LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit V100 152.91s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit V100 152.91s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "7e6fbe4d-378a-414f-ac26-647b586e769e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695118339.9516091\n",
            "Tue Sep 19 10:12:19 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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "b0bc203a-337f-4d62-aada-df7cec0898d3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.8  0.14 0.3 ]\n",
            " [0.14 0.8  0.54]\n",
            " [0.3  0.54 0.71]]\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": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "26ac4914-9e6c-48be-a9e6-e47733d43fb9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.8  0.54 0.14]\n",
            " [0.54 0.71 0.3 ]\n",
            " [0.14 0.3  0.8 ]]\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": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "613c07e0-0d49-411d-f04e-46f305d543a5"
      },
      "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": 17,
      "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": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "35420e05-1b08-426d-bf40-1a68509cb880"
      },
      "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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "20ca5a19-fb3f-4d0d-b167-2d6c09a1c74c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.038156139891543484\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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "06fd7ab0-ad25-432e-8645-b5b65a869bad"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.2987989541143179\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": 21,
      "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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "61c7bbb8-dc89-41bd-912d-54cca3dc2d80"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3818537400657078\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": "078ae692-3237-4e53-8318-b18d04fbfd31"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695118492.8577962\n",
            "Tue Sep 19 10:14:52 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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  "nbformat_minor": 0
}