LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/lightning.gpu 25 qubit A100 (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / lightning.gpu 25 qubit A100 (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "8a99d708-b546-4f9c-f406-30f1ce053e0d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695165356.5134404\n",
            "Tue Sep 19 23:15:56 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-gpu\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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "7f6c6252-a8d1-45cd-9cee-012fa8b9d133"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.01 0.58 0.64]\n",
            " [0.58 0.8  0.66]\n",
            " [0.64 0.66 0.59]]\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": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "3736a18e-cb01-4f97-e02d-19d4409e66eb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.8  0.66 0.58]\n",
            " [0.66 0.59 0.64]\n",
            " [0.58 0.64 0.01]]\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": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "70d84654-6eb7-43a1-bb9c-675c78e473c2"
      },
      "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": 17,
      "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": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "427a723c-48a6-45d7-c8b9-2feaeaf841e7"
      },
      "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.gpu\", 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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "664c362e-fe46-4b8a-e403-140919f4956d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0014959703457878822\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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "bc606483-8925-4d31-fa94-dbe717eeedd9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.11526748342280195\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": 21,
      "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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "d524ad52-5057-4fea-f44e-9f585042a88c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.05837305037442499\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": "6aeb3393-476f-43fc-c10a-985acd4f1f90"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695165376.4924288\n",
            "Tue Sep 19 23:16:16 2023\n"
          ]
        }
      ]
    }
  ],
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      "machine_shape": "hm"
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    "accelerator": "GPU"
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