LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qulacs.simulator 25 qubit V100 336.96s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qulacs.simulator 25 qubit V100 336.96s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e4040d4a-ab28-4a98-cb9c-bf291bdc756d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695140377.2988985\n",
            "Tue Sep 19 16:19:37 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",
        "# !pip install qulacs\n",
        "# !pip install pennylane pennylane-qulacs --upgrade\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": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "385606a4-54db-4dd4-c093-2d09ab42df99"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.62 0.62 0.69]\n",
            " [0.62 0.85 0.42]\n",
            " [0.69 0.42 0.92]]\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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "2b72f338-32b7-42c8-9995-6e24e87bdc22"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.85 0.42 0.62]\n",
            " [0.42 0.92 0.69]\n",
            " [0.62 0.69 0.62]]\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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "6cb882c4-4f88-4192-8bc0-253257a1e032"
      },
      "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": 31,
      "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": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "7447e4d0-091c-45e4-e385-e91de1def9e1"
      },
      "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(\"qulacs.simulator\", 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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "dc8ef68b-7a6c-4749-f5b1-9ffb28ea88e0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00033107969880941845\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": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "5b9a6ea2-9e8b-4a9f-809a-73c0cb1f277d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.35209710366728425\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": 35,
      "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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "72043341-a604-4929-a8eb-e71e90334427"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.09559033497031742\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": "490956a1-79ea-4f68-d594-42ce48a41913"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695140714.2579744\n",
            "Tue Sep 19 16:25:14 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",
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      "nbconvert_exporter": "python",
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}