LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit T4 53.20s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit T4 53.20s (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "1bd5a2e1-fde8-4b8b-b502-558631abd63a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701157167.4809287\n",
            "Tue Nov 28 07:39:27 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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "77d32f01-99e3-4865-ff36-d7ed8de1e125"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.5  0.4  0.38]\n",
            " [0.4  0.89 0.72]\n",
            " [0.38 0.72 0.09]]\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": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "2cefdcba-27d2-4da5-bbfb-b6a5fc78a55d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.89 0.72 0.4 ]\n",
            " [0.72 0.09 0.38]\n",
            " [0.4  0.38 0.5 ]]\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": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "c8d38409-14d9-42ad-dd60-8a5449553636"
      },
      "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": 61,
      "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": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 65
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "ae2c6138-4e7c-44b6-ba79-5722b8a9831f"
      },
      "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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "0743c796-ecc6-4db6-ea2a-cbd4a9f6b87f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0003873238914130871\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": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "49622c8d-51e6-4fec-b68b-1f6c890d7855"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.25634507979169074\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": 65,
      "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": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "e9bafa7f-9f64-4ed1-ecbc-fc013b3e66b4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4230415188252645\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": "e22b60af-6832-46c3-a552-afb63c36ac23"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701157220.678681\n",
            "Tue Nov 28 07:40:20 2023\n"
          ]
        }
      ]
    }
  ],
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