qiskit squeezing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c4c8d6ad-628b-4444-97d8-b05a25df4e0e",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Phase estimation with CSS and SSS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "e5d2135e-d424-4dde-bf85-af8853912ef7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Importing standard Qiskit libraries\n",
    "from qiskit import *\n",
    "from qiskit.circuit.library import U1Gate, UnitaryGate, ZGate, XGate, HamiltonianGate\n",
    "from qiskit.quantum_info import Operator\n",
    "from qiskit.visualization import *\n",
    "from qiskit_aer import AerSimulator\n",
    "from qiskit.circuit.library import RealAmplitudes\n",
    "from qiskit.circuit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "from qiskit_ibm_runtime import * #Session, SamplerV2 as Sampler, QiskitRuntimeService, Result\n",
    "\n",
    "\n",
    " \n",
    "#service = QiskitRuntimeService()\n",
    "\n",
    "import qiskit.quantum_info as qi\n",
    "from math import pi,log2,sqrt\n",
    "\n",
    "\n",
    "# qiskit-ibmq-provider has been deprecated.\n",
    "# Please see the Migration Guides in https://ibm.biz/provider_migration_guide for more detail.\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator, Options\n",
    "\n",
    "# Loading your IBM Quantum account(s)\n",
    "service = QiskitRuntimeService(channel=\"local\")\n",
    "#service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"7daa54d02c4d0c593133ac851113fff5fa4b901a45e6965578ce9f2a2349ceba0a55c163216402411d45caffa06ca9b1460b93e648c32eb26bc76b0580d358ef\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "8df8c1db-a899-4f1c-a840-38926e9b8f3c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import expm\n",
    "from statistics import variance\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "import qutip as qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "b213569b-893d-4b24-93b5-3a28c6ea95ef",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "N=4\n",
    "#Pauli matrices\n",
    "sx = qt.sigmax()\n",
    "sy = qt.sigmay()\n",
    "sz = qt.sigmaz()\n",
    "id2 = qt.qeye(2)\n",
    "#Total spin operators in the three axes\n",
    "Sx = qt.tensor([sx,id2,id2,id2])+qt.tensor([id2,sx,id2,id2])+qt.tensor([id2,id2,sx,id2])+qt.tensor([id2,id2,id2,sx])\n",
    "Sy = qt.tensor([sy,id2,id2,id2])+qt.tensor([id2,sy,id2,id2])+qt.tensor([id2,id2,sy,id2])+qt.tensor([id2,id2,id2,sy])\n",
    "Sz = qt.tensor([sz,id2,id2,id2])+qt.tensor([id2,sz,id2,id2])+qt.tensor([id2,id2,sz,id2])+qt.tensor([id2,id2,id2,sz])\n",
    "#We don't use this, it would be for the squeezed state in Maa et al, but there are still some threads to look after \n",
    "ev = Sx.eigenstates() \n",
    "unitary = np.array([[ev[1][j][i][0] for i in range (0,16)] for j in range(0,16)])\n",
    "InitialSSS = UnitaryGate(unitary,label='SSSBasis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "deb443a7-5f18-44a3-b79a-1da243e02229",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sx and Sz in matrix and Qiskit operator form\n",
    "SxMat = np.array([[Sx[i][0][j] for j in range(0,16)] for i in range(0,16)])\n",
    "SxOp = Operator(SxMat)\n",
    "SzMat = np.array([[Sz[i][0][j] for j in range(0,16)] for i in range(0,16)])\n",
    "SzOp = Operator(SzMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "ad08b665-cdbc-4219-9c64-7d6c7518fc2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Qiskit allows for total spin operators by using this syntax. We won't use this\n",
    "op = qi.SparsePauliOp('XIII')+qi.SparsePauliOp('IXII')+qi.SparsePauliOp('IIXI')+qi.SparsePauliOp('IIIX')\n",
    "#print(op.to_matrix())\n",
    "#print(Sx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c2cece9-db61-4c2f-8a21-ea54193346af",
   "metadata": {
    "tags": []
   },
   "source": [
    "# CSS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d42af736-04a5-4b8b-9dc9-13e83796a004",
   "metadata": {},
   "source": [
    "We start just generating a coherent state in the $z$-axis direction, $|1\\rangle ^{\\otimes N}$, and measure the total $S_x$ spin, which is equivalent to measure all the individual qubit spins in the $x$ direction and add them (we will do the sum after running the circuit).\n",
    "\n",
    "To measure the spin of individual qubits in each direction, we follow ```https://docs.quantum.ibm.com/guides/specify-observables-pauli```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "3a26cfcc-0c9f-4d51-9006-856eac031274",
   "metadata": {},
   "outputs": [],
   "source": [
    "PMx = QuantumCircuit(N) #Phase Measure\n",
    "for i in range(0,N):\n",
    "    PMx.x(i) #CSS = |1> ^\\tensor n\n",
    "    PMx.h(i) #measure Sx\n",
    "PMx.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "b5846617-bc07-41e1-8a13-1507cb27c964",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 747.609x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PMx.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e62065fe-b452-4787-b2f4-d7b3dd29ebea",
   "metadata": {},
   "source": [
    "# SSS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76364512-f5d2-4e51-9c71-b7e3a1159259",
   "metadata": {},
   "source": [
    "Now we generate the squeezed spin state of Kitagawa and Ueda (one-axis twisting ot OAT).\n",
    "We do the squeezing in the $x$ direction, from the coherent state pointing along the $z$ axis.\n",
    "But, to assure that the minimal and maximal variance occur when measuring $S_x$ and $S_y$, we\n",
    "rotate the operator in the squeezing Hamiltonian by the twisting angle $-\\delta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "4210bdb7-ed98-494c-972a-77319026012d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#From Kitagawa and Ueda, page 5140\n",
    "mu = (24)**(1/6)*(N/2)**(-2/3)\n",
    "A = 1-np.cos(mu)**(N-2)\n",
    "B = 4*np.sin(mu/2)*np.cos(mu/2)**(N-2)\n",
    "delta = (1/2)*np.arctan(B/A)\n",
    "  \n",
    "squeezing_strength = mu/2\n",
    "\n",
    "#rotate Sx by -delta before using it as operator inside the squeezing Hamiltonian\n",
    "rot_spin_oper = (expm(1j * delta  *SzMat) @ SxMat @ expm(-1j * delta  *SzMat))\n",
    "\n",
    "# The operator introducing the squeezing when applied to a coherent state, written as a Hamiltonian evolution\n",
    "sqz_op = HamiltonianGate( squeezing_strength * (rot_spin_oper @ rot_spin_oper), 1.0, label=\"Squeeze\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "a9fa49ba-ab12-48bc-a824-0496b37f745e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we measure Sx in every qubit of the squeezed spin state, obtained by\n",
    "# applying the squeezing operator to the CSS |1> ^{tensor N)\n",
    "SPMx = QuantumCircuit(4) #Squeezed Phase Measure\n",
    "for i in range(0,4):\n",
    "    SPMx.x(i) #CSS = |1> ^\\tensor n\n",
    "SPMx.append(sqz_op,[0,1,2,3]) #squeezing\n",
    "for i in range(0,4):\n",
    "    SPMx.h(i) #to measure Sx\n",
    "SPMx.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "a7e29c41-6fcd-4ba6-9191-f8515bb0061f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 914.831x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SPMx.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "714b2b31-afc4-4b75-bb59-bc927d501dfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We relicate the same circuit, but now we measure Sy in every qubit.\n",
    "\n",
    "SPMy = QuantumCircuit(4) #Squeezed Phase Measure\n",
    "for i in range(0,4):\n",
    "    SPMy.x(i) #CSS = |1> ^\\tensor n\n",
    "SPMy.append(sqz_op,[0,1,2,3])\n",
    "for i in range(0,4):\n",
    "    SPMy.sdg(i) #to measure Sy\n",
    "    SPMy.h(i) #to measure Sy\n",
    "SPMy.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "8c8a20fc-4036-4568-b470-396571f1de61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 998.442x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SPMy.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebafe4fa-cb69-43af-a886-e9af60349926",
   "metadata": {},
   "source": [
    "## Running the circuit\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7c02169-0054-482f-b25d-e449e22832ac",
   "metadata": {},
   "source": [
    "Let us get a histogram of the circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "2eab433c-9781-4f5c-a07b-0261c7f7a5ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'1100': 4167, '0011': 4164, '1001': 4115, '0001': 4156, '1111': 3983, '0110': 4203, '0101': 4004, '0111': 4110, '1000': 4151, '1101': 4046, '1010': 3991, '0100': 4114, '1110': 3999, '0000': 4168, '0010': 4113, '1011': 4052}\n",
      "{-2: 4168, -1: 16534, 0: 24644, 1: 16253, 2: 3983}\n",
      "0.9969876728914983\n"
     ]
    }
   ],
   "source": [
    "# CSS\n",
    "aer_sim = AerSimulator()\n",
    "transpiled = transpile(PMx, aer_sim)\n",
    "result = aer_sim.run(transpiled, shots=65536, memory=True).result()\n",
    "data = result.get_memory()\n",
    "statistics = result.get_counts()\n",
    "output_list = []\n",
    "for res in data:\n",
    "    output_list.append(2-res.count(\"0\"))\n",
    "        \n",
    "output = {i:0 for i in [-2,-1,0,1,2]}\n",
    "if \"0000\" in statistics.keys():\n",
    "    output[-2] = statistics[\"0000\"]\n",
    "else:\n",
    "    output[-2] = 0\n",
    "output[-1] = statistics[\"0001\"]+statistics[\"0010\"]+statistics[\"0100\"]+statistics[\"1000\"]\n",
    "output[0] = statistics[\"0011\"]+statistics[\"0101\"]+statistics[\"0110\"]+statistics[\"1001\"]+statistics[\"1010\"]+statistics[\"1100\"]\n",
    "output[1] = statistics[\"1110\"]+statistics[\"1101\"]+statistics[\"1011\"]+statistics[\"0001\"]\n",
    "output[2] = statistics[\"1111\"]\n",
    "print(statistics)\n",
    "print(output)\n",
    "print(variance(output_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "cb72af87-605e-4e89-b4b1-a95e654c3792",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "5a56a93c-26cf-46cb-958c-29d0ee93e5e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{-2: 21057, -1: 450, 0: 22758, 1: 428, 2: 20850}\n",
      "2.571084237093237\n"
     ]
    }
   ],
   "source": [
    "#SSS, Sx spin (max variance)\n",
    "aer_sim2 = AerSimulator()\n",
    "transpiled2 = transpile(SPMx, aer_sim2)\n",
    "result = aer_sim2.run(transpiled2, shots=65536, memory=True).result()\n",
    "data = result.get_memory()\n",
    "statistics = result.get_counts()\n",
    "output_list = []\n",
    "for res in data:\n",
    "    output_list.append(2-res.count(\"0\"))\n",
    "        \n",
    "output = {i:0 for i in [-2,-1,0,1,2]}\n",
    "output[-2] = statistics[\"0000\"]\n",
    "output[-1] = statistics[\"0001\"]+statistics[\"0010\"]+statistics[\"0100\"]+statistics[\"1000\"]\n",
    "output[0] = statistics[\"0011\"]+statistics[\"0101\"]+statistics[\"0110\"]+statistics[\"1001\"]+statistics[\"1010\"]+statistics[\"1100\"]\n",
    "output[1] = statistics[\"1110\"]+statistics[\"1101\"]+statistics[\"1011\"]+statistics[\"0001\"]\n",
    "output[2] = statistics[\"1111\"]\n",
    "\n",
    "print(output)\n",
    "print(variance(output_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "a6cedee8-ad59-4f7a-8753-c15c725155f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAGhCAYAAACqMVpZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA+1ElEQVR4nO3de1xVVeL///c53ETlohgiKYrWR0Qt74qWeSFQmRpm7GJZmVl+ddBS+lhW5iUzyzJtuplJaqNMl2k0UyNJvIyK9yFL07FGxVK8hHK8ct2/P/yxPx4BlR148PB6Ph486qy9zt5r7cXxvFl7nX1shmEYAgAAQLnZXd0AAACA6xVBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALDI09UNcGdFRUU6dOiQ/Pz8ZLPZXN0cAABwFQzD0KlTpxQaGiq7/fJzTgSpSnTo0CE1atTI1c0AAAAWHDx4UA0bNrxsHYJUJfLz85N0YSD8/f1d3BoAAHA1HA6HGjVqZL6PXw5BqhIVX87z9/cnSAEAcJ25mmU5LDYHAACwiCAFoFqYOnWqOnbsKD8/PwUHBys+Pl579uwxt2dnZ2vkyJFq3ry5fH19FRYWpieffFI5OTlmnXnz5slms5X6c/ToUUnS6tWrS92elZVl7qewsFAvvviiwsPD5evrq2bNmmny5MkyDOPanRAAFYJLewCqhTVr1ighIUEdO3ZUQUGBnn/+ecXExGjXrl2qVauWDh06pEOHDumNN95QZGSkDhw4oGHDhunQoUP6xz/+IUm6//771adPH6f9Pvroozp//ryCg4Odyvfs2eN0Sf/i7a+99pref/99zZ8/Xy1bttTWrVs1ePBgBQQE6Mknn6zEswCgotkM/gSqNA6HQwEBAcrJyWGNFFDFHDt2TMHBwVqzZo26d+9eap3PP/9cDz30kM6cOSNPz5J/dx47dkw33nijkpKS9PDDD0u6MCPVs2dPnThxQoGBgaXu9w9/+IPq16+vpKQks6x///7y9fXVggULfn/nAPwu5Xn/5tIegGqp+JJd3bp1L1vH39+/1BAlSR9//LFq1qype+65p8S2Nm3aqEGDBrrzzju1fv16p21du3bVypUr9Z///EeS9N1332ndunXq27ev1e4AcBEu7QGodoqKijRq1Ch169ZNrVq1KrXO8ePHNXnyZA0dOrTM/SQlJenBBx+Ur6+vWdagQQPNmjVLHTp0UG5urubMmaMePXpo06ZNateunSRp7NixcjgcioiIkIeHhwoLCzVlyhQNHDiwYjsKoNIRpABUOwkJCfrhhx+0bt26Urc7HA7FxcUpMjJSEydOLLVOenq6fvzxR/3tb39zKm/evLmaN29uPu7atat+/vlnzZgxw6z72WefaeHChUpOTlbLli2VkZGhUaNGKTQ0VIMGDaqYTgK4JghSAKqVESNGaOnSpVq7dm2pdyw+deqU+vTpIz8/Py1atEheXl6l7mfOnDlq06aN2rdvf8VjdurUySm0jRkzRmPHjtWAAQMkSa1bt9aBAwc0depUghRwnalya6Su9BHlixmGob59+8pms2nx4sVO2zIzMxUXF6eaNWsqODhYY8aMUUFBgVOd1atXq127dvLx8dFNN92kefPmlTjGu+++qyZNmqhGjRrq3LmzNm/eXFFdBXANGYahESNGaNGiRUpLS1N4eHiJOg6HQzExMfL29taSJUtUo0aNUvd1+vRpffbZZxoyZMhVHTsjI0MNGjQwH589e7bE93d5eHioqKioHD0CUBVUuRmpK31E+WIzZ84s9a6jhYWFiouLU0hIiDZs2KDDhw/rkUcekZeXl1555RVJ0r59+xQXF6dhw4Zp4cKFWrlypR5//HE1aNBAsbGxkqRPP/1UiYmJmjVrljp37qyZM2cqNjZWe/bsKfFRZwBVW0JCgpKTk/Xll1/Kz8/PvK9TQECAfH19zRB19uxZLViwQA6HQw6HQ5J0ww03yMPDw9zXp59+qoKCAj300EMljjNz5kyFh4erZcuWOn/+vObMmaO0tDStWLHCrHPXXXdpypQpCgsLU8uWLfXvf/9bb775ph577LFKPgsAKpxRxR09etSQZKxZs8ap/N///rdx4403GocPHzYkGYsWLTK3LV++3LDb7UZWVpZZ9v777xv+/v5Gbm6uYRiG8cwzzxgtW7Z02uf9999vxMbGmo87depkJCQkmI8LCwuN0NBQY+rUqVfV9pycHEOSkZOTc9X9BVA5JJX6M3fuXMMwDGPVqlVl1tm3b5/TvqKioowHH3yw1OO89tprRrNmzYwaNWoYdevWNXr06GGkpaU51XE4HMZTTz1lhIWFGTVq1DCaNm1qvPDCC+a/TwBcqzzv31VuRupSpX1E+ezZs3rwwQf17rvvKiQkpMRz0tPT1bp1a9WvX98si42N1fDhw7Vz5061bdtW6enpio6OdnpebGysRo0aJUnKy8vTtm3b9Nxzz5nb7Xa7oqOjlZ6eXmpbc3NzlZubaz4u/ms2Pz9f+fn55j6KP6Vz8TR+cXlBQYHT3Y09PDxkt9vLLC/eb7Hij2lfehmzrHIvLy8VFRWpsLDQLLPZbPL09CyzvKy20yf6VJX7lJeXV2afioqK1KNHD+Xl5ZXZ9ov7W3w7g0vPgZeXl/73f/9Xo0ePvmyfatSooTfeeEMzZ84s0fbCwsJqPU70iT5VlT5drSodpMr6iPLo0aPVtWtX/fGPfyz1eVlZWU4hSpL5uHg6v6w6DodD586d04kTJ1RYWFhqnd27d5d63KlTp2rSpEklylesWKGaNWtKksLCwtS2bVvt2LFDmZmZZp3mzZsrIiJCmzdv1rFjx8zyNm3aqHHjxlq7dq1OnTpllkdFRSk4OFgrVqxwGvCePXvK19dXy5cvd2pDv379dO7cOa1atcos8/T0VFxcnI4fP+4UDv38/NSrVy8dPHhQGRkZZvkNN9ygrl27au/evU7r1ugTfaJP9Ik+0Sd36tOl9367nCp9Z/Phw4fr66+/1rp168xP1yxZskRPP/20/v3vf6t27dqSLiTRRYsWKT4+XpI0dOhQHThwQN988425r7Nnz6pWrVpavny5+vbtq//5n//R4MGDnWacli9frri4OJ09e1YnTpzQjTfeqA0bNigqKsqs88wzz2jNmjXatGlTifaWNiPVqFEjHT9+3LwzKomfPtEn+kSf6BN9qtp9ys7OVlBQ0FXd2bzKzkiV9RHltLQ0/fzzzyW+eqF///66/fbbtXr1aoWEhJT4dN2RI0ckybwUGBISYpZdXMff31++vr7y8PCQh4dHqXVKu5woST4+PvLx8SlR7uXlVeIj1MX7v1RZd1Auq7ysj2aXp9xut5f4BNHlystqO32iT+Utp0/0SaJPZbWxvOX0qfL7VJoqd/sD4wofUR47dqx27NihjIwM80eSZsyYoblz50q6MK34/fffm9/GLkmpqany9/dXZGSkWWflypVO+05NTTVnn7y9vdW+fXunOkVFRVq5cqXTDBUAAKi+qtyM1JU+ohwSElLqjFBYWJgZumJiYhQZGamHH35Y06ZNU1ZWlsaNG6eEhARzxmjYsGF655139Mwzz+ixxx5TWlqaPvvsMy1btszcZ2JiogYNGqQOHTqoU6dOmjlzps6cOaPBgwdfgzMBAACqPOsfDqwcusJHlMt6zsW3PzAMw9i/f7/Rt29fw9fX16hXr57x9NNPG/n5+U51Vq1aZbRp08bw9vY2mjZtWuox3n77bSMsLMzw9vY2OnXqZGzcuPGq+8LtDwAAuP6U5/27Si82v945HA4FBARc1WI1AABQNZTn/bvKrZECAAC4XhCkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUm5k6tSp6tixo/z8/BQcHKz4+Hjt2bPHqc7s2bPVo0cP+fv7y2az6eTJkyX2k52drYEDB8rf31+BgYEaMmSITp8+bW7fv3+/bDZbiZ+NGzeadXr06FFqnbi4uErrPwAA1xpByo2sWbNGCQkJ2rhxo1JTU5Wfn6+YmBidOXPGrHP27Fn16dNHzz//fJn7GThwoHbu3KnU1FQtXbpUa9eu1dChQ0vU+/bbb3X48GHzp3379ua2f/7zn07bfvjhB3l4eOjee++t2E4DAOBCVe5Li2FdSkqK0+N58+YpODhY27ZtU/fu3SVJo0aNkiStXr261H38+OOPSklJ0ZYtW9ShQwdJ0ttvv61+/frpjTfeUGhoqFk3KCio1C+QlqS6des6Pf7kk09Us2ZNghQAwK0wI+XGcnJyJJUMNZeTnp6uwMBAM0RJUnR0tOx2uzZt2uRU9+6771ZwcLBuu+02LVmy5LL7TUpK0oABA1SrVq1y9AAAcK1czfKQ8+fPKyEhQUFBQapdu7b69++vI0eOONXZsmWLevfurcDAQNWpU0exsbH67rvvzO1XszxEkj7//HNFRESoRo0aat26tZYvX155nf8dmJFyU0VFRRo1apS6deumVq1aXfXzsrKyFBwc7FTm6empunXrKisrS5JUu3ZtTZ8+Xd26dZPdbtcXX3yh+Ph4LV68WHfffXeJfW7evFk//PCDkpKSfl+ngHJoMnaZq5tQIfa/yrpCXBvFy0M6duyogoICPf/884qJidGuXbvMP4JHjx6tZcuW6fPPP1dAQIBGjBihP//5z1q/fr0k6fTp0+rTp4/uvvtuvffeeyooKNCECRMUGxurgwcPysvLyzzet99+q5YtW5qPg4KCzP/fsGGDHnjgAU2dOlV/+MMflJycrPj4eG3fvr1c72nXAkHKTSUkJOiHH37QunXrKnzf9erVU2Jiovm4Y8eOOnTokF5//fVSg1RSUpJat26tTp06VXhbAAAV40rLQ3JycpSUlKTk5GT16tVLkjR37ly1aNFCGzduVJcuXbR7925lZ2frpZdeUqNGjSRJEyZM0C233KIDBw7opptuMvd/ueUhb731lvr06aMxY8ZIkiZPnqzU1FS98847mjVrVmV03zIu7bmhESNGaOnSpVq1apUaNmxYrueGhITo6NGjTmUFBQXKzs4u8xdekjp37qyffvqpRPmZM2f0ySefaMiQIeVqBwDAtS5dHrJt2zbl5+crOjrarBMREaGwsDClp6dLkpo3b66goCAlJSUpLy9P586dU1JSklq0aKEmTZo47f9yy0PS09OdjiNJsbGx5nGqEoKUGzEMQyNGjNCiRYuUlpam8PDwcu8jKipKJ0+e1LZt28yytLQ0FRUVqXPnzmU+LyMjQw0aNChR/vnnnys3N1cPPfRQudsCAHCN0paHZGVlydvbW4GBgU5169evby798PPz0+rVq7VgwQL5+vqqdu3aSklJ0ddffy1PzwsXwYqXh3z++edatmyZbrvtNsXHxzuFqaysLNWvX7/M41QlXNpzIwkJCUpOTtaXX34pPz8/8xcuICBAvr6+ki78cmZlZZmzR99//738/PwUFhamunXrqkWLFurTp4+eeOIJzZo1S/n5+RoxYoQGDBhgfmJv/vz58vb2Vtu2bSVduNXBRx99pDlz5pRoU1JSkuLj452ufQMAqjary0POnTunIUOGqFu3bvr73/+uwsJCvfHGG4qLi9OWLVvk6+tb7uUhVR1Byo28//77ki7cDPNic+fO1aOPPipJmjVrliZNmmRuK74twsV1Fi5cqBEjRqh3796y2+3q37+//vrXvzrtc/LkyTpw4IA8PT0VERGhTz/9VPfcc49TnT179mjdunVasWJFBfYSAFCZipeHrF271ml5SEhIiPLy8nTy5EmnWakjR46YSz+Sk5O1f/9+paeny263m2V16tTRl19+qQEDBpR6zM6dOys1NdXpWJd+GvDi41QlBCk3YhjGFetMnDhREydOvGydunXrKjk5ucztgwYN0qBBg654rObNm19VmwAArmcYhkaOHKlFixZp9erVJZaHtG/fXl5eXlq5cqX69+8v6cIfzJmZmYqKipJ04abPdrtdNpvNfF7x46KiojKPfenykKioKK1cudK896EkpaammsepSghSAADgistDAgICNGTIECUmJqpu3bry9/fXyJEjFRUVpS5dukiS7rzzTo0ZM0YJCQkaOXKkioqK9Oqrr8rT01M9e/aUdHXLQ5566indcccdmj59uuLi4vTJJ59o69atmj179jU+K1dGkAIAAFe1PGTGjBnmko/c3FzFxsbqvffeM+tGREToq6++0qRJkxQVFSW73a62bdsqJSXFacbpSstDunbtquTkZI0bN07PP/+8br75Zi1evLjK3UNKkmwG114qjcPhUEBAgHJycuTv7+/q5gDVCjfkBGBVed6/uf0BAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGCRp6sbAOuajF3m6iZUiP2vxrm6CQAAWMKMFAAAgEUEKQAAAIu4tAcAQDXE8pCKwYwUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACyqckFq7dq1uuuuuxQaGiqbzabFixc7bT99+rRGjBihhg0bytfXV5GRkZo1a5ZTnfPnzyshIUFBQUGqXbu2+vfvryNHjjjVyczMVFxcnGrWrKng4GCNGTNGBQUFTnVWr16tdu3aycfHRzfddJPmzZtXGV0GAADXqSoXpM6cOaNbb71V7777bqnbExMTlZKSogULFujHH3/UqFGjNGLECC1ZssSsM3r0aH311Vf6/PPPtWbNGh06dEh//vOfze2FhYWKi4tTXl6eNmzYoPnz52vevHkaP368WWffvn2Ki4tTz549lZGRoVGjRunxxx/XN998U3mdBwAA1xVPVzfgUn379lXfvn3L3L5hwwYNGjRIPXr0kCQNHTpUH3zwgTZv3qy7775bOTk5SkpKUnJysnr16iVJmjt3rlq0aKGNGzeqS5cuWrFihXbt2qVvv/1W9evXV5s2bTR58mQ9++yzmjhxory9vTVr1iyFh4dr+vTpkqQWLVpo3bp1mjFjhmJjYyv9PAAAgKqvys1IXUnXrl21ZMkS/frrrzIMQ6tWrdJ//vMfxcTESJK2bdum/Px8RUdHm8+JiIhQWFiY0tPTJUnp6elq3bq16tevb9aJjY2Vw+HQzp07zToX76O4TvE+AAAAqtyM1JW8/fbbGjp0qBo2bChPT0/Z7XZ9+OGH6t69uyQpKytL3t7eCgwMdHpe/fr1lZWVZda5OEQVby/edrk6DodD586dk6+vb4m25ebmKjc313zscDgkSfn5+crPz5ck2e12eXh4qLCwUEVFRWbd4vKCggIZhmGWe3h4yG63l1ruLorPTXFfix8X8/S88Gt66Rq2ssq9vLxUVFSkwsJCs8xms8nT07PM8rLGoyLGiT65pk/u4tJ/O9xtnOiT6/rkLvLz8ytlnK7WdXcm3377bW3cuFFLlixR48aNtXbtWiUkJCg0NLTEDNK1NnXqVE2aNKlE+YoVK1SzZk1JUlhYmNq2basdO3YoMzPTrNO8eXNFRERo8+bNOnbsmFnepk0bs5+nTp0yy6OioiqxJ9fW8uXLJV3oU3BwsFasWOH0S9yzZ0/5+vqa9Yr169dP586d06pVq8wyT09PxcXF6fjx406zh35+furVq5cOHjyojIwMs/yGG25Q165dtXfvXu3Zs8csr8hxok+u6ZO7KD6f7jpO9Ml1fXIXy5cvr/BxWr9+/VUf32ZcHMWqGJvNpkWLFik+Pl6SdO7cOQUEBGjRokWKi4sz6z3++OP65ZdflJKSorS0NPXu3VsnTpxwmpVq3LixRo0apdGjR2v8+PFasmSJ0y/Wvn371LRpU23fvl1t27ZV9+7d1a5dO82cOdOsM3fuXI0aNUo5OTmltre0GalGjRrp+PHj8vf3l1Sxf8U0ff7rcp3Pqmrv5AuXZflrkz5VZJ+avZAid1D8+nDXcaJPrutTk7HL5A72To6p8HHKzs5WUFCQcnJyzPfvslxXM1LFl8gunbb38PAwT1D79u3l5eWllStXqn///pKkPXv2KDMz05zFiYqK0pQpU3T06FEFBwdLklJTU+Xv76/IyEizzqV/CaSmpl52JsjHx0c+Pj4lyr28vOTl5VWizaVdnitrutWdpmEvdem5ufSxlXK73V7q5Z2yyssaj4oaJ/rkmj65g0vPmzuOE31yTZ/cxcXnorLHqdS6V13zGjl9+rR++ukn8/G+ffuUkZGhunXrKiwsTHfccYfGjBkjX19fNW7cWGvWrNHHH3+sN998U5IUEBCgIUOGKDExUXXr1pW/v79GjhypqKgodenSRZIUExOjyMhIPfzww5o2bZqysrI0btw4JSQkmEFo2LBheuedd/TMM8/oscceU1pamj777DMtW+YeCR4AAPx+VS5Ibd26VT179jQfJyYmSpIGDRqkefPm6ZNPPtFzzz2ngQMHKjs7W40bN9aUKVM0bNgw8zkzZsyQ3W5X//79lZubq9jYWL333nvmdg8PDy1dulTDhw9XVFSUatWqpUGDBumll14y64SHh2vZsmUaPXq03nrrLTVs2FBz5szh1gcAAMBUpddIXe8cDocCAgKu6hqrFe5yfXv/q3FXrgSUE68P4PJ4jZStPO/f7nvRFAAAoJIRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABZZDlJr165VZmbmZescPHhQa9eutXoIAACAKs1ykOrZs6fmzZt32Toff/yxevbsafUQAAAAVZrlIGUYxhXrFBUVyWazWT0EAABAlVapa6T27t2rgICAyjwEAACAy3iWp/Jjjz3m9Hjx4sXav39/iXqFhYXm+qi+ffv+rgYCAABUVeUKUhevibLZbMrIyFBGRkapdW02mzp27KgZM2b8nvYBAABUWeUKUvv27ZN0YX1U06ZNNWrUKD311FMl6nl4eKhOnTqqVatWxbQSAACgCipXkGrcuLH5/3PnzlXbtm2dygAAAKqTcgWpiw0aNKgi2wEAAHDdsRykim3evFlbtmzRyZMnVVhYWGK7zWbTiy+++HsPAwAAUOVYDlLZ2dmKj4/X+vXrL3tPKYIUAABwV5aDVGJiotatW6cePXpo0KBBatiwoTw9f/cEFwAAwHXDcvJZunSpOnXqpJUrV3L3cgAAUC1ZvrP5uXPn1L17d0IUAACotiwHqTZt2pR6V3MAAIDqwnKQmjBhgpYsWaKNGzdWZHsAAACuG5bXSGVlZSkuLk533HGHBg4cqHbt2snf37/Uuo888ojlBgIAAFRVloPUo48+KpvNJsMwNG/ePM2bN6/EeinDMGSz2QhSAADALVkOUnPnzq3IdgAAAFx3+IoYAAAAiywvNgcAAKjuLM9IZWZmXnXdsLAwq4cBAACosiwHqSZNmlzVzThtNpsKCgqsHgYAAKDKshykHnnkkVKDVE5Ojr777jvt27dPd9xxh5o0afJ72gcAAFBlWQ5S8+bNK3ObYRiaPn26pk2bpqSkJKuHAAAAqNIqZbG5zWbT//7v/6ply5YaM2ZMZRwCAADA5Sr1U3sdOnRQWlpaZR4CAADAZSo1SP38888sNAcAAG7L8hqpshQVFenXX3/VvHnz9OWXX6p3794VfQgAAIAqwfKMlN1ul4eHR4kfLy8vNWnSRBMmTFBgYKCmT59erv2uXbtWd911l0JDQ2Wz2bR48WJzW35+vp599lm1bt1atWrVUmhoqB555BEdOnTIaR/Z2dkaOHCg/P39FRgYqCFDhuj06dNOdXbs2KHbb79dNWrUUKNGjTRt2rQSbfn8888VERGhGjVqqHXr1lq+fHm5+gIAANyb5Rmp7t27l3r7A7vdrjp16qhjx44aPHiwgoODy7XfM2fO6NZbb9Vjjz2mP//5z07bzp49q+3bt+vFF1/UrbfeqhMnTuipp57S3Xffra1bt5r1Bg4cqMOHDys1NVX5+fkaPHiwhg4dquTkZEmSw+FQTEyMoqOjNWvWLH3//fd67LHHFBgYqKFDh0qSNmzYoAceeEBTp07VH/7wByUnJys+Pl7bt29Xq1atynu6AACAG7IZhmG4uhFlsdlsWrRokeLj48uss2XLFnXq1EkHDhxQWFiYfvzxR0VGRmrLli3q0KGDJCklJUX9+vXTL7/8otDQUL3//vt64YUXlJWVJW9vb0nS2LFjtXjxYu3evVuSdP/99+vMmTNaunSpeawuXbqoTZs2mjVr1lW13+FwKCAgQDk5OfL397d4FsrWZOyyCt+nK+x/Nc7VTYAb4vUBXB6vkbKV5/27wtdIXWs5OTmy2WwKDAyUJKWnpyswMNAMUZIUHR0tu92uTZs26U9/+pPS09PVvXt3M0RJUmxsrF577TWdOHFCderUUXp6uhITE52OFRsb63Sp8VK5ubnKzc01HzscDkkXLknm5+dL+r9LooWFhSoqKjLrFpcXFBTo4mzr4eEhu91earm7KD43xX0tflzM0/PCr+mlH1woq9zLy0tFRUUqLCw0y2w2mzw9PcssL2s8KmKc6JNr+uQuLv23w93GiT65rk/uIj8/v1LG6WpVyJlcv369MjIy5HA45O/vrzZt2qhbt24VsevLOn/+vJ599lk98MADZmLMysoqcTnR09NTdevWVVZWllknPDzcqU79+vXNbXXq1FFWVpZZdnGd4n2UZurUqZo0aVKJ8hUrVqhmzZqSLnzvYNu2bbVjxw6n7yts3ry5IiIitHnzZh07dswsb9OmjRo3bqy1a9fq1KlTZnlUVFTZJ+Y6U7z2LCoqSsHBwVqxYoXTL3HPnj3l6+tbYo1av379dO7cOa1atcos8/T0VFxcnI4fP6709HSz3M/PT7169dLBgweVkZFhlt9www3q2rWr9u7dqz179pjlFTlO9Mk1fXIXxefTXceJPrmuT+5i+fLlFT5O69evv+rj/65Lexs2bNDgwYP1008/SbpwR/PidVM333yz5s6d+7ve8C93aS8/P1/9+/fXL7/8otWrV5tB6pVXXtH8+fOdTqQkBQcHa9KkSRo+fLhiYmIUHh6uDz74wNy+a9cutWzZUrt27VKLFi3k7e2t+fPn64EHHjDrvPfee5o0aZKOHDlSantLm5Fq1KiRjh8/bravIv+Kafr811dzGqu8vZNjJPHXJn2q2D41eyFF7qD49eGu40SfXNcnd7m0t3dyTIWPU3Z2toKCgir30t7OnTsVExOjs2fP6s4771TPnj3VoEEDZWVladWqVVqxYoViY2O1ceNGRUZGWj1MqfLz83XffffpwIEDSktLc+pkSEiIjh496lS/oKBA2dnZCgkJMetcGoaKH1+pTvH20vj4+MjHx6dEuZeXl7y8vJzKij/leKmyplvdaRr2Upeem0sfWym32+2lXt4pq7ys8aiocaJPrumTO7j0vLnjONEn1/TJXVx8Lip7nEpj+cy+9NJLysvL0/Lly/XNN99o7NixGjRokJ599lmlpKRo+fLlOn/+vF566SWrhyhVcYjau3evvv32WwUFBTltj4qK0smTJ7Vt2zazLC0tTUVFRercubNZZ+3atU5/AaSmpqp58+aqU6eOWWflypVO+05NTXWrS2oAAOD3sRykVq9erXvuuUd9+vQpdXufPn10zz33OF3HvRqnT59WRkaGeT133759ysjIUGZmpvLz83XPPfdo69atWrhwoQoLC5WVlaWsrCzl5eVJklq0aKE+ffroiSee0ObNm7V+/XqNGDFCAwYMUGhoqCTpwQcflLe3t4YMGaKdO3fq008/1VtvveW0uPypp55SSkqKpk+frt27d2vixInaunWrRowYYeFsAQAAd2Q5SOXk5JRYsH2p8PBw5eTklGu/W7duVdu2bdW2bVtJUmJiotq2bavx48fr119/1ZIlS/TLL7+oTZs2atCggfmzYcMGcx8LFy5URESEevfurX79+um2227T7Nmzze0BAQFasWKF9u3bp/bt2+vpp5/W+PHjzXtISVLXrl2VnJys2bNn69Zbb9U//vEPLV68mHtIAQAAk+WFN6Ghodq4ceNl62zatMmcBbpaPXr00OXWv1/N2vi6deuaN98syy233KJ//etfl61z77336t57773i8QAAQPVkeUbq7rvv1urVq/Xiiy/q/PnzTtvOnz+vCRMmaNWqVfrjH//4uxsJAABQFVmekXrxxRe1dOlSvfLKK/rggw/UqVMn1a9fX0eOHNGWLVt07NgxNW3aVC+++GJFthcAAKDKsBykgoKCtHHjRj3zzDP65JNPnG4aVqNGDQ0ePFivvfaa6tatWyENBQAAqGp+182J6tWrp48++kgffPCBdu/ebd7ZPCIiosx7XwAAALiLcgepKVOm6MyZM5o0aZIZlry8vNS6dWuzTl5enl544QX5+flp7NixFddaAACAKqRci82//fZbjR8/XkFBQZedcfL29lZQUJBeeOGFct9HCgAA4HpRriD18ccfq06dOld1U8qEhATVrVtXc+fOtdw4AACAqqxcQWrDhg2Kjo4u9fvkLuXj46Po6OhyfYMyAADA9aRcQerQoUNq2rTpVdcPDw/X4cOHy90oAACA60G5gpTdbnf6ot8ryc/Pd+tvnAYAANVbuVJOaGiofvjhh6uu/8MPP+jGG28sd6MAAACuB+UKUrfffrvS0tK0f//+K9bdv3+/0tLS1L17d6ttAwAAqNLKFaQSEhKUn5+ve+65R8ePHy+z3m+//aZ7771XBQUFGj58+O9uJAAAQFVUrhtytmvXTqNGjdLMmTMVGRmpYcOGqWfPnmrYsKEk6ddff9XKlSs1e/ZsHTt2TImJiWrXrl2lNBwAAMDVyn1n8+nTp6tGjRp6/fXXNWXKFE2ZMsVpu2EY8vDw0HPPPaeXX365whoKAABQ1ZQ7SNlsNr3yyisaMmSI5s6dqw0bNigrK0uSFBISom7duunRRx9Vs2bNKryxAAAAVYnlLy1u1qwZM04AAKBa4yZPAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGDRdRmkfv31Vz300EMKCgqSr6+vWrdura1bt5rbDcPQ+PHj1aBBA/n6+io6Olp79+512kd2drYGDhwof39/BQYGasiQITp9+rRTnR07duj2229XjRo11KhRI02bNu2a9A8AAFwfrrsgdeLECXXr1k1eXl76+uuvtWvXLk2fPl116tQx60ybNk1//etfNWvWLG3atEm1atVSbGyszp8/b9YZOHCgdu7cqdTUVC1dulRr167V0KFDze0Oh0MxMTFq3Lixtm3bptdff10TJ07U7Nmzr2l/AQBA1eXp6gaU12uvvaZGjRpp7ty5Zll4eLj5/4ZhaObMmRo3bpz++Mc/SpI+/vhj1a9fX4sXL9aAAQP0448/KiUlRVu2bFGHDh0kSW+//bb69eunN954Q6GhoVq4cKHy8vL00UcfydvbWy1btlRGRobefPNNp8AFAACqr+suSC1ZskSxsbG69957tWbNGt144436y1/+oieeeEKStG/fPmVlZSk6Otp8TkBAgDp37qz09HQNGDBA6enpCgwMNEOUJEVHR8tut2vTpk3605/+pPT0dHXv3l3e3t5mndjYWL322ms6ceKE0wxYsdzcXOXm5pqPHQ6HJCk/P1/5+fmSJLvdLg8PDxUWFqqoqMisW1xeUFAgwzDMcg8PD9nt9lLL3UXxuSnua/HjYp6eF35NCwoKrqrcy8tLRUVFKiwsNMtsNps8PT3LLC9rPCpinOiTa/rkLi79t8Pdxok+ua5P7iI/P79SxulqXXdn8r///a/ef/99JSYm6vnnn9eWLVv05JNPytvbW4MGDVJWVpYkqX79+k7Pq1+/vrktKytLwcHBTts9PT1Vt25dpzoXz3RdvM+srKxSg9TUqVM1adKkEuUrVqxQzZo1JUlhYWFq27atduzYoczMTLNO8+bNFRERoc2bN+vYsWNmeZs2bdS4cWOtXbtWp06dMsujoqKucKauH8uXL5d0oU/BwcFasWKF0y9xz5495evra9Yr1q9fP507d06rVq0yyzw9PRUXF6fjx48rPT3dLPfz81OvXr108OBBZWRkmOU33HCDunbtqr1792rPnj1meUWOE31yTZ/cRfH5dNdxok+u65O7WL58eYWP0/r166/6+Dbj4ih2HfD29laHDh20YcMGs+zJJ5/Uli1blJ6erg0bNqhbt246dOiQGjRoYNa57777ZLPZ9Omnn+qVV17R/PnznU62JAUHB2vSpEkaPny4YmJiFB4erg8++MDcvmvXLrVs2VK7du1SixYtSrSttBmpRo0a6fjx4/L395dUsX/FNH3+ayunsMrZOzlGEn9t0qeK7VOzF1LkDopfH+46TvTJdX1qMnaZ3MHeyTEVPk7Z2dkKCgpSTk6O+f5dlutuRqpBgwaKjIx0KmvRooW++OILSVJISIgk6ciRI05B6siRI2rTpo1Z5+jRo077KCgoUHZ2tvn8kJAQHTlyxKlO8ePiOpfy8fGRj49PiXIvLy95eXk5lXl4eJR6ea6s6VZ3moa91KXn5tLHVsrtdnupl3fKKi9rPCpqnOiTa/rkDi49b+44TvTJNX1yFxefi8oep9Jcd2e2W7duJWaS/vOf/6hx48aSLiw8DwkJ0cqVK83tDodDmzZtMi+HRUVF6eTJk9q2bZtZJy0tTUVFRercubNZZ+3atU5/JaSmpqp58+alXtYDAADVz3UXpEaPHq2NGzfqlVde0U8//aTk5GTNnj1bCQkJki5MWY4aNUovv/yylixZou+//16PPPKIQkNDFR8fL+nCDFafPn30xBNPaPPmzVq/fr1GjBihAQMGKDQ0VJL04IMPytvbW0OGDNHOnTv16aef6q233lJiYqKrug4AAKqY6+56UceOHbVo0SI999xzeumllxQeHq6ZM2dq4MCBZp1nnnlGZ86c0dChQ3Xy5EnddtttSklJUY0aNcw6Cxcu1IgRI9S7d2/Z7Xb1799ff/3rX83tAQEBWrFihRISEtS+fXvVq1dP48eP59YHAADAdN0tNr+eOBwOBQQEXNViNSvcZaHg/lfjXN0EuCFeH8Dl8RopW3nev6+7S3sAAABVBUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAFVyKuvviqbzaZRo0aZZT169JDNZnP6GTZsmNPzMjMzFRcXp5o1ayo4OFhjxoxRQUHBNW49ULkufX1kZ2dr5MiRat68uXx9fRUWFqYnn3xSOTk5Ts/bsmWLevfurcDAQNWpU0exsbH67rvvXNADuCOCFFBFbNmyRR988IFuueWWEtueeOIJHT582PyZNm2aua2wsFBxcXHKy8vThg0bNH/+fM2bN0/jx4+/ls0HKlVpr49Dhw7p0KFDeuONN/TDDz9o3rx5SklJ0ZAhQ8w6p0+fVp8+fRQWFqZNmzZp3bp18vPzU2xsrPLz813RFbgZghRQBZw+fVoDBw7Uhx9+qDp16pTYXrNmTYWEhJg//v7+5rYVK1Zo165dWrBggdq0aaO+fftq8uTJevfdd5WXl3ctuwFUirJeH61atdIXX3yhu+66S82aNVOvXr00ZcoUffXVV+aM7O7du5Wdna2XXnpJzZs3V8uWLTVhwgQdOXJEBw4ccFWX4EYIUkAVkJCQoLi4OEVHR5e6feHChapXr55atWql5557TmfPnjW3paenq3Xr1qpfv75ZFhsbK4fDoZ07d1Z624HKdqXXx8VycnLk7+8vT09PSVLz5s0VFBSkpKQk5eXl6dy5c0pKSlKLFi3UpEmTSm45qgNPVzcAqO4++eQTbd++XVu2bCl1+4MPPqjGjRsrNDRUO3bs0LPPPqs9e/bon//8pyQpKyvLKURJMh9nZWVVbuOBSnal18fFjh8/rsmTJ2vo0KFmmZ+fn1avXq34+HhNnjxZknTzzTfrm2++McMW8HvwWwS40MGDB/XUU08pNTVVNWrUKLXOxW8KrVu3VoMGDdS7d2/9/PPPatas2bVqKnDNXc3ro5jD4VBcXJwiIyM1ceJEs/zcuXMaMmSIunXrpr///e8qLCzUG2+8obi4OG3ZskW+vr6V3Au4O4IU4ELbtm3T0aNH1a5dO7OssLBQa9eu1TvvvKPc3Fx5eHg4Padz586SpJ9++knNmjVTSEiINm/e7FTnyJEjkqSQkJBK7gFQea729XHq1Cn16dNHfn5+WrRokby8vMz6ycnJ2r9/v9LT02W3282yOnXq6Msvv9SAAQOueb/gXghSgAv17t1b33//vVPZ4MGDFRERoWeffbZEiJKkjIwMSVKDBg0kSVFRUZoyZYqOHj2q4OBgSVJqaqr8/f0VGRlZuR0AKtHVvD4cDodiY2Pl4+OjJUuWlJi5Onv2rOx2u2w2m1lW/LioqOia9APujSAFuJCfn59atWrlVFarVi0FBQWpVatW+vnnn5WcnKx+/fopKChIO3bs0OjRo9W9e3fzY+AxMTGKjIzUww8/rGnTpikrK0vjxo1TQkKCfHx8XNEtoEJc6fXhcDgUExOjs2fPasGCBXI4HHI4HJKkG264QR4eHrrzzjs1ZswYJSQkaOTIkSoqKtKrr74qT09P9ezZ0xXdgpshSAFVmLe3t7799lvNnDlTZ86cUaNGjdS/f3+NGzfOrOPh4aGlS5dq+PDhioqKUq1atTRo0CC99NJLLmw5UPm2b9+uTZs2SZJuuukmp2379u1TkyZNFBERoa+++kqTJk1SVFSU7Ha72rZtq5SUFHNWF/g9CFJAFbN69Wrz/xs1aqQ1a9Zc8TmNGzfW8uXLK7FVQNVw8eujR48eMgzjis+58847deedd1Ziq1CdcR8pAAAAiwhSAAAAFnFpD6ggTcYuc3UTKsT+V+Nc3QS4IXd5fUi8RuCMGSkAAACLCFJX4d1331WTJk1Uo0YNde7cucTNDwEAQPVEkLqCTz/9VImJiZowYYK2b9+uW2+9VbGxsTp69KirmwYAAFyMIHUFb775pp544gkNHjxYkZGRmjVrlmrWrKmPPvrI1U0DAAAuRpC6jLy8PG3btk3R0dFmmd1uV3R0tNLT013YMgAAUBXwqb3LOH78uAoLC1W/fn2n8vr162v37t0l6ufm5io3N9d8nJOTI0nKzs5Wfn6+pAtBzMPDQ4WFhU7f81RcXlBQ4HSDOQ8PD9nt9lLLi3LPVkxHXey3336T9H99LT5XxTw9L/yaFhQUXFW5l5eXioqKVFhYaJbZbDZ5enqWWV7WeJRnnNx1PMr6nazq4+Ru42Hl34iqNE7uMh7ShTGpyH/LXTVO7jImv/32W4X+W26325WdnS1JV3XDV4JUBZo6daomTZpUojw8PNwFrbl+1Jvp6hbgYoxH1cJ4VD2MSdVSmeNx6tQpBQQEXLYOQeoy6tWrJw8PDx05csSp/MiRIwoJCSlR/7nnnlNiYqL5uKioSNnZ2QoKCnL65vHrhcPhUKNGjXTw4EH5+/u7ujnVHuNRtTAeVQvjUfVcz2NiGIZOnTql0NDQK9YlSF2Gt7e32rdvr5UrVyo+Pl7ShXC0cuVKjRgxokR9Hx8f+fj4OJUFBgZeg5ZWLn9//+vuReDOGI+qhfGoWhiPqud6HZMrzUQVI0hdQWJiogYNGqQOHTqoU6dOmjlzps6cOaPBgwe7umkAAMDFCFJXcP/99+vYsWMaP368srKy1KZNG6WkpJRYgA4AAKofgtRVGDFiRKmX8tydj4+PJkyYUOJyJVyD8ahaGI+qhfGoeqrLmNiMq/lsHwAAAErghpwAAAAWEaQAAAAsIkgBAABYRJACAACwiCCFK+LzCMDlORwOp+8yA/B/3P09hNsf4IqKv97GMIzr8qtugMpw/PhxffLJJ5o+fbrq1aungIAA3XbbbXrooYfUrFkzXiuALnwbSPGXMhd/sbLd7l5zONz+AGXKzc3V/PnzlZ+fr/79+5f6/YJAdfXYY4/pu+++U9++feXv76/jx4/rxx9/1MGDBxUREaGJEycqIiLC1c2sVs6dOydfX19XNwP/v927d2vmzJlKS0tTly5dNGnSJIWHh7vdH+UEKZTq119/1ciRI5Weni5PT08dPnxYb731lhISElzdtGopJydHmZmZioiIkJeXl6ubU+0ZhqHatWtr2bJl6tGjh1n2888/61//+pfmzJmjnJwcffbZZ4qMjHRtY6uRp59+Wt26dVP79u0VEhJS6o0gf/vtNwUFBbmgddVP586dVbNmTUVHR2vx4sU6duyYVq9erSZNmph18vLy5O3t7bpGVgD3ml9DhXn99deVm5urRYsW6eDBgxo/frzef/99HTx4UEVFRZIuvAB2797t4pZWD+PHj9ett96qvn37avbs2frll19K1Dl8+LDmzJmj/Px8F7Swetm1a5eaNm2q2rVrm2U2m0033XSTBg8erG+//VYeHh767LPPXNjK6iU5OVkzZszQgAED1LNnTz333HNatWqVjh49qoKCAknSmTNnNGTIEH3//fcubq37mz9/vs6ePasvvvhCL7zwglavXq2GDRvq1VdflfR/66ZmzJihw4cPu7Kpv58BlKJhw4bGokWLzMe5ubnGbbfdZowdO9Yse/31141evXq5oHXVT+vWrY3HH3/ceOSRR4yAgACjdu3aRv/+/Y1FixYZ2dnZhmEYxvPPP2906dLFxS2tHs6ePWv06tXL6N69u/Hf//7XKCoqKlFn+vTpRvv27V3QuuppyJAhxvDhw42ff/7ZePnll40mTZoYNpvNaNeunTF16lRj+/btxkcffWR4enq6uqnVwt133208++yzhmEYRl5enmEYhpGSkmLcfPPNxv79+w3DMIxVq1YZNpvNZW2sKMxIoYQff/xRQUFBuummm8wyb29vjRo1Sn/729+UlZUlSfr4448VExPjqmZWG5mZmQoJCVGPHj00f/58HTx4UB9++KEcDofuu+8+tWzZUn/5y180Z84c3Xvvva5ubrXg6+url19+WQ6HQw8//LCSk5N1+PBhnTt3TtKF9YUbN25U8+bNXdzS6qGgoEBNmzZVYGCgmjZtqhdeeEH79u1TRkaGOnTooFdffVXdu3fX//t//08PP/ywq5vr9nJzc+Xl5aXAwEAZhiEvLy8VFBQoNjZWDRs21KxZsyRJH374oe677z4Xt7YCuDrJoerZvXu3ER0dbSxYsMCpvLCw0OjSpYsxbtw4IzMz07Db7caZM2dc1Mrq4+jRo8bcuXONjRs3GoZxYRyK/fLLL8bMmTONpk2bGna73Th37pyrmlkt7dixw7j33nuNGjVqGPXq1TPi4+ONYcOGGeHh4UbHjh2N7777ztVNrDZOnDhh7N692zCMCzPol84SLliwwLDZbEZGRoYrmletFBUVGdu2bTOmT59uPi62ePFio169ekZmZqYREBBgrFu3zlXNrDAsNkepTp8+LQ8PD/n6+prXsm02m+bOnaukpCTddNNN2rt3r9avX+/illYfl/vY8ODBg/XLL78oNTX1GrcKknT06FEtXbpUixcvlq+vr1q1aqV77rlHLVq0cHXTqrWioiIZhiEPDw99+OGHeuqpp3T27FlXN6vaMS76lF5eXp7i4+OVmZkph8OhzMxMF7fu9yNIoYTiX/qL/5uTkyM/Pz9JUteuXbVlyxYtX75cffr0cXFr3Z9xyUeFi8cjMDBQknTq1Cl16dJF48eP1/333++iVqKYO94nxx28+eabKiws1JgxY1zdlGqr+N+y5ORkPfTQQ5o4caLGjx/v6mb9bgQplKmwsFAeHh5KSkrS7t27NW3aNNlsNn344YeaMWOGdu3a5eomViuXjsfrr78uSTp79qw2bNig6OhoF7cQqLry8/Pl4eFByK0CDMPQ1q1b1bRpU7e4FQVBCmUq/sv6lltu0X333adx48aZ206fPu300W9UvsuNBwDANQhSuKyDBw+qSZMm+umnnxQeHi6Jr4pxJcYDAKoW5jhxWSdPntTMmTPNN21JvGm7EOMBAFULM1K4IhbPVi2MBwBUHQQpAAAAi/izFgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBF/x/d1d6szAH/cQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "8c22f332-6c4a-4f9f-9dd0-5a741f9688a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{-2: 5200, -1: 417, 0: 54125, 1: 451, 2: 5330}\n",
      "0.6561312561896643\n"
     ]
    }
   ],
   "source": [
    "#SSS, Sy spin (min variance)\n",
    "aer_sim2 = AerSimulator()\n",
    "transpiled2 = transpile(SPMy, aer_sim2)\n",
    "result = aer_sim2.run(transpiled2, shots=65536, memory=True).result()\n",
    "data = result.get_memory()\n",
    "statistics = result.get_counts()\n",
    "output_list = []\n",
    "for res in data:\n",
    "    output_list.append(2-res.count(\"0\"))\n",
    "        \n",
    "output = {i:0 for i in [-2,-1,0,1,2]}\n",
    "output[-2] = statistics[\"0000\"]\n",
    "output[-1] = statistics[\"0001\"]+statistics[\"0010\"]+statistics[\"0100\"]+statistics[\"1000\"]\n",
    "output[0] = statistics[\"0011\"]+statistics[\"0101\"]+statistics[\"0110\"]+statistics[\"1001\"]+statistics[\"1010\"]+statistics[\"1100\"]\n",
    "output[1] = statistics[\"1110\"]+statistics[\"1101\"]+statistics[\"1011\"]+statistics[\"0001\"]\n",
    "output[2] = statistics[\"1111\"]\n",
    "\n",
    "print(output)\n",
    "print(variance(output_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "7efc3dc5-9dfd-471f-8ad8-1deca1cb7373",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "299c9a51-a797-4b0a-82dc-b7263c320eca",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0ac1e2fc59f7433da5696468a28a3a17": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "245f2b2e15bb498695ec2ddd67b0c479": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "margin": "0px 0px 10px 0px"
      }
     },
     "2c3e2bb2309446cdade51e4e87da20f6": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HBoxModel",
      "state": {
       "children": [
        "IPY_MODEL_d88c1c05e0124b51800856116d90dfc8",
        "IPY_MODEL_49afd3cfb542450b8ba0338d9381c830",
        "IPY_MODEL_7b277db40e2840fa96c9b18c764dd639",
        "IPY_MODEL_6a892d9841684317ad6aaa72467725d2",
        "IPY_MODEL_4cb0c35ad0974b6697bc075d3e591a56"
       ],
       "layout": "IPY_MODEL_601792cfdf5c432b8410f8933e540cfa"
      }
     },
     "49afd3cfb542450b8ba0338d9381c830": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_91858b419bb9459da0f7ae53709519f4",
       "style": "IPY_MODEL_cff9992547804d7694a6e6d08c5c0c4f",
       "value": "<h5>Backend</h5>"
      }
     },
     "4cb0c35ad0974b6697bc075d3e591a56": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_6ef3df6bcf744726a4d2dd7de2afbfab",
       "style": "IPY_MODEL_0ac1e2fc59f7433da5696468a28a3a17",
       "value": "<h5>Message</h5>"
      }
     },
     "587c641ca43946e18807801bad020975": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "5fa34db8802241bf992e3a798ee92a02": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ButtonModel",
      "state": {
       "button_style": "primary",
       "description": "Clear",
       "layout": "IPY_MODEL_6204f6c673b74e20bc372b89de1e2d3d",
       "style": "IPY_MODEL_e18b8824f9d447aaaa00642d9e5f204f",
       "tooltip": null
      }
     },
     "601792cfdf5c432b8410f8933e540cfa": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "margin": "0px 0px 0px 37px",
       "width": "600px"
      }
     },
     "6204f6c673b74e20bc372b89de1e2d3d": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "grid_area": "right",
       "padding": "0px 0px 0px 0px",
       "width": "70px"
      }
     },
     "65c43cf2f3224e7cab7a4f539fc7a7cb": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "6771bbd6922140adbffd85cb28e8c712": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "6a892d9841684317ad6aaa72467725d2": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_83f1bc8c6f7a47c9ac7a831f97b2493c",
       "style": "IPY_MODEL_af9c770ccd2e406eb6027b79f86856b1",
       "value": "<h5>Queue</h5>"
      }
     },
     "6ef3df6bcf744726a4d2dd7de2afbfab": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "7b277db40e2840fa96c9b18c764dd639": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_842aae400bca4c3ea1f8eb3c1084ba1c",
       "style": "IPY_MODEL_587c641ca43946e18807801bad020975",
       "value": "<h5>Status</h5>"
      }
     },
     "7d94490ecdec4c97befb11564a941c47": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "GridBoxModel",
      "state": {
       "children": [
        "IPY_MODEL_5fa34db8802241bf992e3a798ee92a02"
       ],
       "layout": "IPY_MODEL_d608b1c4726e4db49748d59f10beb17b"
      }
     },
     "83f1bc8c6f7a47c9ac7a831f97b2493c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "width": "70px"
      }
     },
     "842aae400bca4c3ea1f8eb3c1084ba1c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "width": "95px"
      }
     },
     "91858b419bb9459da0f7ae53709519f4": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "width": "145px"
      }
     },
     "a191a8b671df4046a0a8545927ca5fb8": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_245f2b2e15bb498695ec2ddd67b0c479",
       "style": "IPY_MODEL_65c43cf2f3224e7cab7a4f539fc7a7cb",
       "value": "<p style='font-family: IBM Plex Sans, Arial, Helvetica, sans-serif; font-size: 20px; font-weight: medium;'>Circuit Properties</p>"
      }
     },
     "af9c770ccd2e406eb6027b79f86856b1": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "cff9992547804d7694a6e6d08c5c0c4f": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLStyleModel",
      "state": {
       "description_width": "",
       "font_size": null,
       "text_color": null
      }
     },
     "d608b1c4726e4db49748d59f10beb17b": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "grid_template_areas": "\n                                       \". . . . right \"\n                                        ",
       "grid_template_columns": "20% 20% 20% 20% 20%",
       "width": "100%"
      }
     },
     "d88c1c05e0124b51800856116d90dfc8": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "HTMLModel",
      "state": {
       "layout": "IPY_MODEL_fd6cbdd960be47aa9d233d24add7daf3",
       "style": "IPY_MODEL_6771bbd6922140adbffd85cb28e8c712",
       "value": "<h5>Job ID</h5>"
      }
     },
     "e18b8824f9d447aaaa00642d9e5f204f": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ButtonStyleModel",
      "state": {
       "font_family": null,
       "font_size": null,
       "font_style": null,
       "font_variant": null,
       "font_weight": null,
       "text_color": null,
       "text_decoration": null
      }
     },
     "fd6cbdd960be47aa9d233d24add7daf3": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "width": "190px"
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}