LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit V100 58.23s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit V100 58.23s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6fcea750-e04c-4129-fe17-a2f294632313"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701155932.3178854\n",
            "Tue Nov 28 07:18:52 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-kokkos\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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "696a84bd-0b39-43bf-9edf-fa38e015746a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.55 0.28 0.45]\n",
            " [0.28 0.09 0.28]\n",
            " [0.45 0.28 0.05]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "cb281d50-6cde-4932-98e8-506452d0baba"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.09 0.28 0.28]\n",
            " [0.28 0.05 0.45]\n",
            " [0.28 0.45 0.55]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "e89d31ad-91a7-44de-d98f-37e847be75c6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d36d696c-4e85-448d-dd50-f6bd50e0e0a0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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ii8Xj02mnnZZbbrkl119/fTo6Ot7X//XWWy/jx4/vNd7V1ZVvfvObxfItLS2ZOnVqTj755IwbN+598fb29kyYMCGnnXZar/GGhoZsvfXWOf3004vx7bbbLqecckqv8a6urnz3u9/N9ddfX4yPGTOm2H6SbL755rn99tt7jbe0tOSuu+4q1t/Q0JBlllkmHR0dxfKvv/56sf2mpqasvPLKfcYrlUrGjh3ba7yn3dbW1mL/Flxwwdx5553F/v3tb3/L1VdfXczfaaedlgkTJvQa7+7uzvHHH1/MT319fR599NEMHDgwN9xwQ6/j+9Of/lSMd3R0pKmpKW+88UYx/uUvfzkvvfRSr/Hu7u7U19cXy7e2tqalpaUYr6ury+TJk7PUUkvlxhtv7HX/GjZsWD71qU/1Gq+rq0tXV1eWWGKJXuM9z9dXX331Yvk77rijGG9ubs4RRxxR7F/P8bFUvqurK//617+yxhpr9Brvub4rle95vrn00ksX+7/vvvvm2GOPzR133PG+9wdbW1vz7LPP5phjjuk13tHRkSuvvDInnHBCr/H6+vrstttu+dGPftRrvL29PXfddVcx3vP5KbXf2tqap556Kscdd1yv8Z7jy09+8pNe4y0tLXnzzTfz4x//uNd4Y2NjNtlkk+L26ejoyDXXXFNsv6GhITvssEOx/z3Hn1L/mpubM2zYsBx99NHF7fvVr361WL6xsTEbbrhhjj/++F7jdXV12X///Yv1d3V15ZxzzinmZ/To0VlyySWL429tbc3jjz9e3D96zh99bb91110355xzTq/xtra2TJo0qZif0aNHZ5lllulz+0+dOrU4vubm5sw///zF+hsbGzNq1Kji9hs9enQWX3zx4vjb2try+uuv5zOf+UwGDhzY6/XhFVdckUUXXbTXeGtraxZaaKGsssoqxfK//OUvs9JKK/Uab25uzkYbbZRll122WP8KK6yQxRdfvFj/CSeckFGjRvUar6+vz5577pltt922GP/Wt76VzTffvBg/55xzssACCxTbHzt2bIYNG9ZrvKGhISeeeGKGDh3aa7yzszNjx44t9r+xsTFHHnlk5p9//l7jHR0defvtt4v119XV5aSTTsrqq69erH+rrbbKlltuWez/8ccfnwUXXLCYn1VXXbUYb2pqyje/+c0stthixe172mmnFeMdHR157bXXssgiixTH97vf/a64/dvb2zPvvPNm4YUXLsaHDBmSurq6XuOjR4/OzjvvXBxfXV1dfvWrXxU/H93d3bn55puL+299fX1+9rOf5VOf+lRx/+p5RlFq/+yzz87w4cOL9Z988slZeumle413dXXlzjvvzIgRI4r7Z1dXV7H95ubmbLXVVsXxd3V1TXs2UNp/VlpppWJ+u7q68te//rW4fTo7O/PMM88U89/W1pYFFliguH2S5De/+U3x+NPY2JiDDjqoOL6mpqZ8+ctfzsiRI4vxr33ta1luueWK+8dVV12V5Zdfvtj/wYMHF/vX0NCQQw45pFi+oaEhhx12WOrr64ufryeeeKJYvqWlJRtssEHx89PQ0JDW1tYMGTKkmL/777+/WL6rqyu33HJLcfu1tLRk3XXXLR4fWlpasvzyy2fllVcu7h9/+9vfiueflpaWrLjiisX229vb89JLLxXrr6+vzzHHHNNn+VdffbUYr6ury6mnnlrsX2dnZx544IFi/uvr63PUUUcV+9fW1pa6urri57e1tTVLLbVUcf9ob2/Ps88+mzXWWKP4+V9jjTWK55fu7u78/ve/z2qrrVbcfw444IDi9UNdXV1++tOfZtVVVy1+vpqamvLpT3+6GN9zzz37PH7cfffdxfrb2toyderU4vgaGhqy//77F8fX0tKSZZZZprj9mpqast1222WttdYqll9yySWL8fb29jz11FPFeHNzcz796U+noaGh2P4OO+xQ7F9DQ0P23XffrLnmmsXtd9dddxW3T5KceeaZxfa7u7tz8cUXZ+211y7W//zzzxevfxobG/PVr361eP3a2dmZCRMmFOPd3d254IILssEGGxSPT3/84x+z/vrrF+sfP3581ltvveL+88orrxTjdXV1+dGPflSMd3V15corr8w666xTvD7ZcMMNi9uvubk5K6+8cnH87e3t+ec//1kcX0NDQ0aPHp2NN964GP/GN75R3H4dHR255557+ty+l156aTbddNNifOLEicXrs87Ozlx//fXZZJNNivvfySefXIx3d3dPe8ZS2r/+67/+KxtuuGFx+3/mM5/pc3y33XZb8fzf1taWZ555pnj939LSkqFDhxa3T0NDQ3bdddd89rOfLeZ34sSJaWxsLJbfeeeds9lmmxXHt+qqqxbjdXV1Ofzww/u8//rud79b7H9HR0duv/32Yv1NTU357Gc/Wyw/evTorL766sXx19XV5cgjjyzmv7GxMdtuu20+97nPFft36623ZosttijWf9BBBxXvn9rb23P//fcX7y9Hjx6dFVZYIVtvvXUxP1/5yleK7Xd0dOTmm28ulm9pacmgQYOy1VZbFdtfaaWVivW3trbmtddeK8a7urpy0UUXFcfX0tKSeeedtxhvamrKTjvtVLx+SZKjjjoq22yzTbF/c889d9Zdd93i+L70pS8V778aGxtz+OGHF+8fWltb88ILL2S77bYr5ueLX/xiMd7a2pqXX365mJ/Ozs48+eSTWWihhYrbZ+211y4+v+h596O0fbq6unL++ecXyzc2NuYLX/hCn8fHU089tdj/jo6O/OMf/yief9rb29Pd3V28Puvo6MgNN9xQ3H5dXV3p6Ogolm9tbc2wYcOK11/d3d257rrrsswyyxT3z7XXXrvP68P77rsvK6ywQvH4Pc888xTjTU1N+frXv168v25vb8+gQYP6fP7x8ssvF/ffpqamfPe73y0+n2pubs7nP//54v7d2dmZK664onj8SpJjjjmmGO/u7s5Pf/rTYv66u7tz2WWXFa/v29vb88YbbxTPj52dnXnssceK998dHR1JUrz/bG9vz5QpU4rnj7a2tjzyyCPFz09HR0eefvrp4v1RS0tLhgwZUjy/trS0ZJVVVimOb/To0VlvvfWKx6+WlpYsssgixeuzurq6/O///m+x/42NjTn00EOLx5eGhoZ86UtfKn6+m5qassUWWxTbb21tzfDhw4ufr46Ojjz33HPFeHd3d/785z8Xn1/W19dnn332KW7f9vb2PP74431eH2+yySbF+5empqZ861vfKj6fSJKf/exnxeu/9vb23HvvvcXza3Nzc9Zff/3i8aGxsTF77bVX8f6/oaEh3/72t4vH17a2trz55pt93l9de+21xf23ra0tSy+9dPH40N3dnVtvvbX4fK69vT1Dhw4tHn/a29szYMCA4vG1u7s7t99+e/H5apJccsklxed3XV1duffee4vHz7q6uvzkJz8pbp/6+vocd9xxfR5/Jk+eXGy/qakpu+++e/H5ZkNDQw488MCsuOKKxfofeeSRLLHEEsX9Y4899ig+n2hubs5aa61VjCfJOeecU7w/b21tzRJLLFF8/tfU1JR99tmneP/V2tqahoaG4vG3rq4uF198cfH4M3r06Hzxi1/MkksuWdw+N954Y/Hz19ramkUXXbS4fRsaGnL00UcXz58dHR159NFHi+Xb2try/PPPF6+PmpubM2LEiGK8q6srU6ZMKX4+Ojo68q9//avP+ZONN964ePyrq6tLW1tbn8/n11lnneLxJUkuv/zyPve/5ubmYv319fX5f//v/2WjjTYqbv9jjz22ePzo6OjICy+8UMx/Y2Nj9ttvv+Lnr6GhId///veL55fRo0dn9OjRxf0zSc4777zi56erqysXXnhh8fje0tKSAQMGFK+vm5ub86lPfap4f9nc3JzFFluseH3V2NiYzTffvHh+b2try5NPPlmsv62tLQsvvHAxv0ly9dVXFz+fra2tmW+++Yrnn9bW1sw///zF82t9fX2++c1vFrdfW1tbHnvsseL4W1tbs/rqqxevD0aPHp0dd9yxz+v7BRdcsLh/jh49OqNGjSreP3R0dGTSpEnF8XV3d+d3v/tdMd7S0pL6+vri/UtnZ2fuuOOO4vmpq6sr48aNKz6f7ejoyN///vfi9WOSjBkzpvj8r66uLj/+8Y+L8fr6+vzf//1f8fqvqakpW2+9dZ/XXw0NDcXna11dXfnDH/5QzE9jY2P++7//u/h8tKOjI52dncX629vb89BDD/VZ/+c///ni86vu7u6cffbZxedLra2tefvtt4vxrq6u/Pa3vy0ev0ePHp1ll122eP/U1taWF198sXj+a2xszHe+853i/FCSnHbaacXtlyTHHXdc8fjR8/xh4403Tn19fS655JL3je/8888vxpubm7Pwwgtno4026jXec/9Sivc839pwww17jfc8XynFe97/KPUv+ffz4TXWWKPXeM/zi2WWWaY4/ilTpqRarRbLDx06tBivq6vL73//+0ydOrXXeM/86ttvv13cvl/4wheK5Xuuz0rlk+T6668vlu85f5bK97yfUirf8/yhUqn0Gu+Zvy/Fe+4Pe3L53nhbW1tGjBhRbL/n+Uhp+/e8P1Oqv2f+qa/8nHjiicXyo0ePzq677lqMt7S05LOf/Wyxfz3nv77q33nnnTPXXHMVx/evf/2rGO95f6cU73n/qdS/5N/vP5Xy1/N+Tinec/9Zive8nzNgwIBi/84888xivGf+qBTvuf8sjT/59/XRwIEDi/vHk08+WYw3NzdPuzYsjW/eeefNoEGDivvHBhtsUIz3PL8oxdva2qbde5fK77PPPsXt0/P8qFS+5/2w0vYbPXp0vvKVr2Tuuecu5ufee+/NvPPOW8zPrbfeWizf8/7RPPPMU+z/QQcdVIy3tbVlscUWK8Z77l9K7fe8/1Uq3/N+U1/lL7744uL27Xl/ppTfnufD8803XzH+2muvFdvvuT8YPHhwcf9bd911i/npub8utd/zfKNUf8/zx9L5GwDof1/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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.kokkos\", 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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "36b01f77-39c8-47fb-b53a-f911cd05382a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0005740636574512265\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "ca6acf36-2b9e-48be-f626-4bf136cc0576"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5737332734752568\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "71368e47-33df-4ce4-87cd-f15b38352444"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3924535263951754\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": "44456d5f-f4da-4635-c1db-5ba3e4089d95"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701155990.5432258\n",
            "Tue Nov 28 07:19:50 2023\n"
          ]
        }
      ]
    }
  ],
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      "nbconvert_exporter": "python",
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    "colab": {
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      "gpuType": "V100",
      "machine_shape": "hm"
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