LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit A100 48.81s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit A100 48.81s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 97,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6fbd5872-c70c-4fa3-8b1b-fd44a4d4e41a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701141708.776097\n",
            "Tue Nov 28 03:21:48 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": 98,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "7aa77bfe-2b04-4f8f-d44f-57a3927b0a1c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.66 0.33 0.29]\n",
            " [0.33 0.74 0.64]\n",
            " [0.29 0.64 0.53]]\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": 99,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "b937e747-86d8-4e7a-a672-d9a9bfcd9d1d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.74 0.64 0.33]\n",
            " [0.64 0.53 0.29]\n",
            " [0.33 0.29 0.66]]\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": 100,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "c909c5bd-772a-487b-8ae1-b45ce4b09ca2"
      },
      "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": 101,
      "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": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "82a1d432-c6a2-4dac-e248-7dc7111b55e7"
      },
      "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": 103,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "1dd5b1d2-3160-4db3-92b8-7b4b0452ff6d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0005819796980150232\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": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "41e64787-7d80-4d2a-98a6-964a4c632915"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.29786327970977866\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": 105,
      "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": 106,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "22f90767-fe1b-403f-e5b1-c3f90326d849"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.40078711509901643\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": "d280fe8a-dc79-4846-e34b-cbea2d6f70b9"
      },
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701141757.5820012\n",
            "Tue Nov 28 03:22:37 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": [],
      "gpuType": "A100",
      "machine_shape": "hm"
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    "accelerator": "GPU"
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