samples/getting-started/simulation/LargeSimulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "acquired-exhibit",
   "metadata": {},
   "source": [
    "# Simulating quantum programs with large number of qubits\n",
    "\n",
    "The quantum programs with large number of qubits can be efficiently simulated using the [sparse simulator](https://docs.microsoft.com/azure/quantum/machines/sparse-simulator).\n",
    "\n",
    "The sparse simulator is a simulator that utilizes a sparse representation of quantum state vectors, as opposed to the [full state simulator](https://docs.microsoft.com/azure/quantum/user-guide/machines/full-state-simulator). This feature allows the sparse simulator to minimize the memory footprint used to represent quantum states, thus enabling simulations over a larger number of qubits. The sparse simulator is efficient for representing quantum states that are sparse in the computational basis, that is, quantum states for which most of the amplitude coefficients are zero in the computational basis. As such, sparse simulator enables users to explore larger applications than what can be represented using the full state simulator which will waste both memory and time on an exponentially large number of zero-amplitudes.\n",
    "\n",
    "For more information about the sparse simulator, please see [Jaques and Häner (arXiv:2105.01533)](https://arxiv.org/abs/2105.01533).\n",
    "\n",
    "In this sample, we'll look at the advantages of the sparse simulator over the full state simulator.\n",
    "\n",
    "Below, we'll create a few clusters (groups) of qubits, each prepared in a [GHZ state](https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bacterial-trinity",
   "metadata": {},
   "source": [
    "Below, we'll open a few Q# namespaces to provide access to functions for creating manipulating arrays of data, and for helping to visualize our quantum programs. To learn more, check out the [sample on visualizing quantum programs](https://github.com/microsoft/Quantum/tree/main/samples/diagnostics/visualization) and the [Q# API reference](https://docs.microsoft.com/qsharp/api/qsharp/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "shaped-office",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/x-qsharp-data": "[]",
      "text/html": [
       "<ul></ul>"
      ],
      "text/plain": []
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "open Microsoft.Quantum.Arrays;\n",
    "open Microsoft.Quantum.Diagnostics;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "affiliated-value",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/x-qsharp-data": "[\"PrepareAndMeasureGhzState\"]",
      "text/html": [
       "<ul><li>PrepareAndMeasureGhzState</li></ul>"
      ],
      "text/plain": [
       "PrepareAndMeasureGhzState"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "/// # Summary\n",
    "/// Prepares, measures, and resets the GHZ states.\n",
    "///\n",
    "/// # Input\n",
    "/// ## nQubits\n",
    "/// Number of qubits to allocate (must be a multiple of the nClusters input).\n",
    "/// \n",
    "/// ## nClusters\n",
    "/// Number of clusters to break-up qubits into.\n",
    "operation PrepareAndMeasureGhzState(nQubits : Int, nClusters : Int) : Unit {\n",
    "    Message($\"Allocating {nQubits} qubits...\");\n",
    "    // Allocate the qubits:\n",
    "    use qs = Qubit[nQubits];\n",
    "    Message(\"Finished allocating!\");\n",
    "\n",
    "    // Number of qubits in every cluster:\n",
    "    let clusterSize = nQubits / nClusters;\n",
    "    Message($\"Creating {nClusters} clusters of GHZ states between {clusterSize} qubits...\");\n",
    "    // Iterate through the clusters:\n",
    "    for cluster in Chunks(clusterSize, qs) {\n",
    "        // Apply H gate to the first-most qubit in the cluster:\n",
    "        H(Head(cluster));\n",
    "        // Apply CNOT gate to the remaining qubits in the cluster:\n",
    "        ApplyCNOTChain(cluster);\n",
    "        // After this, all qubits in the cluster will have the same state.\n",
    "    }\n",
    "    Message(\"Finished GHZ clusters!\");\n",
    "\n",
    "    // For small states\n",
    "    if nQubits < 15 {\n",
    "        // show the histogram:\n",
    "        DumpMachine();\n",
    "    }\n",
    "\n",
    "    Message(\"Collapse and show final state:\");\n",
    "    // Measure the qubits:\n",
    "    let results = ForEach(M, qs);\n",
    "    Message($\"{results}\");\n",
    "\n",
    "    Message(\"Cleaning up...\");\n",
    "    ResetAll(qs);\n",
    "\n",
    "    Message(\"Done\");\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "flying-business",
   "metadata": {},
   "source": [
    "We'll make the small states displayed conveniently on a histogram.  \n",
    "For more information about `dump.basisStateLabelingConvention`, please see [Configuration settings](https://docs.microsoft.com/qsharp/api/iqsharp-magic/config#configuration-settings)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "foster-barbados",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/x-qsharp-data": "\"\\\"bitstring\\\"\"",
      "text/plain": [
       "\"bitstring\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%config dump.basisStateLabelingConvention = \"bitstring\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tight-array",
   "metadata": {},
   "source": [
    "Now we'll run our Q# operation on the full state simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "copyrighted-railway",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Allocating 6 qubits...\n",
      "Finished allocating!\n",
      "Creating 2 clusters of GHZ states between 3 qubits...\n",
      "Finished GHZ clusters!\n"
     ]
    },
    {
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       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
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       "                                <td>$\\left|000000\\right\\rangle$</td>\r\n",
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       "                                <td>$\\left|000001\\right\\rangle$</td>\r\n",
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       "                                <td>$\\left|000100\\right\\rangle$</td>\r\n",
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       "                                <td>$\\left|000101\\right\\rangle$</td>\r\n",
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       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
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       "                                     document.getElementById(\"round-b6f2569d-2c7a-4717-8720-89e4cbb0e5f9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000111\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-cfe48dfc-375b-417f-a89c-b00091a9d5ea\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-cfe48dfc-375b-417f-a89c-b00091a9d5ea\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1ec5d4f3-9d5f-4831-b323-db7a594d037c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1ec5d4f3-9d5f-4831-b323-db7a594d037c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-cf05116f-7b74-4643-8183-7028b6cbe201\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-cf05116f-7b74-4643-8183-7028b6cbe201\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2987b623-f3e1-4e04-a067-d089f37b67f8\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2987b623-f3e1-4e04-a067-d089f37b67f8\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-94e83488-f4e2-467e-a290-bc3af67980e1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-94e83488-f4e2-467e-a290-bc3af67980e1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4cbb459c-aaee-4c3d-8cc2-ffd8a414be54\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4cbb459c-aaee-4c3d-8cc2-ffd8a414be54\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fee3d367-3e3f-4a67-8baf-136d6098ab78\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fee3d367-3e3f-4a67-8baf-136d6098ab78\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-63db637e-00df-4781-a5ac-ca2bda2150d1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-63db637e-00df-4781-a5ac-ca2bda2150d1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-87142188-329f-457d-8639-ae615a41940c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-87142188-329f-457d-8639-ae615a41940c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3046e894-a1af-4f78-813b-97a304176bd1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3046e894-a1af-4f78-813b-97a304176bd1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4342775b-f2d6-4fa9-92ba-4cb3460663f5\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4342775b-f2d6-4fa9-92ba-4cb3460663f5\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b098b12a-578d-454e-ad4c-188252916235\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b098b12a-578d-454e-ad4c-188252916235\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6074e231-b40d-4bc4-875f-f66efd2fb04d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6074e231-b40d-4bc4-875f-f66efd2fb04d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-28165e56-4fdd-48e9-8352-44442c3a5f6d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-28165e56-4fdd-48e9-8352-44442c3a5f6d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-752c7db0-39cf-44f3-a3a6-bf1ef9189906\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-752c7db0-39cf-44f3-a3a6-bf1ef9189906\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dd7f0044-5ede-42cc-af40-bbd4b07a2501\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-dd7f0044-5ede-42cc-af40-bbd4b07a2501\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fdb4a317-146c-436e-ac67-712d7a659494\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fdb4a317-146c-436e-ac67-712d7a659494\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7f7864a6-4c19-4169-8395-4c637e5988a6\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7f7864a6-4c19-4169-8395-4c637e5988a6\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7d620c39-4a66-4f6f-9aee-b6066e763a16\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7d620c39-4a66-4f6f-9aee-b6066e763a16\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b02a8170-d268-4ed1-9123-d1f502b8d8b3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b02a8170-d268-4ed1-9123-d1f502b8d8b3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-bb4fb38d-6e53-4a12-b0d3-027f9c76ed84\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-bb4fb38d-6e53-4a12-b0d3-027f9c76ed84\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6cdcd869-790b-4fce-be8c-ebe251cf0f2e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6cdcd869-790b-4fce-be8c-ebe251cf0f2e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8beb25e5-de53-439c-ab44-c1e38f2f76f6\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8beb25e5-de53-439c-ab44-c1e38f2f76f6\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5db0e4c1-5c2f-4942-b074-ee51c7135d7c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5db0e4c1-5c2f-4942-b074-ee51c7135d7c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-75181f8a-9063-4706-a7e9-3d55547c5f06\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-75181f8a-9063-4706-a7e9-3d55547c5f06\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2216f53e-32a1-4d8c-a700-126e4f009d0b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2216f53e-32a1-4d8c-a700-126e4f009d0b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6c13c485-a81b-4284-865a-65b86b988057\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6c13c485-a81b-4284-865a-65b86b988057\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-79918e78-9724-451a-aedb-f7accd9b3b86\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-79918e78-9724-451a-aedb-f7accd9b3b86\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dcc4a870-c67a-41b9-9627-6f2439cfd22a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-dcc4a870-c67a-41b9-9627-6f2439cfd22a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fcfb4e0b-329c-4ce4-b63a-f60fb1540b99\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fcfb4e0b-329c-4ce4-b63a-f60fb1540b99\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-25fd33d5-4e29-4745-b9bf-75ff168352d7\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-25fd33d5-4e29-4745-b9bf-75ff168352d7\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-18cf84f9-c14f-470f-beb6-243937d3bb4b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-18cf84f9-c14f-470f-beb6-243937d3bb4b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ba9880f4-c295-4692-aa26-4aa1ae2a2955\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ba9880f4-c295-4692-aa26-4aa1ae2a2955\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d1cf0736-b67a-4b1d-ac04-ef7bc759e063\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d1cf0736-b67a-4b1d-ac04-ef7bc759e063\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9c2f7e75-cbe5-4145-a358-6da540068526\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9c2f7e75-cbe5-4145-a358-6da540068526\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c30048ec-e97d-46cb-9997-bacc669746e3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c30048ec-e97d-46cb-9997-bacc669746e3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dc3236c7-b2f1-4ec3-8c35-e248e72e44a2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-dc3236c7-b2f1-4ec3-8c35-e248e72e44a2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-58e99c42-f3f1-415e-85a9-f36d6f5ad18e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-58e99c42-f3f1-415e-85a9-f36d6f5ad18e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-bcc153fb-b1a5-40fb-81f5-0ab9c45fccfe\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-bcc153fb-b1a5-40fb-81f5-0ab9c45fccfe\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9ac51a8c-4c23-4e38-bd13-01f052af6200\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9ac51a8c-4c23-4e38-bd13-01f052af6200\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f210070d-80d0-4580-bcac-dbb6964e2d03\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f210070d-80d0-4580-bcac-dbb6964e2d03\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110000\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2f2860b9-761d-4b32-b931-0d93692e3d76\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2f2860b9-761d-4b32-b931-0d93692e3d76\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6911eace-250a-424a-add0-abbad505b3f3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6911eace-250a-424a-add0-abbad505b3f3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a9106dea-9929-4fb4-8ce3-d76ac47e2bfe\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a9106dea-9929-4fb4-8ce3-d76ac47e2bfe\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5c1708c4-93e8-4b59-bb7b-e18d9db64c1f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5c1708c4-93e8-4b59-bb7b-e18d9db64c1f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-26453654-e051-462a-90e4-6fe77ad519e9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-26453654-e051-462a-90e4-6fe77ad519e9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8061d384-3b35-4281-b11b-7c5d7380baca\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8061d384-3b35-4281-b11b-7c5d7380baca\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3c5590c0-8235-4efb-bf40-970fb9aadb11\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3c5590c0-8235-4efb-bf40-970fb9aadb11\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d47aae09-85d9-419b-b92c-ac8c18cf5e6d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d47aae09-85d9-419b-b92c-ac8c18cf5e6d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-04a5ef45-7ebf-4a9a-985a-a32f823a4876\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-04a5ef45-7ebf-4a9a-985a-a32f823a4876\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111001\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f3afe0d7-ed92-47d1-a5d0-ffad1269df20\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f3afe0d7-ed92-47d1-a5d0-ffad1269df20\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111010\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-15761501-648c-437e-8284-17572acd346e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-15761501-648c-437e-8284-17572acd346e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111011\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-074a9eff-d1b9-4e5f-b771-f24aa6228489\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-074a9eff-d1b9-4e5f-b771-f24aa6228489\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111100\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-561377bf-45cd-471b-8cd4-b1021464bd4f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-561377bf-45cd-471b-8cd4-b1021464bd4f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d8464605-19c6-481a-b7ba-290a0d41cd95\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d8464605-19c6-481a-b7ba-290a0d41cd95\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-780617a2-20d3-402e-ac0a-5deaa685b02a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-780617a2-20d3-402e-ac0a-5deaa685b02a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111111\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8548f975-9ad3-408c-8543-74a965f63f25\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8548f975-9ad3-408c-8543-74a965f63f25\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000000⟩\t0.5000000000000001 + 0𝑖\n",
       "|000001⟩\t0 + 0𝑖\n",
       "|000010⟩\t0 + 0𝑖\n",
       "|000011⟩\t0 + 0𝑖\n",
       "|000100⟩\t0 + 0𝑖\n",
       "|000101⟩\t0 + 0𝑖\n",
       "|000110⟩\t0 + 0𝑖\n",
       "|000111⟩\t0.5000000000000001 + 0𝑖\n",
       "|001000⟩\t0 + 0𝑖\n",
       "|001001⟩\t0 + 0𝑖\n",
       "|001010⟩\t0 + 0𝑖\n",
       "|001011⟩\t0 + 0𝑖\n",
       "|001100⟩\t0 + 0𝑖\n",
       "|001101⟩\t0 + 0𝑖\n",
       "|001110⟩\t0 + 0𝑖\n",
       "|001111⟩\t0 + 0𝑖\n",
       "|010000⟩\t0 + 0𝑖\n",
       "|010001⟩\t0 + 0𝑖\n",
       "|010010⟩\t0 + 0𝑖\n",
       "|010011⟩\t0 + 0𝑖\n",
       "|010100⟩\t0 + 0𝑖\n",
       "|010101⟩\t0 + 0𝑖\n",
       "|010110⟩\t0 + 0𝑖\n",
       "|010111⟩\t0 + 0𝑖\n",
       "|011000⟩\t0 + 0𝑖\n",
       "|011001⟩\t0 + 0𝑖\n",
       "|011010⟩\t0 + 0𝑖\n",
       "|011011⟩\t0 + 0𝑖\n",
       "|011100⟩\t0 + 0𝑖\n",
       "|011101⟩\t0 + 0𝑖\n",
       "|011110⟩\t0 + 0𝑖\n",
       "|011111⟩\t0 + 0𝑖\n",
       "|100000⟩\t0 + 0𝑖\n",
       "|100001⟩\t0 + 0𝑖\n",
       "|100010⟩\t0 + 0𝑖\n",
       "|100011⟩\t0 + 0𝑖\n",
       "|100100⟩\t0 + 0𝑖\n",
       "|100101⟩\t0 + 0𝑖\n",
       "|100110⟩\t0 + 0𝑖\n",
       "|100111⟩\t0 + 0𝑖\n",
       "|101000⟩\t0 + 0𝑖\n",
       "|101001⟩\t0 + 0𝑖\n",
       "|101010⟩\t0 + 0𝑖\n",
       "|101011⟩\t0 + 0𝑖\n",
       "|101100⟩\t0 + 0𝑖\n",
       "|101101⟩\t0 + 0𝑖\n",
       "|101110⟩\t0 + 0𝑖\n",
       "|101111⟩\t0 + 0𝑖\n",
       "|110000⟩\t0 + 0𝑖\n",
       "|110001⟩\t0 + 0𝑖\n",
       "|110010⟩\t0 + 0𝑖\n",
       "|110011⟩\t0 + 0𝑖\n",
       "|110100⟩\t0 + 0𝑖\n",
       "|110101⟩\t0 + 0𝑖\n",
       "|110110⟩\t0 + 0𝑖\n",
       "|110111⟩\t0 + 0𝑖\n",
       "|111000⟩\t0.5000000000000001 + 0𝑖\n",
       "|111001⟩\t0 + 0𝑖\n",
       "|111010⟩\t0 + 0𝑖\n",
       "|111011⟩\t0 + 0𝑖\n",
       "|111100⟩\t0 + 0𝑖\n",
       "|111101⟩\t0 + 0𝑖\n",
       "|111110⟩\t0 + 0𝑖\n",
       "|111111⟩\t0.5000000000000001 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collapse and show final state:\n",
      "[One,One,One,Zero,Zero,Zero]\n",
      "Cleaning up...\n",
      "Done\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate PrepareAndMeasureGhzState nQubits=6 nClusters=2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dying-armstrong",
   "metadata": {},
   "source": [
    "In the cell above increase the `nQubits` input (by multiples of `nClusters`) such that the simulation becomes slow (e.g. `nQubits`: 8, 10, 12, 14, ...; `nClusters`: 2). The simulation is expected to become slow at `nQubits=24` and to take about a minute with `nQubits=26`. It is not recommended to make large steps, otherwise the simulation can run too long.  \n",
    "After the number of qubits exceeds 15, the state histogram will not be displayed."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mediterranean-woman",
   "metadata": {},
   "source": [
    "Now we'll run our Q# operation on the sparse simulator, using the [%simulate_sparse](https://docs.microsoft.com/qsharp/api/iqsharp-magic/simulate_sparse) magic command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "empty-commonwealth",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Allocating 6 qubits...\n",
      "Finished allocating!\n",
      "Creating 2 clusters of GHZ states between 3 qubits...\n",
      "Finished GHZ clusters!\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2,3,4,5],\"n_qubits\":6,\"amplitudes\":{\"0\":{\"Real\":0.4999999999999999,\"Imaginary\":0.0,\"Magnitude\":0.4999999999999999,\"Phase\":0.0},\"56\":{\"Real\":0.4999999999999999,\"Imaginary\":0.0,\"Magnitude\":0.4999999999999999,\"Phase\":0.0},\"7\":{\"Real\":0.4999999999999999,\"Imaginary\":0.0,\"Magnitude\":0.4999999999999999,\"Phase\":0.0},\"63\":{\"Real\":0.4999999999999999,\"Imaginary\":0.0,\"Magnitude\":0.4999999999999999,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"24.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-962333fd-1de6-41c2-bfc9-ebe3364baac1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 24.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-962333fd-1de6-41c2-bfc9-ebe3364baac1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000111\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"24.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9fdd4f55-e7e3-4387-b4ab-94a97e5b1cbc\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 24.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9fdd4f55-e7e3-4387-b4ab-94a97e5b1cbc\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"24.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f2340d62-7002-4af4-8dc7-ff3898ad5b95\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 24.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f2340d62-7002-4af4-8dc7-ff3898ad5b95\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111111\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"24.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2ff2de4a-6c2a-4197-8896-1adbe73dbc21\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 24.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2ff2de4a-6c2a-4197-8896-1adbe73dbc21\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000000⟩\t0.4999999999999999 + 0𝑖\n",
       "|000111⟩\t0.4999999999999999 + 0𝑖\n",
       "|111000⟩\t0.4999999999999999 + 0𝑖\n",
       "|111111⟩\t0.4999999999999999 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collapse and show final state:\n",
      "[Zero,Zero,Zero,One,One,One]\n",
      "Cleaning up...\n",
      "Done\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate_sparse PrepareAndMeasureGhzState nQubits=6 nClusters=2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "uniform-lesson",
   "metadata": {},
   "source": [
    "From the histogram above you can see that the sparse simulator only stores non-zero amplitudes, as opposed to the full state simulator (although the visualization functionality allows truncating out amplitudes that are close to zero when printing from the full state simulator as well).\n",
    "\n",
    "By increasing the `nQubits` parameter you can see that the sparse simulator still provides the result quickly enough, even for qubit registers large enough that the full state simulator slows down.\n",
    "\n",
    "You can increase the number of qubits up to 1,024. That is the current hardcoded limit in the sparse simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "155c1b84",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Allocating 1024 qubits...\n",
      "Finished allocating!\n",
      "Creating 8 clusters of GHZ states between 128 qubits...\n",
      "Finished GHZ clusters!\n",
      "Collapse and show final state:\n",
      "[One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,One,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero,Zero]\n",
      "Cleaning up...\n",
      "Done\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate_sparse PrepareAndMeasureGhzState nQubits=1024 nClusters=8"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ignored-sapphire",
   "metadata": {},
   "source": [
    "Now you see that the sparse simulator enables users to explore larger applications than what can be represented using full state simulator alone."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "downtown-member",
   "metadata": {},
   "source": [
    "## See Also\n",
    "* [Quantum simulators](https://docs.microsoft.com/azure/quantum/user-guide/machines/)\n",
    "* [Q# API reference](https://docs.microsoft.com/qsharp/api/qsharp/)"
   ]
  }
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