LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit V100 58.69s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit V100 58.69s (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "db1208ef-4a6b-4c4b-dccc-dd6382524a6b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701156268.8213956\n",
            "Tue Nov 28 07:24:28 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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5bfae75f-2679-4813-a4c2-f6d3cc44e51b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.51 0.42 0.22]\n",
            " [0.42 0.28 0.54]\n",
            " [0.22 0.54 0.69]]\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": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "283cc063-6826-4138-f29a-d8c429b4b4cf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.28 0.54 0.42]\n",
            " [0.54 0.69 0.22]\n",
            " [0.42 0.22 0.51]]\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": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d2c810ce-1f5f-4251-860d-c379914e1d78"
      },
      "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": 61,
      "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": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "84e7d921-9233-4d36-f058-b488336307a6"
      },
      "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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "4ffdf5ba-4676-4b23-dcaf-9eb50f0a1663"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0033365376428770247\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": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "2415aaf5-4d58-40a9-bd86-cb2a02e6b402"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.07233232944431406\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": 65,
      "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": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "94f36eb4-9018-42b8-9ca8-c9887cc58d91"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.18706997949428847\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": "2fc06cac-8e2d-4bee-bbf9-b32005b6779e"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701156327.5158894\n",
            "Tue Nov 28 07:25:27 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": "V100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}