LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qiskit.aer 25 qubit V100 193.68s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qiskit.aer 25 qubit V100 193.68s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "23cde65d-f6e7-4a13-fd6a-1896e6fe8ff0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695113872.9790697\n",
            "Tue Sep 19 08:57:52 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-qiskit\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": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "b1a66f24-1cf2-4ea4-c89d-d997deeb8900"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.87 0.72 0.73]\n",
            " [0.72 0.57 0.88]\n",
            " [0.73 0.88 0.23]]\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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "af31b475-324f-43b8-8bb4-5b819ffcfd99"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.57 0.88 0.72]\n",
            " [0.88 0.23 0.73]\n",
            " [0.72 0.73 0.87]]\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": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "70bea462-9e12-48dd-e4e0-cfaae1683382"
      },
      "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": 24,
      "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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "a7eaba8c-bccb-4a7c-d150-232d93b5209f"
      },
      "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(\"qiskit.aer\", 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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "96d20b7a-08ff-4a5c-af5a-ba87b3a2a455"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.033203125\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "60d70511-5e14-46e7-fb3b-412e1672fff6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.197265625\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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "a39f9265-1e96-475b-87ac-fad4ab08afb3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.0546875\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": "114333d6-cd9a-4971-8e29-9b33074987fe"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695114066.6619537\n",
            "Tue Sep 19 09:01:06 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
}