LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit T4 27.13s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit T4 27.13s (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": "bd2d9a8a-b1b9-4cc5-eba6-2642bc883ba9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701146038.6020916\n",
            "Tue Nov 28 04:33:58 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-gpu custatevec-cu11 --upgrade\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": "c292da13-fdab-4c24-fb7d-09d9ffb329ef"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.26 0.47 0.17]\n",
            " [0.47 0.97 0.53]\n",
            " [0.17 0.53 0.52]]\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": "2932ca00-bca4-4316-e8fc-ee06da7048a8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.97 0.53 0.47]\n",
            " [0.53 0.52 0.17]\n",
            " [0.47 0.17 0.26]]\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": "a2212f7c-e96a-41ba-a9e8-4cb090d55556"
      },
      "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": "2f7c3dcf-a18b-45f7-8da6-07543982e1a4"
      },
      "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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "2bbecf16-fe74-4dd5-ac64-593ea494b226"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0008350503451055617\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": "7872c61d-7c44-49a7-fc3c-1c263787534b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3413499819090791\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": "7c78020a-db71-4b0a-acfe-6c4aead0fdcf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.5179673142633675\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": "967e7da0-4bd9-47e9-97b6-fa94f4b0d8f8"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701146065.727851\n",
            "Tue Nov 28 04:34:25 2023\n"
          ]
        }
      ]
    }
  ],
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    "colab": {
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