LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/qiskit.aer 25 qubit (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / qiskit.aer 25 qubit (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": "f4303537-06fe-42f0-a9d9-fd54cc157b7e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695139236.8192816\n",
            "Tue Sep 19 16:00:36 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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "b37cc5a7-cf63-4d9d-ca5b-8e838fce16f8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.51 0.43 0.07]\n",
            " [0.43 0.76 0.27]\n",
            " [0.07 0.27 0.08]]\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": "dcb51ec3-92e7-4e26-8d58-9edb94408414"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.76 0.27 0.43]\n",
            " [0.27 0.08 0.07]\n",
            " [0.43 0.07 0.51]]\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": "00164c02-721d-47d3-bb8e-2cd80f1746da"
      },
      "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": "68619421-65b0-4aba-cb33-8d7398c6f4db"
      },
      "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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "95984672-cad9-4872-8321-11fa44b98c2a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.005859375\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": "2c2c91ea-7411-44bb-cfef-ef7cfb8898d0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.255859375\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": "cb4b65ae-0aae-438d-bcc4-50d6b4465568"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.087890625\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": "707de4c9-0bd5-4e15-f1b0-032b708dbfb5"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695139433.870385\n",
            "Tue Sep 19 16:03:53 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
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      "gpuType": "V100"
    },
    "accelerator": "GPU"
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}