LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit T4 55.92s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit T4 55.92s (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": "3cacb511-f2c9-407c-eee3-0aa7286d5460"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701156871.240265\n",
            "Tue Nov 28 07:34:31 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": "585eca21-b849-4071-f0a1-c7c246f9a14c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.84 0.66 0.18]\n",
            " [0.66 0.59 0.34]\n",
            " [0.18 0.34 0.66]]\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": "f37076f2-8c38-48ec-f047-2c65903ad840"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.59 0.34 0.66]\n",
            " [0.34 0.66 0.18]\n",
            " [0.66 0.18 0.84]]\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": "fe308039-38f5-40d0-f597-68f91b50ea9b"
      },
      "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": "8dd0b00b-a3e0-4ca6-bb79-ef0f0c4ffbec"
      },
      "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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "8dc3cd1e-5fd9-4db6-e032-d9423480789f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0004701540796156837\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": "0643d663-b026-405a-8700-515690e4ab54"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.40571597833228146\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": "b91ac665-ca5d-4a5b-a160-46e3a55f436e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.40324104958427337\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": "936c8c80-195b-40e3-beff-0f0be227f3b4"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701156927.162415\n",
            "Tue Nov 28 07:35:27 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
}