LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit T4 53.97s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit T4 53.97s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6fb7cca2-45f8-4431-9533-3213648f8c54"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701156747.2085707\n",
            "Tue Nov 28 07:32:27 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5f5472fa-4c3e-4bc5-f788-2f28c93774e6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.77 0.35 0.67]\n",
            " [0.35 0.27 0.39]\n",
            " [0.67 0.39 0.44]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "947fb129-c288-4de5-b73b-1c429c14df73"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.27 0.39 0.35]\n",
            " [0.39 0.44 0.67]\n",
            " [0.35 0.67 0.77]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "55013e34-2802-4293-b1a2-05d3137a74fd"
      },
      "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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d275d091-8793-4149-9e96-85f6af5c7014"
      },
      "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(\"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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "420e1f93-2118-4546-bc18-8982d75fa46f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.00027600967067176966\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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "6c46dd49-ba8c-4195-ba4e-caabd8979f60"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.4195546171077108\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "b43026a8-3ee1-4cb1-b17b-79ab748f951a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.40636842246960936\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": "5c173d67-0a43-414e-f384-ceae857763c5"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701156801.1767933\n",
            "Tue Nov 28 07:33:21 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}