv0VGIJKFIkSLw9PSURGG3Y8cOXLlyha11JBSXO6EP8uuvv+Krr75CWloaXFxc0L17dwQEBCA1NRUWFha5r9u7dy/atGmDPXv2oGXLlgCA7777Djt27MDs2bPxySefQKVSQSaT4fr168jMzMSxY8ewZMkSODs7Y926dbC1tRX0U0pHdnY2KleujFq1amHjxo2i4xBJwtChQ3HmzBmhs8bVajVq1KgBe3t7HDx4UFgOIrbY0Qfp2rUrIiMjcfz4cezbtw8BAQEAgEGDBuF///sfkpKSAGjG1jk6OqJv374YP348QkNDcenSJVStWhUNGjQAABgZGUEul6Ny5crw9PTE559/js2bN+PGjRvYvn27sJ9RSuRyOfz9/bFt2zY8fvxYdBwiSVAoFAgLC0NycrKwDH/88QeUSiVb60g4FnZUIFxcXFCkSBEAwMOHD/Ho0SM8ffoUVlZWAICWLVsiPDwc8+bNw8mTJ1GzZk389ddfsLe3h1wuh0qlAqCZUXbv3r3c41atWhXJycl4+PBh4f9QEtWvXz8YGRlhxYoVoqMQSYKvry+ys7Nx8eJFIedXq9WYNm0a6tWrl/tFlUgUdsWS1jx9+hT29vbIzs6GXP7vd4jU1FR07doVSqUS9+7dw969e9GiRQsAQHJyMiZNmoRly5ahf//+SEhIwPr16xEcHAwfHx9RP4rk9O/fH0eOHEFkZCSMjIxExyESKisrCzY2Npg6dSpGjx5d6Offv38/WrRogQMHDqBp06aFfn6iF7HFjrTG3t4eAHKLuuzsbADA33//jcTERAQEBCAlJQUNGzbMfY+lpSWmT5+OefPmYdu2bahUqRLCw8NZ1P1HQEAA7ty5g3379omOQiScsbExatasKWQCRU5rnZ+fH5o0aVLo5yf6LxZ2VGhyCjylUoknT56gWbNmMDc3h7m5OZ4/f577uiJFimDo0KH48ssvsWXLFlSsWFFUZMny9fVFjRo1uBMF0T8UCgXOnz9f6Oc9evQoTp48icmTJ+dZs5NIFBZ2VOjGjh2L7du35+5YkZ2djW+//RaXLl3K/TsAODs7IysrC0+ePBGWVapkMhkCAwOxd+9e3L59W3QcIuF8fX1x+/ZtxMbGFup5p02bhho1aqBVq1aFel6i12FhR0K8uG5dTEwMQkND0bdvX/z000+4ffs2Dh06hBkzZsDV1VUyWwVJTbdu3VC0aFEsXbpUdBQi4RQKBQAUaqvd33//jSNHjmDSpElsrSPJ4OQJkowlS5ZgwYIFuQOhs7KysHr1au63+AYjRozApk2bcPfuXZiZmYmOQySMWq1GiRIlMGzYMEyZMqVQztm8eXM8ePAAoaGheSaIEYnEwo4kJyIiAkZGRihbtmzuEio5VCoVLl26hAULFmDcuHHw8PAQlFIaIiIi4OHhgQ0bNqBHjx6i4xAJ1bp1awDAnj17tH6uc+fOwc/PD7/++iu6dOmi9fMRvSt+xSDJqVKlCtzd3V8q6gDNIsaPHz/GwYMHUbVqVbRr1w6nTp0SkFIaqlSpgk8++YSTKIigGWd37ty5QtlLedq0aahcuTI6duyo9XMRvQ8WdqRzmjdvjlu3bmHVqlW4efMmPvroI9SrVw9//PFH7sQLQxIQEIC///4bly9fFh2FSCiFQoEnT54gKipKq+cJCQnBH3/8ga+//prrSJLksLAjnWRqaop+/fohLCwMu3btgkqlQtu2beHl5YW1a9ca1ISLDh06oGTJkmy1I4Pn6+sLAFpfz2769OlwcXFBt27dtHoeovxgYUc6TS6Xo127djh58iSOHz8OZ2dn9O3bF66urliwYIHQvSMLi4mJCQYPHox169blWQ+QyNAUL14cFSpU0OrM2LCwMGzfvh1fffUVjI2NtXYeovxiYUd6QSaT5XbHXrp0CQ0aNMDo0aNRvnx5TJkyRe/Xwhs8eDBSUlKwYcMG0VGIhMoZZ6ctM2bMgJOTE3r37q21cxB9CBZ2pHc8PT2xdu1aREZGolevXpg7dy7Kly+PL774Anfu3BEdTyvKlSuHtm3bIigoqFAGjhNJlUKhQHBwMLKysgr82NeuXcOvv/6KCRMmwMTEpMCPT1QQWNiR3nJycsKCBQtw584djB8/Hhs2bICLiwt69eqllxMNAgICcOnSJYOeJUykUCiQkpKC8PDwAj/2zJkzUbp0afTv37/Aj01UUFjYkd5zcHDAN998g+joaPzwww84ceIEvLy80Lp1axw/flxvWriaNm0KFxcXTqIgg1ajRg3I5fICH2cXGRmJDRs2YNy4cVwMnCSNhR0ZDEtLS3zxxRe4efMm1q1bh+joaDRo0AB169bFzp07dX6pFLlcDn9/f2zdurXQ98skkgpLS0tUq1atwMfZfffdd3BwcMDgwYML9LhEBY2FHRkcExMT9OrVC5cuXcIff/wBExMTfPrpp6hatSpWrVqFjIwM0RHzrX///pDJZFi5cqXoKETCFPQEijt37mDNmjUYO3YsLCwsCuy4RNrAwo4Mlkwmy+2OPXXqFCpVqoQBAwagYsWKmDdvnk4uHWJvb4+uXbtiyZIlOt8CSZRfCoUCly9fRkpKSoEcb/bs2bC1tYW/v3+BHI9Im1jYEQGoU6cOdu7ciStXrqBp06aYOHEiypcvj0mTJuHx48ei472XgIAA3L59G/v37xcdhUgIhUIBlUoFpVL5wce6f/8+VqxYgS+//BKWlpYfHo5Iy1jYEb3Aw8MDq1atwq1btzBgwAD8+OOPcHJyQmBgIG7duiU63jvx8/ODt7c3J1GQwapatSosLCwKpDt27ty5sLS0xLBhwwogGZH2sbAjeoWyZcti3rx5iI6Oxtdff41t27bBzc0N3bt3L5BWAG2SyWQIDAzEH3/8obfr9hG9iYmJCXx8fD64sIuJicGSJUswYsQIFC1atIDSEWkXCzuiN7Czs8OkSZNw584d/PTTTzh79ix8fHzQvHlzHD58WLJLpfTo0QPW1tZYunSp6ChEQigUig8u7ObNmwcTExN88cUXBZSKSPtY2BG9AwsLCwQGBuL69evYtGkTYmJi0LhxY/j5+eG3336DSqUSHTEPS0tL9OnTB8uXL9fpWb5E+aVQKBAZGYmnT5/m6/1PnjzBokWLMHz4cBQrVqyA0xFpDws7ovdgbGyMbt26ISQkBPv27YOVlRU6deqEKlWqYNmyZUhPTxcdMZe/vz8eP36M7du3i45CVOgUCgUA4MKFC/l6//z58wEAo0aNKrBMRIWBhR1RPshkstzu2LNnz8LT0xNDhw6Fs7Mz5syZg4SEBNERUbVqVTRo0ICTKMggVaxYEXZ2dvnqjo2Li8NPP/2EgIAAODg4aCEdkfawsCP6QAqFAr/99hsiIiLQpk0bTJ48GeXLl8eECRPw8OFDodkCAgJw/PhxXLlyRWgOosImk8nyvVDxwoULkZmZiTFjxmghGZF2ydRSHf1NpKMePHiABQsWICgoCOnp6ejbty/Gjh0LNze3Qs+SkZGB8uXLo1OnTvj555+RrQaeZwJxmUBcBpCQCWRmA9nQfMszkQM2JkAxU6CYCWBtAshlhR6b6INlq4FZC37B2bDrmDL3RyRkyt7pWk9MTISTkxP69u2LH3/8UfBPQfT+WNgRaUl8fDwWL16MH3/8EY8fP0bHjh0xfvx41KpVq1BzTJo0CZt3/oFfj5zDvQxTZP3zGy8D8Kpf/hcfN5YBFSyBilaAlXHh5CX6EElZwK0k4HYykKUG1Go15ADUspe/obzqWj+wfjG+Hj0Ct27dQpkyZQozOlGBYGFHpGVpaWlYu3Yt5s6di5s3b6Jx48YYP348mjRpAtkrPmwK0rN0IPhxKhJlFlBnZ0Mmf//RFzkffiXMgKo2gJ1pgcck+mDP0oEricDj9Nd/aXkbGdRQQ4antyLQqXYVXuukk1jYERUSlUqF7du3Y/bs2QgODoaPjw/Gjx+Pjh07wti4YJvDVGogPAG4npT/D7n/yjmOuxXgYQMYsYuWJEAb1zrUakAm47VOOomFHVEhU6vVOHz4MGbNmoWDBw+iYsWKGDNmDPr16wcLC4sPPn5cBnD2KZCsxaX1rIwBhZ1mfBKRKLzWiV7Gwo5IoODgYMyZMwfbtm2Dg4MDRowYgcDAQNja2ubreDFpwKknmlYLbf5iy/75X10HwNFciycieg1e60SvxsKOSAJu3ryJefPmYdWqVTAxMcHQoUMxatSo9xq8HZMGnHyi3Q+5/5IB+IgfeFTIeK0TvR4LOyIJefToERYuXIhFixYhJSUFvXv3xtixY1G5cuU3vi8uAzj6WLOUQ2GTA2hYgl1VVDh4rRO9GRcoJpKQkiVLYubMmYiOjsbMmTOxb98+eHh44NNPP8WZM2de+R6VWjPOSNQ3tGwA555pchBpE691ordjYUckQUWLFsWYMWNw69YtLFu2DBEREahTpw4aNmyIP//8Ey82tIcnaAaPi/ysScoCwhMFBiCDwGud6O1Y2BFJmJmZGQYOHIjw8HBs374dqampaNWqFby9vbFhwwY8TsnC9STRKTWuPweeZYhOQfrqWTp4rRO9AxZ2RDpALpfndsceOXIEpUuXRq9evbB832mos0WMNnqZDMCVBNEpSF9dSdRcY1LAa52kjJMniHTU+csRiC5WBZnp6dg87384/ts6JCfEoXwVL3QfOx3V6zd94/vP/Lkdp37/FTcvnUf840dwKF0ONRu3QacRk2FpY5vntaumjEL42WOIvRuFjPQ0FC/rhLptu6Ld0DGwsLTK89rmJbn9GBWspCxg/yPNn/N7vZ/9cwcOrF+M6KuX8Tz+KYraFYd7jdroMmoKyleulue1qclJ2Dx3Ek7v2YbEZ7FwLF8Rrfp/geZ9AvK8jtc6SRELOyIddSkeuJkE/DCsO87s3YbWA0eiVAU3HNm6GpGh5zHl1yOoovj4te/v7+WAYo6loWjeAQ5lyiP66mUcWL8YjuUrYs7eizB7YbHkSZ99jIqeNVHS2RUmZuaICgvB4S0r4eJVC1O3HYf8n63KZABcrQAvW+3+7GRYcq51NYD5+bzet/44FXevh6NCNR8UtXNA/ONHOPzrSsQ9foiZu07D2aM6AM0OMf/rVB+Rly6gRZ9hKFXBDcpj+3H+wC50HzcDHYd/BYDXOkkXCzsiHZStBnY/ACIunsPEdn7o/fVctPcfAwDISEvDl02qoahDCczceeq1xwg7fRTV6jTM89jRbWvx86i+8J+zDE26D3pjht+XzMPa6WMwc9dpuNeonfu4sQxoWxqQS6XfjHRazrWepQZuhOT/en+V+NgYDFWURaNuAzH0u8UAgFN/bMUPAV0QMHcFGncbkPva74d2wsVDexB05g5sHEoA4LVO0sQxdkQ66Hmm5oPuzN5tkBsZoWnPIbnPmZqbo1G3gbgefBpPHtx97TH+W9QBgF+LTwEA929EvDVDiXLOAIDkhPg8j2epgedZb/8ZiN5FzrUOfNj1/io2DiVgZlEkzzUcce4EAODj9t3yvPajdt2QkZ6Gcwd25T7Ga52kiIUdkQ6Ky9T8/+0rIShd0R1FrIvmed7VWwEAiLqifK/jxsdqBjJZ2zm89JwqKwuJz57g2aMHUB47gE1zJ8HCyjr3XHnyccYgFZCcax0omOs9OSEeCU9jcSfiMoLGDkLK80R4ftw49/msjHTIjYxgbJJ3FWIziyIAgFuXg/Pm47VOEsNhn0Q6KC5DM8YnLuYhbEuUeun5Yv889izmwXsdd+ei2ZAbGaFO604vPRd56QK+al8n9++lXSph/MrfYV3MLs/rZADiMwBYvtepiV4p51pXo2Cu94nta+NB5DUAgLmlFTp+MQmNuw3Mfb50xUrIVqlw/eKZPGP2clrynj26n/sYr3WSIhZ2RDooIVPzQZeRlgoTU7OXnjc102xomZGW+s7HPLFjIw5tXoH2AeNQqoLbS8+XdfPA/zb+hbSUZFwLPoXLfx9EWvLLC4upAcRnvvQwUb7kXOtAwVzvw+atQurzRMRE38KRLauQkZaKbJUqdwLQxx16YOuCqVg0ZgAGTf8FpSq4IfT4Aexfu+ilc/BaJyliYUekgzL/WbrO1NwCmRnpLz2fkZ6W+/y7CD97AkFjB8K7QXP0GDfjla8pYl0UXvWaAAAUzdvjxI6NmDOwPeb8eTF3RuF/8xF9qBevpYK43ivV/LfV+aN23TCyURUAQN/J3wMAipUoiQkrfsfCkb0xrWczAJprf8DUn/DzqL4wL5J3eR9e6yQ1HGNHpINyPkuKOZZC/OOHLz0f989jdo6l33qsqPBQzB7YDuUqVcPoJdtgZPxu3/f8Wn4GADj5++bX5iP6UC9eSwVxvb/IyrYYqtVthBM7N+R53KN2ffxy8hbm7gvB9O1/Y8n5+7kzv0tXdH9tPiIpYGFHpINyfnGdPbzx4NZ1pDzPu3nljZCzmuerer/xOI+iIjG9dwvY2JfAV2v3vrTY8JtkZqQjOzsbKYkvL8HPGwsVlBevpQ+93l8lIy31ldewkZERKlT1RmXfj2BhaYVLJw4CADw/bvLafERSwGuSSAeZ/PObW7t1J2SrVPhrw9Lc5zLT03Fkyyq4+fjBoXQ5AEDs/Wjcv3k1zzHiHj/CtJ7NIJfJMWn9ftjYF3/luZIT4pGV+fJAokOblgMAKnrVem0+og/14rX0Idd7wpPHLx378d0oXD55CC6vuIbzvPdpLHYGzYZTFa/c4QivykckBRxjR6SDbEw0m5C7+/ihTpvO2Dh7IhKfPkZJZ1cc3bYGsfeiEDh3Re7rfxrZB+FnjmHb3X/XI5/RuwViom+hfcA4XD3/N66e//vf4zs45m7RdOX0Uaz85gvUbtUJpSq4ISszAxHnTuDsn9vh4lUL9T/rlSebDICtiXZ/fjIcOde6Gh92vX/Z1BOeHzWGc1VvWNoUw6PbN3Bo8wqoMjPRc+KsPOf8X6cGcK9ZByWdXRH/+BEOblyKtOQkTFz1R+4kC4DXOkkTCzsiHVTMFLiVrPnz8PlrsbnMZBzbrtk706myFyau+gMeteu/8RhR4aEAgF1Bc156zqN2g9zCrnxlT1St+wnOH9ilGcukVsPRyQWdRv4P7f3HwsQ073pfagC2pi8dkihfXrzWgfxf7816B+DioT1QHt2H1OTnsLEvger1m+Gzz7+CUxXPPK+t6FkTp//Yimcx92FhVRRe9Zqi+5hpcHSqmOd1vNZJirilGJEOSsgADr7csyQZTRw1LS1EH4rXOtH74egAIh1kbaLZp1KKjGWANfsCqIDwWid6PyzsiHSQXAZUsNSM8ZESGTS5uCk6FRRe60Tvh4UdkY6qaPXvivxSoYYmF1FB4rVO9O5Y2BHpKCtjoISZdFoyZNDksWLXFBUwXutE746FHZEOq2ojnZYMNTR5iLSB1zrRu2FhR6TD7EwBd4l0B7lba/IQaQOvdaJ3w8KOSMd52ACWRuK6qWTQdEl5FBUUgAwGr3Wit2NhR6TjjGSAn73YDzuFnSYHkTbxWid6OxZ2RHqgmClQ16HwP/BkAD5y0JyfqDDwWid6M+48QaRHYtKAU080g7u1/Ysth+aDroS5lk9E9Aq81olejYUdkZ6JywDOPgWSVdo7h5WxpkuKrRckEq91opexsCPSQyo1EJ4AXE/SdCEVxC95znHcrTWDxznOiKSA1zpRXizsiPTYs3TgSiLwOD3/H3o57ythplm7i8s8kBTxWifSYGFHZACSsoBbScDtZCDrn9/41334vfi48T/7dFa04ir7pBt4rZOhY2FHZECy1cDzLM3YpPgMID4TyMwGsqEZIG4iB2xNAFtTzZgia2Nuck66idc6GSoWdkRERER6guvYEREREekJFnZEREREeoKFHREREZGeYGFHREREpCdY2BERERHpCRZ2RERERHqChR0RERGRnmBhR0RERKQnWNgRERER6QkWdkRERER6goUdERERkZ5gYUdERESkJ1jYEREREekJFnZEREREeoKFHREREZGeYGFHREREpCdY2BERERHpCRZ2RERERHqChR0RERGRnmBhR0RERKQnWNgRERER6QkWdkRERER6goUdERERkZ5gYUdERESkJ1jYEREREekJFnZEREREeoKFHREREZGe+D+QU4XtQQk1hAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "\n",
        "# interpret diagonal of matrix as node attributes\n",
        "node_labels = {n: A[n,n] for n in range(len(A))}\n",
        "np.fill_diagonal(A, np.zeros(len(A)))\n",
        "\n",
        "G1 = nx.Graph(A)\n",
        "pos1=nx.spring_layout(G1)\n",
        "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G1,'weight')\n",
        "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n",
        "\n",
        "# interpret diagonal of permuted matrix as node attributes\n",
        "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n",
        "np.fill_diagonal(A_perm, np.zeros(len(A)))\n",
        "\n",
        "G2 = nx.Graph(A_perm)\n",
        "pos2=nx.spring_layout(G2)\n",
        "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G2,'weight')\n",
        "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n",
        "\n",
        "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n",
        "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "eUhWZ9_3jAmi"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "def perm_equivariant_embedding(A, betas, gammas):\n",
        "    \"\"\"\n",
        "    Ansatz to embedd a graph with node and edge weights into a quantum state.\n",
        "\n",
        "    The adjacency matrix A contains the edge weights on the off-diagonal,\n",
        "    as well as the node attributes on the diagonal.\n",
        "\n",
        "    The embedding contains trainable weights 'betas' and 'gammas'.\n",
        "    \"\"\"\n",
        "    n_nodes = len(A)\n",
        "    n_layers = len(betas) # infer the number of layers from the parameters\n",
        "\n",
        "    # initialise in the plus state\n",
        "    for i in range(n_nodes):\n",
        "        qml.Hadamard(i)\n",
        "\n",
        "    for l in range(n_layers):\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            for j in range(i):\n",
        "            \t# factor of 2 due to definition of gate\n",
        "                qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            qml.RX(A[i,i]*betas[l], wires=i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glOVsqRvjAmi"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "a14eee92-ad81-48f1-e465-f8209073c209"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"qulacs.simulator\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev)\n",
        "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n",
        "    \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n",
        "\n",
        "    perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n",
        "    return qml.expval(observable)\n",
        "\n",
        "\n",
        "A = create_data_point(n_qubits)\n",
        "betas = np.random.rand(n_layers)\n",
        "gammas = np.random.rand(n_layers)\n",
        "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n",
        "\n",
        "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIHRQVnDjAmi"
      },
      "source": [
        "Validating the equivariance\n",
        "===========================\n",
        "\n",
        "Let\\'s now check if the circuit is really equivariant!\n",
        "\n",
        "This is the expectation value we get using the original adjacency matrix\n",
        "as an input:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "c3215836-f4f2-4d14-e464-5ef17964f56f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.013399408925456074\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ncmkAwH-jAmj"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "0ac43a3e-7b6b-433c-d9ad-bc4f60de2029"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5052761815197134\n"
          ]
        }
      ],
      "source": [
        "perm = [2, 3, 0, 1, 4]\n",
        "A_perm = permute(A, perm)\n",
        "result_Aperm = eqc(A_perm, observable, betas, gammas)\n",
        "print(\"Model output for permutation of A: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOIqQmysjAmj"
      },
      "source": [
        "Why are the two values different? Well, we constructed an *equivariant*\n",
        "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n",
        "that embedding a permutation of the adjacency matrix leads to the same\n",
        "state as an embedding of the original matrix. An *equivariant* ansatz\n",
        "embeds the permuted adjacency matrix into a state where the qubits are\n",
        "permuted as well.\n",
        "\n",
        "As a result, the final state before measurement is only the same if we\n",
        "permute the qubits in the same manner that we permute the input\n",
        "adjacency matrix. We could insert a permutation operator\n",
        "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n",
        "the observables!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "MgYVIMP6jAmj"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pb21hBrLjAmj"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "0ef36ec4-a80e-424d-a761-c57632fa774b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4985035660903844\n"
          ]
        }
      ],
      "source": [
        "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n",
        "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0wblJk9mjAmj"
      },
      "source": [
        "Et voilà!\n",
        "\n",
        "Conclusion\n",
        "==========\n",
        "\n",
        "Equivariant graph embeddings can be combined with other equivariant\n",
        "parts of a quantum machine learning pipeline (like measurements and the\n",
        "cost function). [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n",
        "pipeline as part of a reinforcement learning scheme that finds heuristic\n",
        "solutions for the traveling salesman problem. Their simulations compare\n",
        "a fully equivariant model to circuits that break permutation\n",
        "equivariance and show that it performs better, confirming that if we\n",
        "know about structure in our data, we should try to use this knowledge in\n",
        "machine learning.\n",
        "\n",
        "References\n",
        "==========\n",
        "\n",
        "1.  Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n",
        "    Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n",
        "    weighted graphs.\n",
        "    [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n",
        "2.  Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n",
        "    Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n",
        "    (2022). Theory for Equivariant Quantum Neural Networks.\n",
        "    [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n",
        "\n",
        "About the author\n",
        "================\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "seconds = time.time()\n",
        "print(\"Time in seconds since end of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "HFTIJBPqph2f",
        "outputId": "7500a574-739a-43ab-b44a-34111752a87a"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695112970.7547305\n",
            "Tue Sep 19 08:42:50 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
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}