perturbed_graph_states.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "13657ec9-6d06-4ad3-aea2-9c911fbafcc4",
   "metadata": {},
   "source": [
    "# Random Graph State"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39b40c2d-71a6-40d8-b109-639693560a39",
   "metadata": {},
   "source": [
    "This code constructs a graph state with random controlled unitary grates rather than `CNOT` or `CZ` gates for entangling qubits. This gives a more general model of entanglement. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f0d88a1f-ffe1-4864-a945-528b19236c03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit:\n",
      "      ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐   ┌────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐   ┌────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐\n",
      "0: ────@──────────────────────────────────────────────────────────────@──────────────────────────────────────────────────────────────@──────────────────────────────────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "       │                                                              │                                                              │                                                              │\n",
      "1: ────┼──────────────────────────────────────────────────────────────┼────────────────────────────@─────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────@────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "       │                                                              │                            │                                 │                                                              │                            │\n",
      "2: ────┼────────────────────────────@─────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────┼────────────────────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "       │                            │                                 │                            │                                 │                            │                                 │                            │                            │\n",
      "       │                            ┌                           ┐     │                            │                                 │                            │                                 │                            │                            │\n",
      "3: ────┼────────────────────────────│ 0.169+0.573j  0.116+0.794j│─────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────┼────────────────────────────@─────────────────────────────────@────────────────────────────────────────────────────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "       │                            │-0.299-0.744j  0.142+0.58j │     │                            │                                 │                            │                                 │                            │                            │                            │                                 │                                                            │\n",
      "       │                            └                           ┘     │                            │                                 │                            │                                 │                            │                            │                            │                                 │                                                            │\n",
      "       │                                                              │                            │                                 │                            │                                 │                            │                            │                            │                                 │                                                            │\n",
      "       ┌                           ┐                                  │                            ┌                           ┐     │                            ┌                           ┐     │                            │                            │                            ┌                           ┐     │                                                            │\n",
      "4: ────│-0.173-0.827j  0.524+0.109j│──────────────────────────────────┼────────────────────────────│-0.48 -0.371j -0.686+0.403j│─────┼────────────────────────────│ 0.326-0.293j  0.788-0.432j│─────┼────────────────────────────┼────────────────────────────┼────────────────────────────│ 0.845-0.316j -0.43 +0.003j│─────┼──────────────────────────@─────────────────────────────────┼─────────────────────────────────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "       │-0.524-0.108j -0.487+0.69j │                                  │                            │-0.524-0.598j  0.572-0.201j│     │                            │-0.773+0.458j  0.418-0.131j│     │                            │                            │                            │-0.038-0.429j  0.236-0.871j│     │                          │                                 │                                                             │\n",
      "       └                           ┘                                  │                            └                           ┘     │                            └                           ┘     │                            │                            │                            └                           ┘     │                          │                                 │                                                             │\n",
      "                                                                      │                                                              │                                                              │                            │                            │                                                              │                          │                                 │                                                             │\n",
      "                                                                      │                                                              │                                                              │                            │                            ┌                           ┐                                  ┌                         ┐│                                 │                                                             │\n",
      "5: ───────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────┼────────────────────────────│ 0.225+0.249j -0.554+0.762j│──────────────────────────────────│0.71 +0.34j  0.608-0.103j│┼─────────────────────────────────┼─────────────────────────────────────────────────────────────┼───────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────\n",
      "                                                                      │                                                              │                                                              │                            │                            │-0.816-0.47j  -0.104+0.319j│                                  │0.013-0.617j 0.44 +0.653j││                                 │                                                             │                               │\n",
      "                                                                      │                                                              │                                                              │                            │                            └                           ┘                                  └                         ┘│                                 │                                                             │                               │\n",
      "                                                                      │                                                              │                                                              │                            │                                                                                                                      │                                 │                                                             │                               │\n",
      "                                                                      ┌                           ┐                                  │                                                              │                            │                                                                                                                      │                                 │                                                             │                               │\n",
      "6: ───────────────────────────────────────────────────────────────────│-0.829+0.265j  0.46 +0.179j│──────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼─────────────────────────────────┼────────────────────────────@────────────────────────────────┼───────────────────────────────┼───────────────────────────────@─────────────────────────────────────────────────────────────\n",
      "                                                                      │-0.424-0.252j -0.302-0.816j│                                  │                                                              │                            │                                                                                                                      │                                 │                            │                                │                               │                               │\n",
      "                                                                      └                           ┘                                  │                                                              │                            │                                                                                                                      │                                 │                            │                                │                               │                               │\n",
      "                                                                                                                                     │                                                              │                            │                                                                                                                      │                                 │                            │                                │                               │                               │\n",
      "                                                                                                                                     ┌                           ┐                                  │                            ┌                           ┐                                                                                          ┌                           ┐     │                            ┌                           ┐    │                               │                               │\n",
      "7: ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│ 0.028-0.009j  0.902-0.431j│──────────────────────────────────┼────────────────────────────│ 0.453-0.611j  0.648-0.046j│──────────────────────────────────────────────────────────────────────────────────────────│-0.398+0.798j  0.194+0.408j│─────┼────────────────────────────│-0.293+0.946j  0.131+0.044j│────┼───────────────────────────────┼───────────────────────────────┼───────────────────────────────@─────────────────────────────\n",
      "                                                                                                                                     │-0.986+0.164j  0.028-0.009j│                                  │                            │-0.232+0.607j  0.716-0.256j│                                                                                          │-0.274+0.359j -0.223-0.864j│     │                            │ 0.129+0.049j -0.375+0.917j│    │                               │                               │                               │\n",
      "                                                                                                                                     └                           ┘                                  │                            └                           ┘                                                                                          └                           ┘     │                            └                           ┘    │                               │                               │                               │\n",
      "                                                                                                                                                                                                    │                                                                                                                                                                                     │                                                             │                               │                               │                               │\n",
      "                                                                                                                                                                                                    ┌                           ┐                                                                                                                                                         ┌                           ┐                                 ┌                           ┐   ┌                           ┐   ┌                           ┐   ┌                         ┐\n",
      "8: ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│-0.985+0.073j  0.118+0.098j│─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│ 0.013-0.098j  0.382-0.919j│─────────────────────────────────│ 0.755-0.359j -0.477-0.271j│───│-0.266+0.204j  0.898+0.285j│───│ 0.938+0.283j -0.076+0.187j│───│0.666+0.281j 0.04 +0.69j │───\n",
      "                                                                                                                                                                                                    │ 0.152-0.019j  0.793+0.59j │                                                                                                                                                         │-0.737+0.668j  0.088-0.045j│                                 │ 0.105-0.538j  0.764-0.339j│   │ 0.925-0.178j  0.24 +0.234j│   │ 0.156+0.128j  0.689-0.696j│   │0.347+0.598j 0.401-0.601j│\n",
      "                                                                                                                                                                                                    └                           ┘                                                                                                                                                         └                           ┘                                 └                           ┘   └                           ┘   └                           ┘   └                         ┘\n",
      "      └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘   └────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘   └────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘\n",
      "Graph:\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "import networkx as nx\n",
    "import cirq\n",
    "\n",
    "# Define the number of qubits\n",
    "num_qubits = 9\n",
    "\n",
    "# Generate a random graph with num_qubits nodes\n",
    "graph = nx.fast_gnp_random_graph(num_qubits, 0.5)\n",
    "\n",
    "# Initialize the circuit with the given qubits\n",
    "qubits = [cirq.LineQubit(i) for i in range(num_qubits)]\n",
    "circuit = cirq.Circuit()\n",
    "\n",
    "# Apply random controlled unitary gates to each edge\n",
    "for edge in graph.edges():\n",
    "    control_qubit, target_qubit = qubits[edge[0]], qubits[edge[1]]\n",
    "    \n",
    "    # Generate a random unitary matrix\n",
    "    random_unitary = cirq.testing.random_unitary(2)\n",
    "    \n",
    "    # Apply the controlled random unitary gate to the circuit\n",
    "    circuit.append(cirq.ControlledGate(cirq.MatrixGate(random_unitary)).on(control_qubit, target_qubit))\n",
    "\n",
    "# Print the circuit and the graph\n",
    "print(\"Circuit:\")\n",
    "print(circuit)\n",
    "print(\"Graph:\")\n",
    "nx.draw(graph, with_labels=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "072c5775-5676-49a4-8fda-effae7ebcc46",
   "metadata": {},
   "source": [
    "This code also constructs a graph state with random controlled unitary grates rather than `CNOT` or `CZ` gates for entangling qubits. This gives a more general model of entanglement. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "21be11f8-05e2-4462-88ce-ce3107c35680",
   "metadata": {},
   "outputs": [],
   "source": [
    "import cirq\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "\n",
    "def graph_state_circuit(num_qubits):\n",
    "    \"\"\"Returns a graph state circuit on num_qubits qubits\"\"\"\n",
    "    # Generate a random graph with num_qubits nodes\n",
    "    graph = nx.fast_gnp_random_graph(num_qubits, 0.5)\n",
    "\n",
    "    # Initialize the circuit with the given qubits\n",
    "    qubits = [cirq.LineQubit(i) for i in range(num_qubits)]\n",
    "    circuit = cirq.Circuit()\n",
    "\n",
    "    # Apply Hadamard gates to all qubits\n",
    "    circuit.append(cirq.H.on_each(qubits))\n",
    "\n",
    "    # Apply random controlled unitary gates to each edge\n",
    "    for edge in graph.edges():\n",
    "        control_qubit, target_qubit = qubits[edge[0]], qubits[edge[1]]\n",
    "\n",
    "        # Generate a random unitary matrix\n",
    "        random_unitary = cirq.testing.random_unitary(2)\n",
    "\n",
    "        # Apply the controlled random unitary gate to the circuit\n",
    "        circuit.append(cirq.ControlledGate(cirq.MatrixGate(random_unitary)).on(control_qubit, target_qubit))\n",
    "\n",
    "    return circuit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd14ad2c-be9d-485b-acce-a803960e60cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"overflow: auto; white-space: pre;\">                                                                          ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐   ┌───────────────────────────────────────────────────────────────────────────────────────┐                                                                   ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐\n",
       "0: ───H───@───────────────────────────────@────────────────────────────────@──────────────────────────────────────────────────────────────@──────────────────────────────────────────────────────────────@────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │                               │                                │                                                              │                                                              │\n",
       "1: ───H───┼───────────────────────────────┼────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │                               │                                │                                                              │                            │                                 │                            │\n",
       "          ┌                           ┐   │                                │                                                              │                            │                                 │                            │\n",
       "2: ───H───│-0.842+0.33j  -0.04 +0.426j│───┼────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────@──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │-0.38 -0.195j  0.732-0.531j│   │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "          └                           ┘   │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "                                          │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "                                          ┌                           ┐    │                            ┌                           ┐     │                            │                                 │                            │                            │\n",
       "3: ───H───────────────────────────────────│ 0.661+0.26j  -0.439-0.55j │────┼────────────────────────────│ 0.156+0.607j -0.408+0.664j│─────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────┼────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "                                          │ 0.19 +0.678j -0.175+0.689j│    │                            │-0.576-0.525j  0.018+0.626j│     │                            │                                 │                            │                            │                                │\n",
       "                                          └                           ┘    │                            └                           ┘     │                            │                                 │                            │                            │                                │\n",
       "                                                                           │                                                              │                            │                                 │                            │                            │                                │\n",
       "4: ───H────────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────@────────────────────────────────@──────────────────────────────────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────\n",
       "                                                                           │                                                              │                            │                                 │                            │                            │                                │                               │                                │                                                              │\n",
       "                                                                           ┌                           ┐                                  │                            ┌                           ┐     │                            │                            │                                │                               │                                │                                                              │\n",
       "5: ───H────────────────────────────────────────────────────────────────────│ 0.782+0.119j -0.499+0.354j│──────────────────────────────────┼────────────────────────────│ 0.515-0.75j  -0.35 -0.223j│─────┼────────────────────────────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────┼────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────@────────────────────────────────@───────────────────────────────\n",
       "                                                                           │-0.095+0.604j  0.454+0.648j│                                  │                            │-0.394+0.129j -0.314-0.854j│     │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                           └                           ┘                                  │                            └                           ┘     │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                                                                                          │                                                              │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                                                                                          ┌                           ┐                                  │                            │                            ┌                           ┐    ┌                           ┐   ┌                           ┐    │                            ┌                           ┐     │                            │                                │\n",
       "6: ───H───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│-0.551+0.094j  0.045+0.828j│──────────────────────────────────┼────────────────────────────┼────────────────────────────│ 0.477-0.262j -0.831+0.113j│────│-0.168+0.901j -0.157-0.367j│───│-0.487-0.26j   0.455-0.698j│────┼────────────────────────────│-0.181+0.893j -0.195+0.364j│─────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────\n",
       "                                                                                                                                          │ 0.361+0.747j -0.528+0.183j│                                  │                            │                            │ 0.114+0.831j -0.124+0.53j │    │-0.181-0.356j -0.8  -0.449j│   │-0.784-0.283j -0.233+0.501j│    │                            │-0.388+0.14j   0.91 -0.049j│     │                            │                                │\n",
       "                                                                                                                                          └                           ┘                                  │                            │                            └                           ┘    └                           ┘   └                           ┘    │                            └                           ┘     │                            │                                │\n",
       "                                                                                                                                                                                                         │                            │                                                                                                                              │                                                              │                            │                                │\n",
       "                                                                                                                                                                                                         │                            ┌                           ┐                                                                                                  ┌                           ┐                                  │                            ┌                           ┐    │\n",
       "7: ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────────────────────│ 0.747-0.292j  0.584+0.126j│──────────────────────────────────────────────────────────────────────────────────────────────────│-0.409-0.553j -0.707+0.165j│──────────────────────────────────┼────────────────────────────│-0.673+0.008j -0.405-0.619j│────┼───────────────────────────────\n",
       "                                                                                                                                                                                                         │                            │-0.387-0.454j  0.096+0.796j│                                                                                                  │ 0.619+0.38j  -0.563+0.395j│                                  │                            │ 0.375+0.638j  0.306-0.599j│    │\n",
       "                                                                                                                                                                                                         │                            └                           ┘                                                                                                  └                           ┘                                  │                            └                           ┘    │\n",
       "                                                                                                                                                                                                         │                                                                                                                                                                                                                          │                                                             │\n",
       "                                                                                                                                                                                                         ┌                           ┐                                                                                                                                                                                              ┌                           ┐                                 ┌                           ┐\n",
       "8: ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│ 0.174+0.586j  0.789-0.066j│──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│-0.167-0.176j -0.793-0.558j│─────────────────────────────────│-0.231-0.703j  0.021+0.672j│───\n",
       "                                                                                                                                                                                                         │-0.379-0.695j  0.585-0.177j│                                                                                                                                                                                              │-0.6  -0.762j  0.184+0.157j│                                 │ 0.32 -0.592j  0.521-0.525j│\n",
       "                                                                                                                                                                                                         └                           ┘                                                                                                                                                                                              └                           ┘                                 └                           ┘\n",
       "                                                                          └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘   └───────────────────────────────────────────────────────────────────────────────────────┘                                                                   └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘</pre>"
      ],
      "text/plain": [
       "                                                                          ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐   ┌───────────────────────────────────────────────────────────────────────────────────────┐                                                                   ┌──────────────────────────────────────────────────────────┐   ┌──────────────────────────────────────────────────────────┐\n",
       "0: ───H───@───────────────────────────────@────────────────────────────────@──────────────────────────────────────────────────────────────@──────────────────────────────────────────────────────────────@────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │                               │                                │                                                              │                                                              │\n",
       "1: ───H───┼───────────────────────────────┼────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────@───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │                               │                                │                                                              │                            │                                 │                            │\n",
       "          ┌                           ┐   │                                │                                                              │                            │                                 │                            │\n",
       "2: ───H───│-0.842+0.33j  -0.04 +0.426j│───┼────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────@──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "          │-0.38 -0.195j  0.732-0.531j│   │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "          └                           ┘   │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "                                          │                                │                            │                                 │                            │                                 │                            │                            │\n",
       "                                          ┌                           ┐    │                            ┌                           ┐     │                            │                                 │                            │                            │\n",
       "3: ───H───────────────────────────────────│ 0.661+0.26j  -0.439-0.55j │────┼────────────────────────────│ 0.156+0.607j -0.408+0.664j│─────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────┼────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "                                          │ 0.19 +0.678j -0.175+0.689j│    │                            │-0.576-0.525j  0.018+0.626j│     │                            │                                 │                            │                            │                                │\n",
       "                                          └                           ┘    │                            └                           ┘     │                            │                                 │                            │                            │                                │\n",
       "                                                                           │                                                              │                            │                                 │                            │                            │                                │\n",
       "4: ───H────────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────┼────────────────────────────┼─────────────────────────────────┼────────────────────────────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────@────────────────────────────────@──────────────────────────────────────────────────────────────@─────────────────────────────────────────────────────────────────────────────────────────────\n",
       "                                                                           │                                                              │                            │                                 │                            │                            │                                │                               │                                │                                                              │\n",
       "                                                                           ┌                           ┐                                  │                            ┌                           ┐     │                            │                            │                                │                               │                                │                                                              │\n",
       "5: ───H────────────────────────────────────────────────────────────────────│ 0.782+0.119j -0.499+0.354j│──────────────────────────────────┼────────────────────────────│ 0.515-0.75j  -0.35 -0.223j│─────┼────────────────────────────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────┼────────────────────────────────┼────────────────────────────@─────────────────────────────────┼────────────────────────────@────────────────────────────────@───────────────────────────────\n",
       "                                                                           │-0.095+0.604j  0.454+0.648j│                                  │                            │-0.394+0.129j -0.314-0.854j│     │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                           └                           ┘                                  │                            └                           ┘     │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                                                                                          │                                                              │                            │                            │                                │                               │                                │                            │                                 │                            │                                │\n",
       "                                                                                                                                          ┌                           ┐                                  │                            │                            ┌                           ┐    ┌                           ┐   ┌                           ┐    │                            ┌                           ┐     │                            │                                │\n",
       "6: ───H───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│-0.551+0.094j  0.045+0.828j│──────────────────────────────────┼────────────────────────────┼────────────────────────────│ 0.477-0.262j -0.831+0.113j│────│-0.168+0.901j -0.157-0.367j│───│-0.487-0.26j   0.455-0.698j│────┼────────────────────────────│-0.181+0.893j -0.195+0.364j│─────┼────────────────────────────┼────────────────────────────────┼───────────────────────────────\n",
       "                                                                                                                                          │ 0.361+0.747j -0.528+0.183j│                                  │                            │                            │ 0.114+0.831j -0.124+0.53j │    │-0.181-0.356j -0.8  -0.449j│   │-0.784-0.283j -0.233+0.501j│    │                            │-0.388+0.14j   0.91 -0.049j│     │                            │                                │\n",
       "                                                                                                                                          └                           ┘                                  │                            │                            └                           ┘    └                           ┘   └                           ┘    │                            └                           ┘     │                            │                                │\n",
       "                                                                                                                                                                                                         │                            │                                                                                                                              │                                                              │                            │                                │\n",
       "                                                                                                                                                                                                         │                            ┌                           ┐                                                                                                  ┌                           ┐                                  │                            ┌                           ┐    │\n",
       "7: ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────────────────────│ 0.747-0.292j  0.584+0.126j│──────────────────────────────────────────────────────────────────────────────────────────────────│-0.409-0.553j -0.707+0.165j│──────────────────────────────────┼────────────────────────────│-0.673+0.008j -0.405-0.619j│────┼───────────────────────────────\n",
       "                                                                                                                                                                                                         │                            │-0.387-0.454j  0.096+0.796j│                                                                                                  │ 0.619+0.38j  -0.563+0.395j│                                  │                            │ 0.375+0.638j  0.306-0.599j│    │\n",
       "                                                                                                                                                                                                         │                            └                           ┘                                                                                                  └                           ┘                                  │                            └                           ┘    │\n",
       "                                                                                                                                                                                                         │                                                                                                                                                                                                                          │                                                             │\n",
       "                                                                                                                                                                                                         ┌                           ┐                                                                                                                                                                                              ┌                           ┐                                 ┌                           ┐\n",
       "8: ───H──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│ 0.174+0.586j  0.789-0.066j│──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────│-0.167-0.176j -0.793-0.558j│─────────────────────────────────│-0.231-0.703j  0.021+0.672j│───\n",
       "                                                                                                                                                                                                         │-0.379-0.695j  0.585-0.177j│                                                                                                                                                                                              │-0.6  -0.762j  0.184+0.157j│                                 │ 0.32 -0.592j  0.521-0.525j│\n",
       "                                                                                                                                                                                                         └                           ┘                                                                                                                                                                                              └                           ┘                                 └                           ┘\n",
       "                                                                          └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘   └───────────────────────────────────────────────────────────────────────────────────────┘                                                                   └──────────────────────────────────────────────────────────┘   └──────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_qubits = 9\n",
    "circuit = graph_state_circuit(num_qubits)\n",
    "circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a18fa86-a908-40c9-84d0-011cbefc279c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.5 64-bit ('anaconda3': virtualenv)",
   "language": "python",
   "name": "python385jvsc74a57bd0474c67ce7e36ad5731492349411c4ce02ca5c170a680b2d1efe1eb0325e35fe7"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}