LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit TPU 43.13s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit TPU 43.13s (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": "c6601602-40c9-412a-9721-69393c3e1ac8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701146586.0616202\n",
            "Tue Nov 28 04:43:06 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 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": "fe249e51-02ed-472d-98b8-190fb5595490"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.84 0.41 0.82]\n",
            " [0.41 0.13 0.84]\n",
            " [0.82 0.84 0.35]]\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": "bdbebac9-3f70-42f4-e555-2346402150d5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.13 0.84 0.41]\n",
            " [0.84 0.35 0.82]\n",
            " [0.41 0.82 0.84]]\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": "e6960ef9-e3f8-445b-bd84-9057da97840d"
      },
      "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": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "a78ec00d-f8ae-4cd2-de07-dfd213a69dad"
      },
      "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": "7d66793f-bc5b-44f7-e7ae-92838ba11d4e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 1.352629488677956e-05\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": "138fc8ad-3de7-494f-de48-1b49ec4c8442"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.05867604406040228\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": "9fba81f3-d4ce-427b-b3bb-77ca7d4b1c24"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.06206909117478031\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": "39532a3c-4708-45da-89c2-4565a4195021"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701146629.187732\n",
            "Tue Nov 28 04:43:49 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      },
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
    },
    "accelerator": "TPU"
  },
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}