LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit V100 57.32s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit V100 57.32s (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": "e2faa623-9194-4bf3-ace1-0295cd0abea1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701155455.2984176\n",
            "Tue Nov 28 07:10:55 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 custatevec-cu11 pennylane-lightning-kokkos\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": "e98bb06d-fa11-4f6b-ac94-4b20c115a545"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.27 0.69 0.38]\n",
            " [0.69 0.54 1.  ]\n",
            " [0.38 1.   0.11]]\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": "f7fc025a-0063-4bac-8c50-bb5a914b15ab"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.54 1.   0.69]\n",
            " [1.   0.11 0.38]\n",
            " [0.69 0.38 0.27]]\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": "3a0470c1-82b3-46c2-c7d1-dc424285ce0c"
      },
      "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": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "86741ee7-40d7-4fd4-da25-e171912c53b1"
      },
      "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.kokkos\", 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": "bd613ee6-5239-4b4e-e09b-cd7146a3da81"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.02393189811640871\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": "bc6efcc8-9bb4-48f6-9037-b165ac3341a4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.24702734327850562\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": "b106d116-1766-44a9-9e70-ae434a4c370d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.27078478963458263\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": "a96431b2-a03a-429f-c7d3-cc199a2b7d2d"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701155512.6226256\n",
            "Tue Nov 28 07:11:52 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
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      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "gpuType": "V100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
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}