LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit A100 47.52s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit A100 47.52s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 108,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "44b04482-4a07-4e07-8515-dddbf2eada4e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701141837.3016696\n",
            "Tue Nov 28 03:23:57 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": 109,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "d9e058c9-4b87-4d11-fbd0-7946f7eb2f05"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.84 0.88 0.87]\n",
            " [0.88 0.07 0.35]\n",
            " [0.87 0.35 0.67]]\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": 110,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "a6fa773e-1eb3-4d64-dc86-148b66ec8729"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.07 0.35 0.88]\n",
            " [0.35 0.67 0.87]\n",
            " [0.88 0.87 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": 111,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "495c285e-ef5a-403b-f7ea-c29817e8744b"
      },
      "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": 112,
      "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": 113,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "69dc3dfb-4d31-4976-fc73-b9c6208e35f8"
      },
      "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": 114,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "85c1e209-7ea3-467a-863e-b54e8505cf8a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 2.195845316082667e-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": 115,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "3c781984-3760-4619-fe0b-873d4930a720"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.24520932453606015\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": 116,
      "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": 117,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "4964a32b-b089-482f-d682-a4773fd6c175"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.12710878851802834\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": "3773ca41-964e-4cdf-d718-d14d7d8b99e6"
      },
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701141884.8266263\n",
            "Tue Nov 28 03:24:44 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": "A100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}