LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit V100 58.18s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit V100 58.18s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "342522af-5973-4ee2-e4a6-88ad6516f306"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701156082.194251\n",
            "Tue Nov 28 07:21:22 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "9f5b1d9f-aea7-41bf-940a-0c521521aca0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.02 0.15 0.28]\n",
            " [0.15 0.86 0.81]\n",
            " [0.28 0.81 0.39]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "18446861-df03-45e4-a38f-b09f0f3e187f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.86 0.81 0.15]\n",
            " [0.81 0.39 0.28]\n",
            " [0.15 0.28 0.02]]\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d8d03590-762c-4221-eb91-be493f641897"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "0e964473-68bb-46ef-9322-4c4096480f8e"
      },
      "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "3e3b15fe-e041-4680-a5c9-67292c390c29"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0033937200951741162\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "bc6cff29-9aa8-4738-dbd2-47e28a08dbe6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.1366938645334364\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "a4cf47e3-653d-43d7-f75c-4e816f27b01b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.22267490770842396\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": "6ddbcf91-d0c2-4373-b58e-ee8041f8aa87"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701156140.3750591\n",
            "Tue Nov 28 07:22:20 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
}