LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit A100 20.04s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit A100 20.04s (3) 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": "6f6bad9c-dbb7-4451-8c87-4f27d876189e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695165571.6561136\n",
            "Tue Sep 19 23:19:31 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": "e16878bc-de46-4013-be95-f8a4ca6cb58d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.43 0.5  0.23]\n",
            " [0.5  0.71 0.65]\n",
            " [0.23 0.65 0.73]]\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": "2d7566f7-3749-42ac-de78-c76787ded31a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.71 0.65 0.5 ]\n",
            " [0.65 0.73 0.23]\n",
            " [0.5  0.23 0.43]]\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": "4f2a3d12-5b35-4ac4-da57-8bf95b06aee7"
      },
      "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": 88
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "5812687b-68d2-416f-c321-da6a8e724a74"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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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": "b98b4ab0-76aa-4279-9242-bc620bdaedf8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 5.044967423935267e-07\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": "0d57e1f4-6928-4b3f-8803-fcbf52cce607"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.4740953260352644\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": "72d64039-4c1b-4e8b-a348-09eb70d0bb42"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.34296764822026055\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": "9879b6eb-4f23-4c57-d32e-a56893217bf8"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695165591.6979823\n",
            "Tue Sep 19 23:19:51 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
}