LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit V100 23.01s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit V100 23.01s (4) 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": "a72d1279-46ea-4e5d-e64f-18b29a4dd2ae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695116363.609416\n",
            "Tue Sep 19 09:39:23 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": "992399fb-fc42-4a35-ac5d-9a15afa04ff2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.58 0.58 0.27]\n",
            " [0.58 0.52 0.46]\n",
            " [0.27 0.46 0.4 ]]\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": "3e40598e-1404-4405-c4c4-2072e52c11dc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.52 0.46 0.58]\n",
            " [0.46 0.4  0.27]\n",
            " [0.58 0.27 0.58]]\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": "843c871a-f1ec-4da3-b4c8-ac8e909f8b9c"
      },
      "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": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d1ede778-274d-4f8f-deaa-9070753408d4"
      },
      "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": "57c5cd0a-80b5-4924-83b3-7f53000aa5a7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0012100854818252686\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": "35b8dd85-6ab0-46de-f832-4caa42e39456"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.50323597238008\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": "211ad89a-6970-4b2d-8dc2-8e4530afd6c7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.49052474657702494\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": "7b663aef-e811-4d4a-a277-7cd294696d96"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695116386.6188414\n",
            "Tue Sep 19 09:39:46 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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}