LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit V100 153.22s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit V100 153.22s (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "f5fb02f1-46a7-45e7-8d1c-0a8836a05a23"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695118677.4267457\n",
            "Tue Sep 19 10:17:57 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "c7024884-5325-45ee-f17e-cec326f5c6d7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.86 0.32 0.59]\n",
            " [0.32 0.56 0.64]\n",
            " [0.59 0.64 0.27]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "c7cba571-70ef-4550-ee2c-acc5009a847f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.56 0.64 0.32]\n",
            " [0.64 0.27 0.59]\n",
            " [0.32 0.59 0.86]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "70a2626a-e620-40c4-c110-4dd82a796669"
      },
      "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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d18c5517-38cf-46a6-d3e9-f2d1308c08b2"
      },
      "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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "4d869582-f149-4eb5-e77b-e50b00ca07cf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.01106155883310607\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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "53f55b4b-52d6-4fea-e03c-666fc4bb98be"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3164523490704596\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "69640757-852b-449f-d44f-1ca8deac1121"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.2598949521780014\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": "51c654be-cda8-496c-b277-a79061aefc76"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695118830.6418507\n",
            "Tue Sep 19 10:20:30 2023\n"
          ]
        }
      ]
    }
  ],
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    "colab": {
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