LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit CPU 67.49s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit CPU 67.49s (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": "d919c2a2-be96-459d-909e-b10f0e6c65c7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701142603.7773807\n",
            "Tue Nov 28 03:36:43 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "eb186463-49c9-4851-87de-033cb14bec37"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.43 0.13 0.32]\n",
            " [0.13 0.93 0.74]\n",
            " [0.32 0.74 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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "b453877e-d86c-42db-ea5f-7e381310cb8d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.93 0.74 0.13]\n",
            " [0.74 0.05 0.32]\n",
            " [0.13 0.32 0.43]]\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": "3775b146-948f-40fc-82f6-54b8883b01e1"
      },
      "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": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "54613ca9-de96-4a7f-8864-ec0f07c21878"
      },
      "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": "c7b94ff1-dd0c-436e-8697-da843eec70f7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0013347451240742344\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": "2ad59afc-a9d5-41cf-bc69-1036ee0a2072"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3837859493026558\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": "1463f82f-3d5b-4eb3-9fb0-2f6242caf82e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.1978472527033724\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": "6220bcad-d9b2-4d1e-8f97-9abe4d47df49"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701142671.263797\n",
            "Tue Nov 28 03:37:51 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
}