LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit T4 54.10s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit T4 54.10s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "5cd7e7e1-7ee5-4b9f-bf98-31714d2d35c8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701157034.7170763\n",
            "Tue Nov 28 07:37:14 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "1e99880f-8409-4fdc-9ddc-e7d7dea7cdbe"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.43 0.27 0.58]\n",
            " [0.27 0.02 0.49]\n",
            " [0.58 0.49 0.26]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "ecb21179-7a40-4a7c-f5c7-b4b73205338d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.02 0.49 0.27]\n",
            " [0.49 0.26 0.58]\n",
            " [0.27 0.58 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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "04c0027d-67bd-4160-e9fd-18e5c5a3153a"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "26a22925-1c65-4a3e-9e13-6850871ea1a5"
      },
      "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "231790e7-c838-4c9d-94b4-0713be0a98d2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.001859489484395547\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "2d57e529-32f0-484e-c173-a7f1967c340e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.35222118408852277\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "3b7851c9-12ab-483a-b14c-f6f05c7afb40"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.42968323064683\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": "4bf1fe35-2f84-4c90-e7e0-94e409be6956"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701157088.8144777\n",
            "Tue Nov 28 07:38:08 2023\n"
          ]
        }
      ]
    }
  ],
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    "colab": {
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