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

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[404218]: / Code / PennyLane / Benchmarking Devices / default.qubit 25 qubit (3) 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": "71cef828-8560-4127-e0ae-282c29ffc48a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695142477.0239346\n",
            "Tue Sep 19 16:54:37 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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "b149382c-5ebd-465f-ac4f-0540b54d9663"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.06 0.83 0.52]\n",
            " [0.83 0.17 0.25]\n",
            " [0.52 0.25 0.95]]\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": "19997ea2-faa5-495f-9751-9965b1ad8573"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.17 0.25 0.83]\n",
            " [0.25 0.95 0.52]\n",
            " [0.83 0.52 0.06]]\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": "226f9ba7-7d0f-437e-b5af-9b76c2b28e6a"
      },
      "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": "00ea0ff2-c5d9-4b5b-8736-c41811401b75"
      },
      "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(\"default.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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "af1d12e9-85e8-4419-d2f4-3daf7390edd5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.4718372016870722\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": "9aaa679c-701f-462a-aa43-4ba1e51cb565"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.9475945680623137\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": "d0e3ee11-086a-4829-e364-56a965f8bdbd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.9573719771855758\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": "ffa5f808-1f9a-4db6-8280-076b70e89b7f"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695143233.9315827\n",
            "Tue Sep 19 17:07:13 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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}