LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit T4 27.14s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit T4 27.14s (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": "e4945583-781a-4fb3-ee41-fde8582b4630"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701145573.3307877\n",
            "Tue Nov 28 04:26:13 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-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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "ddcda5d9-9017-4597-baaa-6f48e24b4c68"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.44 0.64 0.81]\n",
            " [0.64 0.88 0.94]\n",
            " [0.81 0.94 0.53]]\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": "8d5a7e35-ad28-476c-beee-195d0e189109"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.88 0.94 0.64]\n",
            " [0.94 0.53 0.81]\n",
            " [0.64 0.81 0.44]]\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": "2bf4ab9f-06b1-47a6-9dd4-5e43636ae5f7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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          },
          "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": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "da4323e4-0930-49ac-dcb3-d14025fa43cb"
      },
      "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": "537c3c70-faf0-4718-880a-b1e3b757a63c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 1.9247763179531192e-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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "2c42fbf5-0a3b-4131-98e0-84dd84ce6b68"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.08960906820358899\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": "8af81c34-3be2-47e7-cc5d-6bfb5a1d453a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.33115523987938383\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": "0dd953ab-cbab-42c0-acda-571fbb9fee0d"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701145600.470499\n",
            "Tue Nov 28 04:26:40 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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      "codemirror_mode": {
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}