LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/cirq.qsim 25 qubit (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / cirq.qsim 25 qubit (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 201,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "36e2b025-ee7d-45c0-8fa8-2f7e0ec500cd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695111426.4607856\n",
            "Tue Sep 19 08:17:06 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-Cirq\n",
        "# !pip install qsimcirq\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": 202,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "4297bb3f-1d95-4a00-9926-b95dcd57975f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.95 0.44 0.31]\n",
            " [0.44 0.91 0.18]\n",
            " [0.31 0.18 0.9 ]]\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": 203,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "1932bca0-a07f-470c-9f49-3770442b987f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.91 0.18 0.44]\n",
            " [0.18 0.9  0.31]\n",
            " [0.44 0.31 0.95]]\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": 204,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "df88db59-5700-4c16-eda1-64cb10c4b687"
      },
      "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": 205,
      "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": 206,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "a31741ec-d103-4843-8c11-397aa329b51d"
      },
      "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(\"cirq.qsim\", 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": 207,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "49f4676c-4ee0-4173-88ff-124ec695a326"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0035495578629193836\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": 208,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "da6e18b5-97db-4051-9ac8-bb52cd62759b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.20846803729364183\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": 209,
      "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": 210,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "ad9fcb4b-0b96-47ee-cb78-e35fb5a109ed"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.312942449352704\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": "797c3582-ee9a-4e98-c6d2-03d3c0502d0c"
      },
      "execution_count": 211,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695111572.691772\n",
            "Tue Sep 19 08:19:32 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "display_name": "Python 3",
      "name": "python3"
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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  "nbformat_minor": 0
}