LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/lightning.gpu 25 qubit A100 (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / lightning.gpu 25 qubit A100 (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e9ed761a-6154-4fe4-b044-8d73920f8ee8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1696311833.9403813\n",
            "Tue Oct  3 05:43:53 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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "19250f07-9d42-4762-e778-abc2df0b6fe7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.14 0.73 0.38]\n",
            " [0.73 0.92 0.68]\n",
            " [0.38 0.68 0.43]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "1c6f4ccd-10f2-4979-e8eb-67b1dde8c2e5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.92 0.68 0.73]\n",
            " [0.68 0.43 0.38]\n",
            " [0.73 0.38 0.14]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "9766e253-1910-4976-95f2-77a9df221079"
      },
      "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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "9fb5f0b3-6d58-488d-d5b7-28ee6feed633"
      },
      "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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "7c1d3705-638d-4ef8-ab60-4547e4130be7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0005837356492687498\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "06177c58-7d44-4bd9-9925-d8b05c759b32"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.4814552000765455\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "033eb6d6-7dbb-4698-d747-f833367ff811"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.03995054901505586\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": "2fffa80a-2108-4654-e7b0-2ee6382abb88"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1696311854.0211723\n",
            "Tue Oct  3 05:44:14 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
}