LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit CPU 65.87s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit CPU 65.87s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "0b05c572-0ebb-4b62-f7ae-c69decfc93b4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701142360.544374\n",
            "Tue Nov 28 03:32:40 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-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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "a9076a4c-391d-442b-f33a-be657dbb28c7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.83 0.05 0.27]\n",
            " [0.05 0.94 0.16]\n",
            " [0.27 0.16 0.6 ]]\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": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "e2cb2ab6-9e40-4b03-b4a8-1a6df732fb1c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.94 0.16 0.05]\n",
            " [0.16 0.6  0.27]\n",
            " [0.05 0.27 0.83]]\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": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "90925d8c-896d-4f0a-c113-d6de604c8c81"
      },
      "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": 17,
      "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": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "280a3ff1-cc75-49d6-a54b-4bd15a51c478"
      },
      "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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "7171f213-b1ff-414c-b063-bffbb638087d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0001139561058273693\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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "7e3e1e09-7ad9-402b-dbca-a60bc997f5a5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.03497096831672538\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": 21,
      "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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "7923fd1c-1859-4400-e8a5-7e603d1c8258"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.40732941430163266\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": "4128e611-4e02-4486-abf3-a9a17f5dfe8d"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701142426.411999\n",
            "Tue Nov 28 03:33:46 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": [],
      "machine_shape": "hm"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}