LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit TPU 180.07s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit TPU 180.07s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6d0199b3-d4b5-4c1f-dbe4-e24d9b106008"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701152997.423728\n",
            "Tue Nov 28 06:29:57 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "8b9eaae1-1cb2-4837-d502-5de4a81db458"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.68 0.68 0.51]\n",
            " [0.68 0.04 0.78]\n",
            " [0.51 0.78 0.06]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "6a0b757e-f6fd-418c-89a1-70f90e56ef99"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.04 0.78 0.68]\n",
            " [0.78 0.06 0.51]\n",
            " [0.68 0.51 0.68]]\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "8dd8bd1a-28a7-49ad-8733-43ef62c5a79c"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "425d9d2d-d9a7-4281-e0e6-3eb35a02be14"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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C\n"
          },
          "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "f1aa04f0-2cf9-4c9d-ae2a-c9ac6014431f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0012009609519565145\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "e025835b-a7c7-4565-8d0d-a93ccc9e1675"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.44229396618902683\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "83cca3b5-8acd-4d5c-a111-c783183bc996"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4746961407363415\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": "0907e192-4974-4f17-9a97-852c8534e431"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701153177.489811\n",
            "Tue Nov 28 06:32:57 2023\n"
          ]
        }
      ]
    }
  ],
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    "colab": {
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