LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit TPU 43.15s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit TPU 43.15s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e154f072-ff23-4f9e-9821-2640cbadeded"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701146713.7705038\n",
            "Tue Nov 28 04:45:13 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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "74f4a8ff-7f23-46eb-9ac9-54ebd25be4cf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.7  0.13 0.31]\n",
            " [0.13 0.87 0.85]\n",
            " [0.31 0.85 0.02]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "3ab8be33-2fcb-4305-e11d-c95be5ac53d4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.87 0.85 0.13]\n",
            " [0.85 0.02 0.31]\n",
            " [0.13 0.31 0.7 ]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "83a0877b-1918-4167-ca18-45990fe2d9c5"
      },
      "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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "6530da69-249f-4894-ea48-0230d50f84e0"
      },
      "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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "7b0330b1-9b23-4449-ba86-b5ed3f86fd16"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00032467468786430924\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "7e2503e6-2a62-4191-c12c-518dd9260ddb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.07015724647641154\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "ea9c8006-1c5d-4907-9ed6-0c9f219477ac"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.0947529656827003\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": "4528c121-a712-4f7f-9a86-d652dc1f5f7d"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701146756.9166775\n",
            "Tue Nov 28 04:45:56 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"
    },
    "accelerator": "TPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}