LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qulacs.simulator 25 qubit V100 320.25s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qulacs.simulator 25 qubit V100 320.25s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "a7af67bf-1586-411c-beff-a26efeb8a6b9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695113070.6650903\n",
            "Tue Sep 19 08:44:30 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 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": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "c09dcdf3-c3f2-4133-a9fe-304e55941275"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.47 0.57 0.4 ]\n",
            " [0.57 0.34 0.06]\n",
            " [0.4  0.06 0.82]]\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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "cf4c9bc0-28fc-4618-e53e-0435bb428ab8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.34 0.06 0.57]\n",
            " [0.06 0.82 0.4 ]\n",
            " [0.57 0.4  0.47]]\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": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "99547e8d-4e45-4314-d6bc-bfaf58849b34"
      },
      "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": 46,
      "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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "a0527232-b408-456d-a9d9-902c69fcae82"
      },
      "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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "d79122a8-348c-4cf4-e01d-b9d218a57731"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.022872210280017378\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "02d53776-8d4c-4818-a0e0-29e5acf1085d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5767677037155972\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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "c11223be-b369-4393-8d3f-59a922246656"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.6229589123817884\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": "fb8a1382-c98b-41df-82e0-072e2c7dfb0b"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695113390.9135835\n",
            "Tue Sep 19 08:49:50 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",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}