LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit TPU 180.26s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit TPU 180.26s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e2cb433a-023d-47c2-cb25-45d4826545d7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701152633.879831\n",
            "Tue Nov 28 06:23:53 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-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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "230ede0e-cadc-49c0-a955-0b55b35229bf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.41 0.21 0.44]\n",
            " [0.21 0.22 0.55]\n",
            " [0.44 0.55 0.14]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "c04a8a15-55e2-4a1f-def9-6c15374ad28c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.22 0.55 0.21]\n",
            " [0.55 0.14 0.44]\n",
            " [0.21 0.44 0.41]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d5fab79f-2e22-41b1-d8de-c46dd35b7800"
      },
      "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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "04b91808-3db0-4595-f047-c9c3daa05593"
      },
      "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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "e4939913-9475-46fb-db46-d91a90039761"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0027089886533848834\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "6cd2e0e8-323d-4e62-bbb2-70741bf9cf01"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.2424854189157486\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "2a38061a-9998-44bf-cb40-40c683c1fc45"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.32785777235403657\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": "e153024c-3d6e-4336-cce7-7385c4ea20b7"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701152814.1389172\n",
            "Tue Nov 28 06:26:54 2023\n"
          ]
        }
      ]
    }
  ],
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
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