LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit A100 48.30s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit A100 48.30s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "5812e791-d623-4b1f-84f9-75b4f9a7c0c7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701141529.7481747\n",
            "Tue Nov 28 03:18:49 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": 87,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "2313ce45-5988-4a31-9459-5130f40dee66"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.8  0.93 0.6 ]\n",
            " [0.93 0.9  0.58]\n",
            " [0.6  0.58 0.77]]\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": 88,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "76049375-f618-4a28-85c6-0ce074f2bccb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.9  0.58 0.93]\n",
            " [0.58 0.77 0.6 ]\n",
            " [0.93 0.6  0.8 ]]\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": 89,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "a19ab7e2-8eb6-4cf3-de46-e84538e9a9de"
      },
      "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": 90,
      "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": 91,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d04177e3-7fda-4d5e-a95a-c33dc95cfdf2"
      },
      "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": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "d967fc70-cee6-4301-e028-47eb53806891"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.07216130373811014\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": 93,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "4d092665-856f-486c-ce7d-33b97b99f29e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5766187685652239\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": 94,
      "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": 95,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "3a98fb30-2417-433b-b871-aa9031c38653"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.6662302244301935\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": "f3738701-459d-461d-d6a5-fc8618f5ee89"
      },
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701141578.047809\n",
            "Tue Nov 28 03:19:38 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
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      },
      "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
}