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

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[404218]: / Code / PennyLane / Benchmarking Devices / lightning.qubit 25 qubit (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "24fcea27-086c-400d-bca0-9ebc0a5c799b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695105109.2222176\n",
            "Tue Sep 19 06:31:49 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",
        "\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": 69,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "427a799c-c87d-43b3-d93a-b28c51e296f6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.88 0.31 0.55]\n",
            " [0.31 0.43 0.47]\n",
            " [0.55 0.47 0.13]]\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": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "062497bd-ca7f-4e52-eb31-111794461acf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.43 0.47 0.31]\n",
            " [0.47 0.13 0.55]\n",
            " [0.31 0.55 0.88]]\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": 71,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "8c0b35d4-b941-4d66-9bcd-df8cb3e2a1a4"
      },
      "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": 72,
      "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": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "3bf5a4ce-3750-418d-8cd4-77c3794be6b0"
      },
      "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(\"lightning.qubit\", 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": 74,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "17e3488b-f2b2-4ee8-fb2c-b4b5fbb6c7e1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.000505965269898961\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": 75,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "1ff06058-4e87-45d7-daca-5c4f7ed0c799"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3864897942864832\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": 76,
      "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": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "f0a039ae-73b7-41ab-b6a4-811db837e40f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3063716971342133\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": "57d18367-4cf0-4003-fa39-6eebc69fa291"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695105248.1126435\n",
            "Tue Sep 19 06:34:08 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}