LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit TPU 42.76s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit TPU 42.76s (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": "c4fa1541-6357-4d2b-fec5-e2fb5b13b5af"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701147132.7418845\n",
            "Tue Nov 28 04:52:12 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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5d6ab580-b30a-452c-beb6-cf9a1350bdfa"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.41 0.47 0.54]\n",
            " [0.47 0.78 0.65]\n",
            " [0.54 0.65 0.09]]\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": "c1097d51-12c1-48ef-dbab-d16c2bb5554b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.78 0.65 0.47]\n",
            " [0.65 0.09 0.54]\n",
            " [0.47 0.54 0.41]]\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": "0ce94b06-8d03-4ce8-a5d9-19a06cdecb14"
      },
      "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": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "c40408d2-f571-4a08-9d03-46914b960f5c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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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": "f81fa70e-a6a0-4c79-a611-47b5b2211b0a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0040771850212961355\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": "8b62d160-b85f-4c8a-aaf9-99310d0121ea"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.4080545105271444\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": "194d3fb6-1f50-4d58-a0b5-6018cad7a971"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.2836884224330902\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": "094a86e5-bc38-4980-d5a1-e714d8d712c4"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701147175.5002127\n",
            "Tue Nov 28 04:52:55 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
    },
    "accelerator": "TPU"
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}