getting_started_with_qiskit_runtime.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f2a203e8",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Simple demo to show how to get access to Qiskit IBM runtime\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e48ff7a-68c4-4288-9945-23dc89e24fc8",
   "metadata": {},
   "source": [
    "## Starting with Qiskit\n",
    "![Intro](./images/intro.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d7ede35-ea58-41eb-ada8-e5d08077e799",
   "metadata": {},
   "source": [
    "### Get access to Qiskit documentation\n",
    "https://qiskit.org/documentation/index.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876e5c2e-6430-4490-8828-ab4303186d0b",
   "metadata": {},
   "source": [
    "### Qiskit Architecture Overview\n",
    "![Intro](./images/qiskit-architecture-overview.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a39bffc",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### _Prepare environment, libs, APIs, etc._\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e11ca67e",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/stefan.kister/opt/virtual/qiskit/lib/python3.9/site-packages/urllib3/__init__.py:34: NotOpenSSLWarning: urllib3 v2 only supports OpenSSL 1.1.1+, currently the 'ssl' module is compiled with 'LibreSSL 2.8.3'. See: https://github.com/urllib3/urllib3/issues/3020\n",
      "  warnings.warn(\n",
      "/var/folders/xp/_lkpwwss4kz10m14lgzy2p5m0000gp/T/ipykernel_12260/1529719541.py:3: DeprecationWarning: The package qiskit_ibm_provider is being deprecated. Please see https://docs.quantum.ibm.com/api/migration-guides/qiskit-runtime to get instructions on how to migrate to qiskit-ibm-runtime (https://github.com/Qiskit/qiskit-ibm-runtime).\n",
      "  from qiskit_ibm_provider import least_busy\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, AncillaRegister, ClassicalRegister, QuantumRegister\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler, EstimatorV2 as Estimator, Session, Options\n",
    "from qiskit_ibm_provider import least_busy\n",
    "from qiskit.visualization import plot_distribution\n",
    "from qiskit.quantum_info import Statevector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be279bdb-4139-447f-80ef-10d12e78f71a",
   "metadata": {},
   "source": [
    "### _Two ways of using Qiskit IBM Runtime_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23317148-0943-466a-9cf5-a4aee039470c",
   "metadata": {},
   "source": [
    "# Devices in IBM Quantum \n",
    "\n",
    "You need an IBM ID to access the devices that are free available on this website. The IBM ID is free of charge, anyone who provide name and e-mail address can request.\n",
    "https://quantum-computing.ibm.com/\n",
    "\n",
    "Qiskit is an open-source SDK for working with quantum computers at the level of circuits, algorithms, and application modules.\n",
    "This project contains a provider that allows accessing the IBM Quantum systems and simulators.\n",
    "\n",
    "https://github.com/Qiskit/qiskit-ibm-provider\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "9286d812-d580-48ca-8476-72f846b635d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IBMBackend('simulator_statevector')>,\n",
       " <IBMBackend('simulator_stabilizer')>,\n",
       " <IBMBackend('ibm_brisbane')>,\n",
       " <IBMBackend('ibm_kyoto')>,\n",
       " <IBMBackend('ibm_osaka')>,\n",
       " <IBMBackend('ibmq_qasm_simulator')>,\n",
       " <IBMBackend('simulator_extended_stabilizer')>,\n",
       " <IBMBackend('simulator_mps')>]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Option 1 - using Qiskit Runtime Services in IBM Quantum\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "service.backends()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "ba63ef90-e3b2-49f3-b881-64b400fd185e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<IBMBackend('ibmq_qasm_simulator')>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#device = least_busy(provider.backends(simulator=True))\n",
    "device = service.backend(\"ibmq_qasm_simulator\")\n",
    "device"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f2ffd1-83af-4a09-bf50-6610d9d8f6e3",
   "metadata": {},
   "source": [
    "Another option to access IBM Quantum devices are the Qiskit runtime services in IBM Cloud.\n",
    "You need an IBM Cloud access (either per credit card or per subscription provided by your company) to use these services:\n",
    "\n",
    "https://cloud.ibm.com/catalog/services/qiskit-runtime-beta\n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "0279f6c5-8862-441b-9197-e4824406ab07",
   "metadata": {},
   "source": [
    "# Option 2 - using Qiskit Runtime Services in IBM Cloud\n",
    "\n",
    "QiskitRuntimeService.save_account(\n",
    "    channel=\"ibm_cloud\",\n",
    "    token=\"my created Cloud API token\",\n",
    "    instance=\"my resource number crn:v1:...::\",\n",
    "    overwrite=True\n",
    ")\n",
    "\n",
    "\n",
    "service = QiskitRuntimeService()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db3055bd",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### First steps with Qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "diverse-philadelphia",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 747.609x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a sample circuit with Qiskit -> GHZ Circuit\n",
    "\n",
    "qc1 = QuantumCircuit(3)\n",
    "qc1.h(0)\n",
    "qc1.cx(0, 1)\n",
    "qc1.cx(0, 2)\n",
    "qc1.measure_all()\n",
    "\n",
    "qc1.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "ceead808-d9f1-496d-b85d-7ff0fd3fb70f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'111': 510, '000': 514}\n"
     ]
    }
   ],
   "source": [
    "# Circuit results simulated with Aer\n",
    "from qiskit import transpile\n",
    "from qiskit.providers.basic_provider import BasicProvider\n",
    "backend = BasicProvider().get_backend('basic_simulator')\n",
    "\n",
    "qc1_trans = transpile(qc1, backend)\n",
    "job = backend.run(qc1_trans)\n",
    "\n",
    "result = job.result()\n",
    "counts=result.get_counts()\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "8620c588-c270-4dca-b041-704711d1c61c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "dbafee7e-e85b-4182-9d2a-7912632dcabc",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Circuit running on a real quantum device\n",
    "\n",
    "#small_devices = provider.backends(min_num_qubits=5, simulator=False, operational=True)\n",
    "#backend = least_busy(small_devices)\n",
    "#print(backend)\n",
    "\n",
    "#job = execute(qc1, backend = backend, shots=4000)\n",
    "#result = job.result()\n",
    "#counts=result.get_counts()\n",
    "#print(counts)\n",
    "#plot_distribution(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c7fda38-93eb-4e6a-bbb8-aafb682a4898",
   "metadata": {},
   "source": [
    "![Intro](./images/real_device_stats.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81eca427-03a1-4afb-a260-e746cbc4b555",
   "metadata": {},
   "source": [
    "### Building quantum circuits: Bernstein-Vazirani algorithm\n",
    "\n",
    "Bernstein-Vazirani algorithm is one of special quantum algorithms which showed that there can be advantages in using a quantum computer as a computational tool for more complex problems.\n",
    "\n",
    "There is a function returning the bitwise product of the input with a hidden string of bits $ s $. Its length is $ n $.\n",
    "\n",
    "$$ f(x) = s ⋅ x (\\mathrm{mod} 2) $$\n",
    "\n",
    "To find the hidden string, we would need to call the function $f$ for $ n $ times. However, using a quantum computer, we can solve this problem with 100% confidence after **only one call** to the function . The quantum Bernstein-Vazirani algorithm to find the hidden bit string is very simple:\n",
    "\n",
    "1. Initialize the inputs qubits to the state $|0\\rangle^{\\otimes n}$, and output qubit to $|-\\rangle$.\n",
    "2. Apply Hadamard gates to the input register\n",
    "3. Query the oracle\n",
    "4. Apply Hadamard gates to the input register\n",
    "5. Measure\n",
    "\n",
    "For more in detailed information about the Bernstein-Vazirani algorithm, feel free to check out this helpful chapter in the Qiskit textbook: **https://learn.qiskit.org/course/ch-algorithms/bernstein-vazirani-algorithm**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "9c28827b-4157-40ca-ac27-abe7e4b78e77",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bernstein_vazirani(string):\n",
    "    \n",
    "    # Save the length of string\n",
    "    string_length = len(string)\n",
    "    \n",
    "    qr = QuantumRegister(string_length, 'qr')\n",
    "    cr = ClassicalRegister(string_length, 'cr')\n",
    "    ar = AncillaRegister(1, 'ancilla')\n",
    "    \n",
    "    # Make a quantum circuit\n",
    "    bv = QuantumCircuit(qr, ar, cr)\n",
    "    \n",
    "    # Initialize each input qubit to apply a Hadamard gate and output qubit to |->\n",
    "    \n",
    "    bv.x(string_length)\n",
    "    bv.h(string_length)\n",
    "    for i in range(string_length):\n",
    "        bv.h(i)\n",
    "\n",
    "    # Apply an oracle for the given string\n",
    "    # Note: In Qiskit, numbers are assigned to the bits in a string from right to left\n",
    "    bv.barrier()\n",
    "    \n",
    "    for i in reversed(range(string_length)):\n",
    "        if string[i] == '1':\n",
    "            bv.cx(string_length-1-i, string_length)\n",
    "    \n",
    "    # Apply Hadamard gates after querying the oracle\n",
    "    bv.barrier()\n",
    "    for i in range(string_length):\n",
    "        bv.h(i)\n",
    "    \n",
    "    # Measurement\n",
    "    bv.barrier()\n",
    "    bv.measure(range(string_length), range(string_length))\n",
    "    \n",
    "    return bv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "2dd9bc52-ca8c-4cc7-bea5-b1fcb095d88d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1097.68x451.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "string = '101'\n",
    "circuit = bernstein_vazirani(string)\n",
    "display(circuit.draw(output=\"mpl\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "778c1419-a1af-4615-817e-e396f9dc8427",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Bernstein Varizani Result for 101 :\n",
      "{'101': 1024}\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use local simulator\n",
    "\n",
    "from qiskit_aer import Aer\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "results = backend.run(circuit, shots = 1024).result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "print()\n",
    "print(\"Bernstein Varizani Result for\", string, \":\")\n",
    "print(answer)\n",
    "print()\n",
    "plot_distribution(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "850ded9e-8863-43f3-8a9a-ccc77602d36b",
   "metadata": {},
   "source": [
    "## Qiskit IBM Runtime \n",
    "**Runtime Architecture**\n",
    "![Qiskit IBM Runtime](./images/runtime-architecture.png)\n",
    "https://qiskit.org/documentation/partners/qiskit_ibm_runtime/getting_started.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46d1bd98",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Using Qiskit IBM Runtime Primitives - Sampler"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8554661-6bff-4a7f-8781-4dd3323f0ff9",
   "metadata": {},
   "source": [
    "|       |     |          |\n",
    "| :---        |    :---   |          :--- |\n",
    "| Sampler      | Allows a user to input a circuit and then generate quasiprobabilities. This generation enables users to more efficiently evaluate the possibility of multiple relevant data points in the context of destructive interference.       | ![Sampler](./images/sampler.png) |\n",
    "|    |      |         |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "9cce6f0b-e2d0-467b-a59f-4602bf44fc33",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 747.609x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 3\n",
    "qc2 = QuantumCircuit(N)\n",
    "qc2.h(0)\n",
    "for x in range(1, N):\n",
    "  qc2.cx(0,x)\n",
    "qc2.measure_all()\n",
    "\n",
    "\n",
    "qc2.draw(output='mpl')\n",
    "#qc2.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "20236179-8ac1-4f85-8fe5-e8ddce93427b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit.primitives import StatevectorSampler as Sampler, StatevectorEstimator as Estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "70a51df1-ff46-4ad3-989d-a257a4a89ec2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The counts are: {'111': 4032, '000': 3968}\n"
     ]
    }
   ],
   "source": [
    "sampler = Sampler()\n",
    "result = sampler.run([qc2], shots=8000).result()\n",
    "\n",
    "data_pub = result[0].data\n",
    "\n",
    "# Get counts for the classical register \"meas\"\n",
    "counts = data_pub.meas.get_counts()\n",
    "print(f\"The counts are: {counts}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "a2f1a921-31fe-45b8-826f-94e455f7e915",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c30b17d4-d6e1-4e32-accb-d7a4898759e4",
   "metadata": {},
   "source": [
    "### Using Qiskit IBM Runtime Primitives - Estimator "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4607c0a9-ce0c-425f-b404-5a6baef99d38",
   "metadata": {},
   "source": [
    "|       |     |          |\n",
    "| :---        |    :---   |          :--- |\n",
    "| Estimator   | Allows a user to specify a list of circuits and observables and selectively group between the lists to efficiently evaluate expectation values and variances for a parameter input. It is designed to enable users to efficiently calculate and interpret expectation values of quantum operators that are required for many algorithms.        |  ![Sampler](./images/estimator.png)   |\n",
    "|    |      |         |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "b5d07630-6684-4e3d-b59e-ea1f0e044b6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pZj6rr5zbsN3AO6+j7lQ1q8bcQ4fuF3LNu49SuHEHVSXlpC9cyrG9B4lPGWHhT+I70dHRTJs2zeoYIpZxeg142gd3/vltvli0DIDw2CgmrX+a/LSvqCouUx8UcTin14CnfbD71cPpecP3WXvNfKrLThAS3ZG66loA2/VBvSnEIaIGJlJz4iTFO7MByHzzE7pfNYyA4HNn1oTrx7L31fcBKD94mMKNO4lPGenPuJYpLS3lww8/pLS01OooIpZwcg140wdPlZ5o+O/A9qG4XC5chlziyslrQMQTTq4Bb/rgwLuu48s/rqC6rL4fVh0txV1X58+4rcbIIzRO1CH+QiKT47nugycabgsMCyE89twPA+3QtTPluUcavi4/eJj2XTv7JafV8vPzmT9/Pq+++iodO3a0Oo6I3zm5BrzpgwD9fvEjkqdfTfhF0Wyc83zDKRhO5+Q1IOIJJ9eAN33wgj7diB7ci8H/NYV2IUFkrvgXu19+159xW40GGgc58sV+PvjJww1fT93xsoVpRET8z5s+uPvld9n98rtE9u/BZc/NJv9fX1JVos+lEBF787QPugLbERF/If+c/FuCL2jPhFUPUZZziNwPP/dX1FajU84cojznUKOjLEEdwggMD+VEYfG52+YV0aHbmTfCdeh+IRV5RedsJyJiJ970wbOV7MrhRGExsWMG+DqiiIhPedMHK/KKOPD3T3HX1VFVXEbeRxnEXNLHn3FbjQYahyjemU1ddS1xlw0CIHn61WS9vYG6UzXnbJvzzib63noVUD/MxI4ZwDf/3OLXvCIirc2bPtgpqVvDf0f06ELUwESO7cv1W1YREV/wpg8e+PundB03BIB2ocHEjhlA8c4cf8ZtNTrlzEHW3/0Mlz59N8GLfklZdiHrZz1LZN/4c7bb8ee3GfvUXdyw6TnctXVsnv8SVcVlFiT2v5CQEPr27UtISIjVUUQs4fQa8LQPDvufW+gQfyHu6hrqauv4bP7LHN+fZ0Fi/3P6GhA5H6fXgKd9cNcL7zD68TuY9K+ncLshZ+1n5KzZZEHif58GGgc5tucb1ky477zb1VRW8a87n/JDorYnMTGRpUuXWh1DxDJOrwFP++BHtz7qhzRtk9PXgMj5OL0GPO2DtVXVfHrvc35I5Hs65czhaqtrCImM4LoPniA0+vxX8hj2wC1cfM9kqo7pjbEi4gzqgyJiOqf3QR2hcbgj6XtZMexOj7dPX7iU9IXOfdVi7969zJgxgyVLltC3b1+r44j4nYk1oD7YmIlrQORsJtaA0/ugjtCIUdxuN9XV1bjdbqujiFhCNSBaA2I61YDzaKARERERERHb0ilnbVRgWAjTMl+zOobHAsOceaUQEbGG3XogqA+KSOtSH/TicS15VDkvl8tFUHio1TFERCyhHigiplMf9JwGGjFKQkICy5Yto2vXrlZHEbGEakC0BsR0qgHn0UAjRgkNDaVXr15WxxCxjGpAtAbEdKoB59FFAcQoBQUFPPzwwxQUFFgdRcQSqgHRGhDTqQacRwONGOX48eOsXr2a48ePWx1FxBKqAdEaENOpBpxHA42IiIiIiNiWBhoREREREbEtDTQiIiIiImJbGmjEKFFRUdx2221ERUVZHUXEEqoB0RoQ06kGnEcDjRglICCAoKAgAgK09MVMqgHRGhDTqQacR79JMUpRUREvvfQSRUVFVkcRsYRqQLQGxHSqAefRQCMiIiIiIralgUZERERERGxLA42IiIiIiNiWBhoxSkREBBMmTCAiIsLqKCKWUA2I1oCYTjXgPC632+22OoRIS23dutXnjzF8+HCfP4a/jFgNddS/krHlOqvTSGvwRw2As+rAadQHvaM+6DyqAdERGjFKVVUVBw8epKqqyuooIpZQDYjWgJhONeA8GmjEKFlZWdx4441kZWVZHUXEEqoB0RoQ06kGnCfQ6gDSNLfbTU2lfV45CAwLweVyWR1DRBzCbj0Q1AdFpHWpD3rxuH5/RPFITWUVr/f6mdUxPDYt8zWCwkOtjiEiDmG3HgjqgyLSutQHPadTzkRERERExLY00IiIiIiIiG3plDMxSnJyMlu2bLE6hohlVAOiNSCmUw04j47QiIiIiIiIbWmgEaPk5OQwY8YMcnJyrI4iYgnVgGgNiOlUA86jgUaMUllZyY4dO6isrLQ6ioglVAOiNSCmUw04jwYaERERERGxLQ00IiIiIiJiW7rKmYPEjh7AhFULGt1WXVFJ6YECMleuZ/fL7+KurbMonYiI76kPiojpTOyDGmgc6MCqNHJTM8DlIizmAnpPuZwRC6bTqU9XNs19wep4loqLi2PBggXExcVZHUXEEqbUgPpg80xZAyLNMaUGTOqDGmgc6Oj2LA68ldbw9d5X3mNy2jMk/fSHZCxaRtXRUgvTWatTp06kpKRYHUPEMqbUgPpg80xZAyLNMaUGTOqDeg+NAWoqqziSsR9XQAAde3SxOo6lSkpKWLFiBSUlJVZHEbGEqTWgPniGqWtA5DRTa8DJfVADjSEiEuoXbtWxcouTWOvQoUM88cQTHDp0yOooIpYwuQbUB+uZvAZEwOwacGofNGKgKSoqYt68efTu3ZvQ0FC6d+/OvffeS0VFBb/4xS9wuVw899xzVsdsNYFhwYRERRAS3ZELkuMZ+cjtRF/ckyMZ+yk9UGB1PLFI4Qlw/99/u4EaZ70f8LxO1kJ6EXxSAJ8dhqKTVicSX1IflKZ8U964D9a6v2tr56mogS1HzvTB46esTiS+ZFIfdPx7aLZt20ZKSgqFhYW0b9+e/v37k5+fz7PPPktmZibFxcUADBkyxNqgrWjovKkMnTe10W3Zaz9j8/0vWZRIrLTxMLyZBRsONf5DPvEDmNwDbkqA6FALA/pYwQlYngWrv4HS6jO3t3PBuDiYmghDoq3LJ76hPiinud3wUQGszK5/UaPhdmDyR3BDj/p/HYOtSuh72WXwtyx49yCcqD1ze0gAXNUVbu4JyZ2syye+YVIfdPRAU1RUxLXXXkthYSFz5szhwQcfJCIiAoDHH3+c++67j8DAQFwuF4MGDbI4bevZu/R9st/ZREBQIJHJ8Qy8exLt46KprTrzUszlz/8KAlz8644/NtwWfEEHJn3yFOkPvcqBVWlNfWuxEbcbntoJbxxo+v6iKvjLPvjHN/DMSEhy4B+zz4tgzhYorzn3vlo3fJhf/29WP5jex//5xHfUBwXqj0Qv2Abrcpu+P/8EPLe7/gWPZ0dBt/Z+jecXnxTA/M/hVBNH5avq4J2D8G4uzB8M18f7P5/4jkl90NGnnM2ePZvc3FxmzZrFk08+2TDMAMybN4/BgwdTU1NDQkICHTt2tDBp6yo9UEhB2nbyUr9gx5/f5qPbFtF5SC9GP3ZHwzab7v8LFw7vS+KksQ23jXrkdg5v2WObxdsS4eHhjBw5kvDwcKuj+Nzze5ofZs525CTM2gR5Fb7P5E97j8OvNjc9zHzbc7vrj+KYwJQaUB9snilrwO2GR75qfpg52zcV9X2wpMr3ufxp6xG4L73pYeZstW5YuK3+BR4TmFIDJvVBxw40u3fvZvny5XTu3JlHH320yW0uueQSAAYPHtxw2+kBaMSIEYSEhOByufyS15eOpO8lc+V6EieNJWZYXwBOHStn45znGfn72wnrEkmPa0YRO2YAm+5z1nXJvy0+Pp7FixcTH+/sl6FyK2DJfs+3Lz4Ff97juzxW+MOOxqdWnM+zO804n9yUGvg29cEzTFkDX5XUH3nxVO4JeMWLvtnWud3w6FfevU/o8a/glBd9065MqYFvc3IfdOxAs2zZMurq6pg2bRodOnRocpuwsDCg8UDz9ddf89ZbbxEbG8vw4cP9ktUfvnxqJXU1tQyde3PDbXkfbyP7nY1c9txsRi36JRvnPE9VibOuevFttbW1lJeXU1vr7I79Vrb3+3yUD0cd8kb5zFLIOOrdPqdPvXA6U2qgKeqD9UxZAytbcNT1nYNw0oOjunawtaj+yJM3ik9BqrPeK94kU2qgKU7tg44daFJTUwEYN25cs9vk5tYfhz57oLnssssoKChg9erVXHHFFb4N6Udl2YVkvb2Biy4bxIUj+zXcnr7gVSISY8lL/YLcjzIsTOgf+/fvZ/z48ezf76CX4ZrQkifmNW54L6/1s1hhTQsHk7UGDDSm1EBT1AfrmbAGKmvgwxY8MS+thvUOuZKv+mDzTKiB5ji1Dzr2ogA5OTkA9OjRo8n7a2pq2LBhA9B4oAkIaP0Zb9iwYRQWFnq1T5A7gAcZ0ao5vnrmLRInjWXo3Jt576bfAfUfslSec5iS3V4cl29CUp8kql3+vw7wTTfd5NX2hw8fBmDdunV8/vnnHu0zefJkr3NZKjCE2GczW7TrwmdeYN6qha0cyP86/fw5woZP8nq/vYXH6NZtYOsH8iF/1AD4vw580QNBfRDM6IPtorsTs3BTi/ad9ZuFnPjQXqfbNCXyP98kJGmM1/ulfbWPblPG+yCR7zi1Bkzrg7GxsaSnp7doX8cONBUV9cdZKysrm7x/+fLlFBUVERERQWJiok+zFBYWkpfn3Uvfwa524OWHuBZu2skrcc0X9fH9ebza7eZm7/935Bfkc8rt/0O3p3/Pnjq9HiorKz3e19vfndVcgcHEtnDfsrIy2/28TQk+cYKwFuxXV1tnu5/fHzUA/q+DlvRAUB/0hAl9MLg6kJgW7nv82DEO2+znbUr7qipCWrBfdXW17X7fTq0B9UHPOXagiY2NpaSkhIyMDEaPHt3ovoKCAubOnQvAoEGDfP7G/9hY759eBrkDwEYffHhR3EWWvDLZvr1319g83bjCwsI83rdr165e57JabVkR7SI6e71feE2ZLX/ebwuuOtai/dzHC2338/ujBsD/dWC3Hgjqg22JKzgId3UVriDvn9JH1FUQZLOftymBFUXn36gJAWVHbPf7dmoNmNYHW/J8+TTHDjRXXHEFu3fv5rHHHuPKK68kKSkJgK1bt3LLLbdQVFRf6P74QM2WHD6rPnGS13v9zAdpfGPf/n0Ehfv/0xm3bt3q1fZ79uxh2bJlpKSkkJyc7NE+Tz/9dAuSWevZXfDq197tExQAn720gKiQBb4J5UdZZTDlY+/3u+/q/vz0Lg+u8dqG+KMGwP91YLceCOqDbc1vM+o/X8UbnYLg07//L6HtfJPJn9KL4M6N3u/3h1t/wFX3qw9+mxU1oD7oOccONPPmzeONN97g4MGDDBgwgOTkZE6ePMnXX39NSkoKCQkJvPfee43eP2Oqf974oNUR/KZ379689957jT6TyIlu6AFLv67/JGxPXREHUS05P6ENSoyAYZ0bfyr4+YQEwMTuvsvUVphSA95SH3SeKQneDzTXxeOIYQbgkmhI6ADZXlysKjoExsX5LlNbYUoNeMvOfdCxVznr1q0baWlpXHPNNYSGhpKdnU1UVBQvvPACa9euZd++fQAaaAwTGBhIZGQkgYGOneWB+k+7vj3J8+2jQ+Cufuffzk7mDIBwL37N/zUQOgb7Lk9bYUoNSPNMWQMDI2Fy09cFalJ8e7itj+/y+JvLBfcPqj/67tH2wK+92N7OTKkBkzh62fbr1481a9ZQVlZGWVkZmzdvZubMmVRUVJCdnU1AQAADB9rrikby78nNzWXOnDkNl+x2spl94bbe59+uSyj8aTTEOewDk/t0gmdHQseg82/7nwPgxgSfR2oTTKoBaZopa8Dlgvsuhms9OPKa0KG+D17gsBc1LukMjw87/1Gndi743VAzjs6AOTVgEkcPNM3ZuXMnbrebPn36EB5+7rO4lStXsnLlSnbt2tXo65ZeSk7ajvLyctLS0igvt9cHRrWEywX39Ic/j4YfxJ5b7F1C4c5keO1y6N3Rkog+NyQalv0Aft4HIpt4opLSFf56Kfysl9+jWcakGpCmmbQGAgPgt0PgyeEwqonLnnVvX/+Cxivfd96LOqd9PxbeuBx+0hM6NHFAYnIPeP1yuMaAU25PM6kGTGHksbbt27cDzZ9uNmXKlCa/vu2223jllVd8mk2ktY2Iqf93uLL+XOpTdfVvfO13Qf0fe6frEgZ394NfJsGuY/DLDfXvLXIBCy+xOJyI+JzLBT+Iq/+XVwEHK+o/SDgqBJI7QYBvL3TaJsR3gDkD4a5k2H0c7jirD/5GZ96LA2igaYLb7c1bqUXs4cKw+n+mCm5Xf8TGxZk/5CJilq7t6/+ZKiwQvqc+KA6kgcZBIvv3YMyTdxLUIYyK3COsv2cxkUndueL1+ZRm5vP+1IWcPFpK76njGTDzGjr16Ub6Q6+y6y9rG77HsAduIeH6MRRvzyL1549b+NOIiHjP0z54Wqc+Xbn2vcfZ99oHbPntKwD0nzmR5OlXU1NxktVXzrXoJxERaRlP++C4JXOJ6H5ho/1Sf/44B99Pt10fNHKgSU1NtTqCT1z69Cw2/OpPFO/MpvfU8Qz/7a18/bePKc3Mb7QYj36VySd3/JGL77nhnO+RvnApx/YeJD5lhD+j+01MTAz33nsvMTEt/QxpEXtzeg142gcBXIHtGPPEneSs29Lo9l0vrqF4exYjHprux+T+4/Q1IHI+Tq8BT/vgxzOeaPjv6MG9uPKN35D38TbAfn3QgDPozRA1MJGaEycp3pkNQOabn9D9qmEEBJ87s5bsyuH4/jyos9nHz7aC6Ohopk2bRnR0tNVRRCzh5Brwpg8CDPmvKWS/s4myAwV+TGk9J68BEU84uQa87YOn9fnJeA68tZ666ho/pGx9Rh6hcaIO8RcSmRzPdR+cmbYDw0IIj42yMFXbU1paypYtWxgxYgQdOzr00l4i38HJNeBNH+w8tA8xlyTx/s0PMWTOj/0Z03JOXgMinnByDbTk+WC70GB6TrqUdyc94I+IPqEjNA5y5Iv9rL5ybsO/6vITVkdqc/Lz85k/fz75+flWRxGxhNNrwJM+2C4smFGLbmfjf/+vBQmt5/Q1IHI+Tq8Bb58P9pg4iuMH8jm25xs/JWx9OkLjEOU5h2jftXPD10EdwggMD+VEYbGFqURE/MfTPhjRI5YOXTsz4a3fARDcsT0EuAju1IFP733On5FFRFpVS54PJv3kh+xfZu/3l2ugcYjindnUVdcSd9kgCtZ/RfL0q8l6ewN1p+x5LqSIiLc87YPH9nzD3wb+ouHrIXN+THCn8IarnImI2JW3zwcjEmKJHtyTj25b5OekrUunnDnI+ruf4ZL507hh42JixwwgfeHSJrfr/eMfMOXzF+hx7WiGzPkxUz5/gaiBiX5OKyLS+jztgyIiTuVNH+zzk/HkrN1MdXmlHxO2Ph2hcZBje75hzYT7zrvd129+wtdvfuL7QG1QSEgIffv2JSQkxOooIpZweg142gfPtu0Pb/ooTdvk9DUgcj5OrwFv+mDGo2/4OI1/6AiNw9VW1xASGcF1HzxBaPT5r+Qx7IFbuPieyVQdK/dDOv9LTExk6dKlJCbqiJSYycQa8LYP9p85kVGLbudkcZkf0vmfiWtA5Gwm1oDT+6CO0DjckfS9rBh2p8fbpy9cqlM0RMRRvO2Du15cw64X1/gwkYiIfzm9D+oIjRhl7969jB07lr1791odRcQSqgHRGhDTqQacRwONGMXtdlNdXY3b7bY6ioglVAOiNSCmUw04j045a6MCw0KYlvma1TE8FhjmzDfWiYg17NYDQX1QRFqX+qAXj2vJo8p5uVwugsJDrY4hImIJ9UARMZ36oOd0ypmIiIiIiNiWjtCIURISEli2bBldu3a1OoqIJVQDojUgplMNOI8GGjFKaGgovXr1sjqGiGVUA6I1IKZTDTiPTjkToxQUFPDwww9TUFBgdRQRS6gGRGtATKcacB4NNGKU48ePs3r1ao4fP251FBFLqAZEa0BMpxpwHg00IiIiIiJiWxpoRERERETEtjTQiIiIiIiIbWmgEaMEBAQwdOhQAgK09MVMqgHRGhDTqQacR79JMUpdXR1ffPEFdXV1VkcRsYRqQLQGxHSqAefRQCMiIiIiIralgUZERERERGxLA42IiIiIiNiWBhoxSkREBBMmTCAiIsLqKCKWUA2I1oCYTjXgPC632+22OoRIS23dutXnjzF8+HCfP4b4z4jVUEf9qzlbrrM6zb/PHzUAqoO2TH1QvKU+6D3VQNumIzRilKqqKg4ePEhVVZXVUUQsoRoQrQExnWrAeTTQiFGysrK48cYbycrKsjqKiCVUA6I1IKZTDThPoNUBpGlut5uaSvu8chAYFoLL5bI6hog4hN16IKgPikjrUh/04nH9/ojikZrKKl7v9TOrY3hsWuZrBIWHWh1DRBzCbj0Q1AdFpHWpD3pOp5yJiIiIiIhtaaARERERERHb0ilnYpTk5GS2bNlidQwRy6gGRGtATKcacB4doREREREREdvSQCNGycnJYcaMGeTk5FgdRcQSqgHRGhDTqQacRwONGKWyspIdO3ZQWVlpdRQRS6gGRGtATKcacB4NNCIiIiIiYlsaaERERERExLZ0lTMHiR09gAmrFjS6rbqiktIDBWSuXM/ul9/FXVtnUToREd9THxQR05nYBzXQONCBVWnkpmaAy0VYzAX0nnI5IxZMp1Ofrmya+4LV8SwVFxfHggULiIuLszqKiCVMqQH1weaZsgZEmmNKDZjUBzXQONDR7VkceCut4eu9r7zH5LRnSPrpD8lYtIyqo6UWprNWp06dSElJsTqGiGVMqQH1weaZsgZEmmNKDZjUB/UeGgPUVFZxJGM/roAAOvboYnUcS5WUlLBixQpKSkqsjiJiCVNrQH3wDFPXgMhpptaAk/ugBhpDRCTUL9yqY+UWJ7HWoUOHeOKJJzh06JDVUUQsYXINqA/WM3kNiIDZNeDUPqhTzhwoMCyYkKiIhnMm+956FdEX9+RIxn5KDxRYHU9ExOfUB0XEdCb1QSMGmqKiIh5//HFWrVpFbm4uMTEx3HDDDTzyyCPMnj2bJUuWsHjxYmbNmmV11FYxdN5Uhs6b2ui27LWfsfn+lyxKJGKtzFJYmQ2fHoLT13WpAzYehlExEOCyMJz4hPqgSGO7jsGKLNhS1LgPZhyFoVHgUh90HJP6oOMHmm3btpGSkkJhYSHt27enf//+5Ofn8+yzz5KZmUlxcTEAQ4YMsTZoK9q79H2y39lEQFAgkcnxDLx7Eu3joqmtOtWwzeXP/woCXPzrjj823BZ8QQcmffIU6Q+9yoFVaU19axFbqayBB7+A1GZeiJr9GSR0gCeHQ0KEf7OJb6kPitQ7dgruT4etRU3fP3MD9L8AnhgOXcL8Gk18zKQ+6Oj30BQVFXHttddSWFjInDlzKCgoICMjg8LCQh577DHWrl3L1q1bcblcDBo0yOq4rab0QCEFadvJS/2CHX9+m49uW0TnIb0Y/dgdDdtsuv8vXDi8L4mTxjbcNuqR2zm8ZY9tFm9LhIeHM3LkSMLDw62OIj52shZmfdb8MHNadjnM+BSyyvyTy2qm1ID6YPNMWQMCpafqB5bmhpnTdh2r74OHK/0Sy3Km1IBJfdDRA83s2bPJzc1l1qxZPPnkk0REnHkJdt68eQwePJiamhoSEhLo2LGjhUl960j6XjJXridx0lhihvUF4NSxcjbOeZ6Rv7+dsC6R9LhmFLFjBrDpPmddl/zb4uPjWbx4MfHx8VZHER9bvAu+LPZs29Jq+O+tUOf2baa2wNQaUB88w9Q1YKLffwkHPHyx5lAl/E+Gb/O0FabWgJP7oGMHmt27d7N8+XI6d+7Mo48+2uQ2l1xyCQCDBw9uuG3lypXceOON9OjRg/DwcJKTk/nNb35Debm9rwbx5VMrqaupZejcmxtuy/t4G9nvbOSy52YzatEv2TjneapK7P1znk9tbS3l5eXU1tZaHUV8qLwaVn/j3T455bDpsG/ytCUm14D6YD2T14BJCk/Ax16+7zvjKOw57ps8bYnJNeDUPujYgWbZsmXU1dUxbdo0OnTo0OQ2YWH1J4uePdA8+eSTtGvXjkceeYR169bxH//xHzz//PNMmDCBurq6Jr+PHZRlF5L19gYuumwQF47s13B7+oJXiUiMJS/1C3I/cv5LM/v372f8+PHs37/f6ijiQ2tzobIFf6dWZrd6lDbH5BpQH6xn8howyaqcM2/+98Zb2a2dpO0xuQac2gcde1GA1NRUAMaNG9fsNrm5uUDjgeadd94hJiam4evLL7+cmJgYpk2bxqeffspll13mdZZhw4ZRWFjo1T5B7gAeZITXj/VdvnrmLRInjWXo3Jt576bfAfUfslSec5iS3V6+nP0tSX2SqHb5f+C76aabvNr+8OH6l+DXrVvH559/7tE+kydP9jqXWKvTLX8kbPSPvd7vk32H6HbjJT5I5Dv+qAHwfx34ogeC+iCoD5oi8u7XCBnwA6/3ezNtO89fk9L6gXzIqTVgWh+MjY0lPT29Rfs6dqDJyckBoEePHk3eX1NTw4YNG4DGA83Zw8xpw4YNAyAvL69FWQoLC73eN9jVDrz8ENfCTTt5Ja75oj6+P49Xu93c7P3/jvyCfE65/X/otqKiwqvtKysrG/7X031b+nsX6wTXQosu1hMUZrvftz9qAPxfBy3pgaA+6An1QTO0px0hLdivtl2w7X7fTq0B9UHPOXagOb1ATy/ab1u+fDlFRUVERESQmJj4nd/r448/BqBfv37fuV1zYmNjvd4nyB3QsmPFFrko7iJLXpls3769V9ufXhdhYWEe79u1a1evc4m1Qqlp2Y4ny2z3+/ZHDYD/68BuPRDUB6VtCao72aL9Ak6dsN3v26k1YFofbMnz5dMcO9DExsZSUlJCRkYGo0ePbnRfQUEBc+fOBWDQoEG4vuPTpPLy8njggQeYMGFCiz+rpiWHz6pPnOT1Xj9r0eNZYd/+fQSFh/r9cbdu3erV9nv27GHZsmWkpKSQnJzs0T5PP/10C5KJlT4ugLneLQ0Apgztyvz/OxXVLvxRA+D/OrBbDwT1QWlbVmbBou3e7zdrwlBm3qs++G1W1ID6oOccO9BcccUV7N69m8cee4wrr7ySpKQkoH7R33LLLRQV1V+U/buGlPLycq6//nqCg4NZsmSJP2Jb4p83Pmh1BL/p3bs37733XqNLeIvzfL8LXBgKh718gfKmBJ/EaVNUA01THxSnSekOz+6CE16c/dPOBZObPlPfUVQDTbNzH3TsVc7mzZtHdHQ0Bw8eZMCAAVx88cX06dOHESNG0LNnT8aPHw80fv/M2SorK7n22mvJysri/fffJy4uzp/xxUcCAwOJjIwkMNCxs7wAgQHw8z7e7fP9LpDUyTd52hLVgGgNmKF9IPykl3f7XBcPMf5/cd3vVAPO49iBplu3bqSlpXHNNdcQGhpKdnY2UVFRvPDCC6xdu5Z9+/YBTQ801dXV3HTTTaSnp7Nu3Tr69+/v7/jiI7m5ucyZM6fhCnfiXDclwLSenm074AJ42F4XN2sx1YBoDZjjjr6Q4uFbP8ZcCPMu9m2etkI14DyOHWig/k38a9asoaysjLKyMjZv3szMmTOpqKggOzubgIAABg4c2Gif059d89FHH/H2228zYkTrXy5PrFNeXk5aWprtPyhVzs/lgv8cUP8HurlXHEMC4MYe8L9j6l/NNIFqQLQGzBHgggXfg/9Ihk7BTW/TPhBu7Q1/HAFBjn5WeIZqwHkM+RPe2M6dO3G73SQlJREeHt7ovrvvvpsVK1bw61//mvDwcD777LOG+3r16tXkZZ1FpG1yueDHiXBDD1hfCJ8ehrJqCGsHyZ1gYnfo2MwfeRERJwhwwS+S4Ge94KN82FoE5TUQ3g4GR8GEbhBu5LNBcRIjl/D27fWX/WjqdLN169YBsGjRIhYtWtTovr/+9a9Mnz7d5/lEpHUFBsD4i+r/iYiYKKQd/Kh7/T8Rp9FA8y3Z2dl+TiMiIiIiIi2lgcZBIvv3YMyTdxLUIYyK3COsv2cxkUndueL1+ZRm5vP+1IWcPFrK9+7/KT1+NJLaqmrqamrJWPQG+Z98CUD/mRNJnn41NRUnWX3lXIt/otYXExPDvffeq1MHxVhOrwFP++ClT99N3GWDqDpaCkD++q9IX7gUgGEP3ELC9WMo3p5F6s8ft/LH8QmnrwGR83F6DXjaByMSYxnzxJ2EdGpPu9BgDn74OekPLQW323bPB40caFJTU62O4BOXPj2LDb/6E8U7s+k9dTzDf3srX//tY0oz8xstxkObd/PlUyupPXmKyP49SPn7Q7w5ZCY1lVXsenENxduzGPHQdOt+EB+Kjo5m2rRpVscQsYzTa8DTPgiw8/nV7PrL2nO+R/rCpRzbe5D4FGdeFMbpa0DkfJxeA572weG/vZVv1m1h98vv0i4kiInrFlEwbjt5qV/Y7vmgIdezcL6ogYnUnDhJ8c5sADLf/ITuVw0jIPjcmTUv9QtqT54CoGT3N+ByERrd0Z9xLVNaWsqHH35IaWmp1VFELOHkGvCmD5rMyWtAxBNOrgFv+qDb7SaoY/3FsdqFBhMQFEjl4WN+TNt61OUdokP8hUQmx3PdB0803BYYFkJ4bNR37tdn6jjKcw5RnnvE1xHbhPz8fObPn8+rr75Kx45mDHEiZ3NyDXjbB/vd/iN6Tx1PRV4RXzy2rOEJgNM5eQ2IeMLJNeBNH9zy27/yw/93P8m3XkVwp/Z8+fRbFO/I8mfcVqOBxkGOfLGfD37ycMPXU3e8/J3bx116MYPnTOH9mxf6OpqIiF942gczFi3jxKEScLuJTxnBFa//hlVj7qHmxEl/RRUR8QlP+2DybRPI+senbF/8d0KjO3L1Wwso2vY1Beu/8lfUVqNTzhyiPOcQ7bt2bvg6qEMYgeGhnCgsbnL7LqP7M/bpu/jo1kWUZub7K6aIiM940wdPFBaD2w3AN+u2UF12gk69dV1vEbE3b/pg8s+v5us3PwHg5NFS8j7KIHbMAH9FbVUaaByieGc2ddW1xF02CIDk6VeT9fYG6k7VnLNtl1H9+P7ie0id/jglu3L8HVVExCe86YPhcWdOv4j5Xh9CoiIozSr0W1YREV/wpg+W5Rym67ihQP1pabFjB3Jszzd+zdtadMqZg6y/+xkuffpughf9krLsQtbPepbIvvHnbDf2D3fRLjiIS5+668y+9yy27SL2RkhICH379iUkJMTqKCKWcHoNeNoHL316FmExnXDX1lFz8hSf/PIPVJedsCCx/zl9DYicj9NrwNM++Om9zzHy97+g/+0/IiA4kIPvpZP1jw0WJP73aaBxkGN7vmHNhPvOu92qsff4IU3blJiYyNKlS62OIWIZp9eAp33w/Zsf8kOatsnpa0DkfJxeA572weIdWay7/n/8kMj3dMqZw9VW1xASGcF1Hzzh0aWZ+8+cyKhFt3OyuMwP6UREfM/bPjjsgVu4+J7JVB0r90M6ERHfc/rzQR2hcbgj6XtZMexOj7ff9eIadr24xoeJrLV3715mzJjBkiVL6Nu3r9VxRPzOxBrwtg+mL1xK+kLnvnpr4hoQOZuJNeD054M6QiNGcbvdVFdX4/6/qxuJmEY1IFoDYjrVgPPoCE0bFRgWwrTM16yO4bHAMGe+sU5ErGG3HgjqgyLSutQHvXhcSx5VzsvlchEUHmp1DBERS6gHiojp1Ac9p1PORERERETEtnSERoySkJDAsmXL6Nq1q9VRRCyhGhCtATGdasB5NNCIUUJDQ+nVq5fVMUQsoxoQrQExnWrAeXTKmRiloKCAhx9+mIKCAqujiFhCNSBaA2I61YDzaKARoxw/fpzVq1dz/Phxq6OIWEI1IFoDYjrVgPNooBEREREREdvSQCMiIiIiIralgUZERERERGxLA40YJSoqittuu42oqCiro4hYQjUgWgNiOtWA87jcbrfb6hAiIiIiIiItoSM0IiIiIiJiWxpoRERERETEtjTQiIiIiIiIbWmgERERERER29JAIyIiIiIitqWBRkREREREbEsDjYiIiIiI2JYGGhERERERsS0NNCIiIiIiYlsaaERERERExLY00IiIiIiIiG1poBEREREREdvSQCMiIiIiIralgUZERERERGxLA42IiIiIiNjW/wcEVyMAZW/xDwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1040x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import TwoLocal\n",
    "\n",
    "qc3 = TwoLocal(3, \"ry\", \"cz\", reps=2, entanglement=\"linear\", insert_barriers=True)\n",
    "\n",
    "#qc3.draw('mpl')\n",
    "qc3.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "5dabc066-9ef7-4236-9ed0-2ef81f622ea3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "job id: db84c256-3860-4efa-9e4e-06ed1c8c54c6\n",
      "\n",
      "Expectation Value of <psi1(theta1)|H1|psi1(theta1)>:\n",
      "PrimitiveResult([PubResult(data=DataBin<>(evs=-1.98903689397857, stds=0.0), metadata={'precision': 0.0})], metadata={})\n"
     ]
    }
   ],
   "source": [
    "# creating sample Hamiltonian and calculating the expectation value\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "import math\n",
    "\n",
    "H1 = SparsePauliOp.from_list([(\"IZZ\", 0.5), (\"ZIZ\", 1), (\"ZZI\", 1.5)])\n",
    "theta1 = [-1.02570186,  0.26172088,  0.81759369,  0.90749673,  0.77320923,  2.58210241,\n",
    "  0.07412267,  0.92345479, -0.24843503]\n",
    "    \n",
    "\n",
    "estimator = Estimator()\n",
    "psi1_H1_result = estimator.run([(qc3, H1, theta1)]).result()\n",
    "\n",
    "print(f\"job id: {job.job_id()}\") \n",
    "print()\n",
    "print(\"Expectation Value of <psi1(theta1)|H1|psi1(theta1)>:\")\n",
    "print(psi1_H1_result)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "615b8d1c-94c7-47cb-a427-6abff7f90fd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1416.5x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc3.measure_all()\n",
    "qc3.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "c229e6d6-d77b-48ad-8b50-c5406697a51d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The counts are: {'100': 982, '010': 5, '011': 6, '111': 1, '101': 5, '110': 1}\n"
     ]
    }
   ],
   "source": [
    "sampler = Sampler()\n",
    "sampler_result = sampler.run([(qc3, theta1)], shots=1000).result()\n",
    "\n",
    "data_pub = sampler_result[0].data\n",
    "counts = data_pub.meas.get_counts()\n",
    "print(f\"The counts are: {counts}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "58a13d90-99c6-477a-8205-f9ccca5c3ff4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<IBMBackend('ibmq_qasm_simulator')>"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2, Session\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "device = service.backend(\"ibmq_qasm_simulator\")\n",
    "device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4cc2aaaa-e8e4-4329-a5a9-59b18bfac203",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "1d0c37e7-6009-4d5e-af3c-7725412ad597",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeJobFailureError",
     "evalue": "'Unable to retrieve job result. Circuits do not match the target definition (non-ISA circuits). -- \\\\n        Transpile your circuits for the target before submitting a primitive query. For\\\\n        example, you can use the following code block given an IBMBackend object `backend`\\\\n        and circuits of type `List[QuantumCircuit]`:\\\\n            from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\\\\n            pm = generate_preset_pass_manager(optimization_level=1, target=backend.target)\\\\n            isa_circuits = pm.run(circuits)\\\\n        Then pass `isa_circuits` to the Sampler or Estimator.\\\\n         -- https://ibm.biz/error_codes#1517'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeJobFailureError\u001b[0m                    Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[108], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m sampler_real \u001b[38;5;241m=\u001b[39m SamplerV2(backend \u001b[38;5;241m=\u001b[39m device)\n\u001b[0;32m----> 2\u001b[0m sampler_result \u001b[38;5;241m=\u001b[39m \u001b[43msampler_real\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43m(\u001b[49m\u001b[43mqc3\u001b[49m\u001b[43m,\u001b[49m\u001b[43mtheta1\u001b[49m\u001b[43m)\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mshots\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m1000\u001b[39;49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mresult\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m data_pub \u001b[38;5;241m=\u001b[39m sampler_result[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m.\u001b[39mdata\n\u001b[1;32m      4\u001b[0m counts \u001b[38;5;241m=\u001b[39m data_pub\u001b[38;5;241m.\u001b[39mmeas\u001b[38;5;241m.\u001b[39mget_counts()\n",
      "File \u001b[0;32m~/opt/virtual/qiskit_v10x/lib/python3.11/site-packages/qiskit_ibm_runtime/runtime_job_v2.py:138\u001b[0m, in \u001b[0;36mRuntimeJobV2.result\u001b[0;34m(self, timeout, decoder)\u001b[0m\n\u001b[1;32m    136\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_reason \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mRAN TOO LONG\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m    137\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m RuntimeJobMaxTimeoutError(error_message)\n\u001b[0;32m--> 138\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m RuntimeJobFailureError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUnable to retrieve job result. \u001b[39m\u001b[38;5;132;01m{\u001b[39;00merror_message\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    139\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_status \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCANCELLED\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m    140\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m RuntimeInvalidStateError(\n\u001b[1;32m    141\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUnable to retrieve result for job \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m. \u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mJob was cancelled.\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mjob_id())\n\u001b[1;32m    142\u001b[0m     )\n",
      "\u001b[0;31mRuntimeJobFailureError\u001b[0m: 'Unable to retrieve job result. Circuits do not match the target definition (non-ISA circuits). -- \\\\n        Transpile your circuits for the target before submitting a primitive query. For\\\\n        example, you can use the following code block given an IBMBackend object `backend`\\\\n        and circuits of type `List[QuantumCircuit]`:\\\\n            from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\\\\n            pm = generate_preset_pass_manager(optimization_level=1, target=backend.target)\\\\n            isa_circuits = pm.run(circuits)\\\\n        Then pass `isa_circuits` to the Sampler or Estimator.\\\\n         -- https://ibm.biz/error_codes#1517'"
     ]
    }
   ],
   "source": [
    "sampler_real = SamplerV2(backend = device)\n",
    "sampler_result = sampler_real.run([(qc3,theta1)], shots=1000).result()\n",
    "data_pub = sampler_result[0].data\n",
    "counts = data_pub.meas.get_counts()\n",
    "print(f\"The counts are: {counts}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6049b148-6293-45eb-8946-75ab65ba42cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(sampler_result.quasi_dists[0].binary_probabilities())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "342e5c1c-9afa-45cd-9ca1-57cb96f2d160",
   "metadata": {},
   "source": [
    "## Dynamic Circuits\n",
    "Dynamic circuits are quantum circuits that contain mid-circuit measurements that affect the control flow of gate execution later in the circuit, otherwise known as feed-forward operations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "8e54572a-3d5a-4da9-a0de-583b8f494150",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 741.811x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "qc4 = QuantumCircuit(qr, cr)\n",
    "\n",
    "q0, q1 = qr\n",
    "b0, b1 = cr\n",
    "\n",
    "qc4.h(q0)\n",
    "qc4.measure(q0, b0)\n",
    "\n",
    "# begin if test block. the contents of the block are executed if b0 == 1\n",
    "with qc4.if_test((b0, 0)) as else_:\n",
    "    qc4.x(q1)\n",
    "with else_:\n",
    "    qc4.h(q1)\n",
    "    \n",
    "qc4.measure(q1, b1)\n",
    "qc4.draw(output=\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "3a244cfc-b101-4f08-be64-7c26c226b675",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 20, '10': 53, '01': 27}\n"
     ]
    }
   ],
   "source": [
    "# running dynamic circuits\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "result = backend.run(qc4, shots=100).result()\n",
    "\n",
    "print(result.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "f47827b7-ca71-4711-b7cd-f08c1dffeab9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A3Ey+ZgDNZrMsFovt/n7jx4+3vb79j4eHh6pWraq9e/eqf//+TikcAAAA9snXDGCbNm1ss37bt29XYGBgjvf9s1gsKl26tDp06KChQ4c6pFAAAAA4Rr4C4NatW23/bTabNWTIEI0bN87RNQEAAMCJ7L4GMCMjw5F1AAAAoJA4dRUwAAAA3E+eZwCfffZZmUwmTZo0Sf7+/nm+wbPJZNLnn39ud4EAAABwLJPVarXmpaPZbJbJZNKhQ4dUo0YNmc15mzw0mUxKT08vUJH3qsTERPn6+iohIUE+Pj6uLgcwjKEzXF0BJGnOSFdXABhLfnJHnmcA//jjD0lSpUqVsrwGAADAvSXPATAoKOiOrwEAAHBvYBEIAACAweR5BvD06dN2HyQwMNDu9wIAAMCx8hwAg4ODc332752YTCalpaXl+30AAABwjjwHwEGDBtkVAAEAAOBe8hwAFyxY4MQyAAAAUFhYBAIAAGAwBEAAAACD4VFwAAAABsOj4JyIR8EBrsGj4NwDj4IDChePggMAAECueBQcAACAwbAIBAAAwGAKHAC/+uor9ejRQ4GBgfL19VVgYKAef/xxff311w4oDwAAAI6W51PAf5WWlqaBAwdqxYoVslqt8vDwUJkyZRQbG6uVK1dq1apV6tWrlxYvXiwPD7sPAwAAAAezewZw8uTJ+u9//6uHH35YO3bs0I0bNxQTE6MbN25o+/btat26tVasWKEpU6Y4sl4AAAAUUJ5vA/NXISEh8vb21i+//JLjDF9qaqrq1aunlJQUnThxosCF3ou4DQzgGtwGxj1wGxigcOUnd9g9AxgTE6NHH30019O7np6eevTRRxUTE2PvIQAAAOAEdgfAKlWqKCkp6Y59kpOTFRgYaO8hAAAA4AR2B8DnnntOy5Yty3WG79y5c1q6dKmee+45u4sDAACA4+V5ee7p06ezvO7bt6++//57NWzYUCNHjlTr1q3l7++vuLg47dixQx9++KFat26tPn36OLxoAAAA2C/fzwL+K6vVmmt75vvS0tIKWOa9iUUggGuwCMQ9sAgEKFxOeRbwoEGDcgx6AAAAuLfkOQAuWLDAiWUAAACgsPAsYAAAAIMhAAIAABhMgR7Se/XqVc2cOVMbN27U+fPnlZKSkq2PyWRSdHR0QQ4DAAAAB7I7AF68eFEtW7ZUdHS0fHx8bCtPbt68qevXr0uSKlasKE9PT4cVCwAAgIKz+xTw+PHjFR0drf/7v//T5cuXJUmvvPKKkpOTtWvXLoWGhio4OFgHDx50WLEAAAAoOLsD4OrVq9WxY0c99dRT2W4P07RpU61Zs0YnT57UhAkTClwkAAAAHMfuABgTE6OGDRvaXlssFtupX0ny8/PTI488omXLlhWsQgAAADiU3QHQ19dXqampttd+fn46e/Zslj4+Pj6Ki4uzvzoAAAA4nN0BMCQkRCdPnrS9btiwoTZs2KA///xTknT9+nWtWrVKgYGBBS4SAAAAjmN3AAwLC9OmTZt07do1SdLw4cN14cIF1a9fX3369FGdOnUUHR2twYMHO6pWAAAAOIDdAfD555/XnDlzbAHwiSee0LRp05ScnKwVK1YoNjZWo0aN0uuvv+6wYgEAAFBwJqvVanXkDtPT0xUfH6/y5ctnWx1sNJn3RkxISJCPj4+rywEMY+gMV1cASZoz0tUVAMaSn9xRoCeB5MRiscjf39/RuwUAAICDFDgAxsTEaMmSJdq3b58SEhLk6+urhg0bqn///qpQoYIjagQAAIADFSgAzpo1S6+//rpSUlJ0+5nkhQsX6s0339T06dP1wgsvFLhIAAAAOI7dAXDJkiV66aWXVLZsWb355pt6+OGH5e/vr7i4OG3fvl0ffvihbXvfvn0dWTMAAAAKwO5FII0aNdLZs2e1f/9+VaxYMdv2s2fPqmHDhgoMDNTPP/9c4ELvRSwCAVyDRSDugUUgQOHKT+6w+zYwhw4dUt++fXMMf5JUuXJl9enTR4cOHbL3EAAAAHACuwNgqVKlVLx48Tv2KVGihEqVKmXvIQAAAOAEdgfAxx57TKtWrVJaWlqO21NTU7Vq1Sr16NHD7uIAAADgeHYHwHfffVfFixdXWFiYfvzxxyzboqKiFBYWppIlS2rKlCl27X/Pnj3q2rWrbaaxefPmWrZsWZ7fv2bNGvXv31+1atVSqVKlVKxYMdWqVUt/+9vfdPTo0Vzft27dOrVt21YlS5aUj4+P2rdvr02bNtk1BgAAAHeU51XAISEh2dpu3rypvXv3qlWrVvLw8FDZsmUVHx9vmxWsUKGCGjVqpOjo6HwVtWXLFoWHh8vb21v9+/dXyZIltWLFCvXr109nzpzRq6++etd9rF69Wj/++KOaNWumRx55RJ6enjp06JAiIyO1aNEirV69Wh06dMjynoULF+rpp59WuXLlbM8wXrp0qTp37qxly5apd+/e+RoHAACAO8rzKuDg4GC7H+32xx9/5LlvWlqaatWqpbNnz+rHH39UgwYNJEkJCQkKDQ3VyZMndfToUQUFBd1xPzdu3JC3t3e29k2bNqlTp05q0qSJ9uzZY2u/fPmyQkJC5OHhoX379qly5cqS/reaWZJOnDihkiVL5nksrAIGXINVwO6BVcBA4XLKo+BOnjxZ0LryZPPmzYqOjtaQIUNs4U+SfH19NXbsWA0ePFiRkZEaN27cHfeTU/iTpI4dO8rPz0/Hjx/P0r58+XJduXJFEyZMsIU/6dZq5hEjRmj8+PH66quvNGjQIPsHBwAA4AbsvgbQWbZu3SpJCgsLy7YtPDxckrRt2za79x8VFaXLly+rTp06hXpcAAAAd1HgZwFLt07bHjlyRImJifLx8VHNmjXl4WHfro8dOyZJql69erZtAQEBKlGihK1PXqxfv14//PCDUlJSdOzYMX377bcqW7asPvjggzwfN7PtbsdNSUlRSkqK7XViYqKkWyuiU1NTJUlms1kWi0Xp6enKyMiw9c1sT0tLy/JYPYvFIrPZnGt75n4zZf5//+vq7NzaPT09lZGRofT0dFubyWSSh4dHru251Z7Z/umnn+r9999XbGys6tevrw8++EBNmzbNcUxz587VwoULdfDgQUlS48aN9fbbb2fp7+XllcP/bWnq1Kl6/fXXC2VMf22/H35O9/OYJE/B9Yz0e48xMSZ3GFN+FCgAXrp0SaNHj9bixYt148YNW3vRokU1cOBATZ48WWXKlMnXPhMSEiTdOuWbEx8fH1ufvFi/fr3ee+892+tq1appyZIlaty4cZ6Pm3ke/W7HnTx5siZMmJBjDcWKFZMkBQYGqmHDhvrll190+vRpW5+aNWuqVq1a2r17ty5evGhrb9CggYKCgrR9+3ZdvXrV1t6iRQuVL19e69evz/IBa9++vYoWLarVq1dnqaFr1666fv26tmzZYmvz8PBQt27dFB8fr6ioKFt7yZIl1aFDB505c0b79++3tZcrV04tW7bUsWPHdOTIEVv77WNavHixZsyYob///e8KCwvTypUr1aVLF3388ce2e0LePqYvvvhCDz30kHr16qXQ0FDNnTtXYWFh+uijj2yfnaNHj8rb29u2Gnvv3r2aOXOmevTooatXrzp9TPfjz+l+H5PE7afcQeZnwUifPcbEmFw5ptwezpETux8Fd+nSJTVv3lzHjx9X6dKl1aRJE1WoUEGxsbH66aef9Oeff6p69eqKiopS6dKl87zfsLAwbdiwQceOHVO1atWyba9UqZKSkpLyFQIlKSkpSb///rvefvttbdy4UfPmzdPAgQNt22vUqKFjx44pNTU12+xlamqqvLy8VK9ePR04cCDXY+Q0A1ilShXFx8fbQuT9/q+RFi1aqEmTJvrwww9lNptlMplUpUoVvfDCC3rjjTfuOiar1So/Pz/NmDFDTz/9dI619+rVS0lJSbZAyL8aGdNf21+YxQygO/jkRWYAGRNjKswxJScnO34RyF9NnDhRx48f1+uvv65x48ZleSrItWvXNHHiRE2dOlXvvPNOlhm4u8mcgcst4CUmJsrPzy/f9ZYoUUKhoaH6+uuv1aRJEw0bNkydO3dWuXLlsh33r7OWmadyc5uVzFSkSBEVKVIkW7unp6c8PbP+hWSxWGSxWLL1ze3UeW7tf92vPe1msznHqePc2nOrPT09XXv37tXYsWOzHKdTp07avXt3tmPnNKarV68qNTVV5cuXz9bf09NTcXFxWrNmjSIjI22r0p05pvvx52SkMcG1jPB7jzExpvy2u8vvPbsXgXzzzTdq166dpk6dmu2RcMWKFdPkyZPVrl07ffXVV/na752ut4uNjVVSUlKO1+nllYeHh9q3b6/k5GT99NNPeTruna4PxP/Ex8crPT1d/v7+Wdr9/f0VGxubp32MHj1aFStWVKdOnXLcHhkZqZIlS+qJJ54ocL0AABiV3QHw/PnzatGixR37tGjRQufPn8/Xftu2bSvp1nVzf7Vu3bosfeyVWdPtybwwjos7mzJlipYsWaKvvvoq19v4zJs3T08++WSu2wEAwN3ZHQB9fX116tSpO/Y5derUXU+b/lXHjh0VEhKixYsXZ7kYMiEhQZMmTZKXl1eWe/HFxMTo8OHD2U4Z3z67d7t169bpq6++UqlSpbIE2L59+8rX11cff/yxzp49a2s/e/asZs6cqbJly6pnz575GovRlC1bVhaLRXFxcVna4+LiFBAQcMf3Tp8+XVOmTNH69etVr169HPvs2LFDR44c0XPPPeewmgEAMCK7A2Dbtm21fPlybdy4McftmzZt0vLly9WuXbt87dfDw0Nz585VRkaG2rRpo2HDhunVV19V/fr1dfToUU2aNEnBwcG2/mPGjNGDDz6Y7VRz06ZNVbduXT355JMaPXq0RowYoTZt2qhLly6Sbs0k3X7q2s/PTzNnzlR8fLwaNWqkl156SS+99JIaNWqkP//8U5988km+ngJiRF5eXmrcuHGWZydnZGRo06ZNd5wtfvfddzVx4kStXbtWTZo0ybXf559/rsaNG6t+/foOrRsAAKOxexFIRESEvvvuO4WHh6tr165q27at/P39FRcXp61bt2rNmjUqVqzYXZ/YkZP27dtr586dioiI0NKlS5Wamqq6detq6tSp6tevX572MWnSJG3ZskXbtm3TxYsXZTabFRgYqGHDhmnkyJF68MEHs73nqaeeUtmyZTVp0iTNnz9fJpNJjRs31ltvvZXrNWnIatSoUXrmmWfUpEkThYaGasaMGUpOTtaQIUMkSYMGDVKlSpU0efJkSbfu5Tdu3DgtXrxYwcHBtmsFS5QooRIlStj2m5iYqOXLl+drQREAAMiZ3beBkaSdO3dq8ODBOnHixK2dmUy2ZdMPPPCAFixYoFatWjmm0nuQUZ8FPHPmTE2bNk2xsbFq0KCBPvroIzVr1kyS1K5dOwUHB2vBggWSbj1jOqdLCSIiIjR+/Hjb69mzZ2vkyJGKiYnJ92UFMB6eBeweeBYwULjykzsKFAAlyWq16vvvv9e+fftsTwJp2LChWrVqZbtNh1EZNQACrkYAdA8EQKBw5Sd32H0K+Nlnn1XdunX1yiuvqHXr1mrdurW9uwIAAEAhsnsRyOLFi3XhwgVH1gIAAIBCYHcAfOCBBxQTE+PIWgAAAFAI7A6Azz77rL777judO3fOkfUAAADAyey+BrBXr17asmWLWrZsqTfeeENNmzaVv79/jgs/AgMDC1QkAAAAHMfuABgSEmK77cvLL7+caz+TyaS0tDR7DwMAAAAHszsADho0yPC3eQEAALgX2R0AM2/kCwAAgHuL3YtAAAAAcG+yewYwU0pKilavXq19+/YpISFBvr6+atiwobp27aoiRYo4okYAAAA4UIEC4MqVKzVs2DBdvHhRtz9RzmQyqXz58po9e7YeffTRAheJ3PHIK/fBY68AAPcKuwPgpk2b1KtXL1ksFj377LN6+OGH5e/vr7i4OG3fvl0LFy7UE088oXXr1qlDhw6OrBkAAAAFYHcAjIiIUNGiRfXDDz+oTp06WbYNGjRIL7/8slq1aqWIiAgCIAAAgBuxexHIvn371K9fv2zhL1O9evXUt29f7d271+7iAAAA4Hh2B8BixYqpXLlyd+xTvnx5FStWzN5DAAAAwAnsDoCdOnXSxo0b79hn48aN6ty5s72HAAAAgBPYHQCnT5+uCxcuaNCgQTpz5kyWbWfOnNHTTz+t+Ph4TZ8+vcBFAgAAwHHsXgTy9NNPy8/PT4sWLdKSJUsUGBhoWwV8+vRppaenq169enrqqaeyvM9kMmnTpk0FLhwAAAD2sTsAbt261fbfaWlpOnHihE6cOJGlz4EDB7K9j+cHAwAAuJbdATAjI8ORdQAAAKCQ8CxgAAAAg3FYADx9+rS2b9/uqN0BAADASRwWAOfPn6/27ds7ancAAABwEk4BAwAAGAwBEAAAwGAIgAAAAAbjsADo6+urwMBAR+0OAAAATuKwADhy5Ej98ccfjtodAAAAnIRTwAAAAAaT5yeBZN7jLzQ0VN7e3vm651+bNm3yXxkAAACcIs8BsF27djKZTDp06JBq1Khhe50X6enpdhcIAAAAx8pzABw3bpxMJpPKli2b5TUAAADuLXkOgOPHj7/jawAAANwbWAQCAABgMHYHwKtXr+rEiRNKTU3N0r506VI9+eST+tvf/qa9e/cWuEAAAAA4Vp5PAf/VG2+8oYULFyouLk6enp6SpE8//VQjRoyQ1WqVJC1ZskQ///yzatWq5ZhqAQAAUGB2zwBu27ZNnTp1UrFixWxtU6ZMUaVKlbR9+3YtW7ZMVqtV06ZNc0ihAAAAcAy7A2BMTIyqVq1qe33o0CGdOXNGL7/8slq3bq3evXvrsccey9f9AgEAgDHNmjVLwcHB8vb2VrNmzbR79+5c+86ZM0cPP/yw/Pz85Ofnp06dOt2xP7KzOwCmpKTIy8vL9nrbtm0ymUwKCwuztYWEhOjcuXMFqxAAANzXli5dqlGjRikiIkJ79+5V/fr1FR4ergsXLuTYf+vWrRowYIC2bNmiqKgoValSRWFhYWSOfLA7AFauXFm//PKL7fW3336r0qVLq169era2P//8UyVKlChYhQAA4L72/vvva+jQoRoyZIhq166tf//73ypWrJjmzZuXY/9FixbphRdeUIMGDVSrVi3NnTtXGRkZ2rRpUyFXfu+yexHII488olmzZum1116Tt7e31q5dq0GDBmXpc/ToUQUGBha4SAAAcH+6efOmfv75Z40ZM8bWZjab1alTJ0VFReVpH9euXVNqaqpKly7trDLvO3YHwDFjxmjVqlV6//33JUkVKlTQ22+/bdt+4cIFff/99xoxYkTBqwQAAPel+Ph4paeny9/fP0u7v7+/Dh8+nKd9jB49WhUrVlSnTp2cUeJ9ye4AGBAQoIMHD9qmW9u0aSMfHx/b9vj4eE2bNk3h4eEFrxIAACAHU6ZM0ZIlS7R161Z5e3u7upx7ht0BUJKKFi2q7t2757itdu3aql27dkF2DwAA7nNly5aVxWJRXFxclva4uDgFBATc8b3Tp0/XlClTtHHjxixrEHB3PAoOAAC4jJeXlxo3bpxlAUfmgo4WLVrk+r53331XEydO1Nq1a9WkSZPCKPW+UqAZwPT0dC1btkwbN27U+fPnlZKSkq2PyWRiVQ4AAMjVqFGj9Mwzz6hJkyYKDQ3VjBkzlJycrCFDhkiSBg0apEqVKmny5MmSpKlTp2rcuHFavHixgoODFRsbK0kqUaIEdx/JI7sDYHJyssLCwvTjjz/KarXKZDLZHgEnyfbaZDI5pFAAAHB/6tevny5evKhx48YpNjZWDRo00Nq1a20LQ06fPi2z+X8nLT/99FPdvHlTvXv3zrKfiIgIjR8/vjBLv2fZfQr4X//6l6KiojRhwgTFx8fLarVq/PjxiomJ0dKlSxUSEqI+ffrkOCsIAABwuxEjRujUqVNKSUnRrl271KxZM9u2rVu3asGCBbbXJ0+elNVqzfaH8Jd3dgfAL7/8Us2bN9dbb72V5b47/v7+6tOnj7Zs2aKNGzfyLGAAAAA3Y3cAPH36tJo3b/6/HZnNWWb7KleurG7duikyMrJgFQIAAMCh7A6AxYsXz3I+3tfXVzExMVn6BAQE6PTp0/ZXBwAAAIezOwAGBQVlCXd16tTR5s2bbbOAVqtVmzZtUoUKFQpeJQAAABzG7gDYsWNHbdmyRWlpaZKkZ555RqdPn1aLFi30+uuvq3Xr1tq/f7969erlsGIBAABQcHbfBmbo0KEqU6aMLl68qAoVKujZZ5/Vvn379Mknn2j//v2SpF69erEiBwAAwM3YHQCrV6+u0aNHZ2n7+OOPNW7cOJ04cUJBQUF3fYQLAAAACl+BngSSk3LlyqlcuXKO3i0AAAAcxOEBEAAAuJehM1xdASRpzkhXV/A/dgfAkJCQPPUzmUyKjo629zAAAABwMLsDYEZGRo7P+U1ISNCVK1ckSRUqVJCXl5fdxQEAAMDx7A6AJ0+evOO2UaNGKS4uThs2bLD3EAAAAHACu+8DeCfBwcFaunSpLl++rDfffNMZhwAAAICdnBIAJcnT01OdO3fWsmXLnHUIAAAA2MFpAVCSrl27pkuXLjnzEAAAAMgnpwXAHTt26IsvvlDNmjWddQgAAADYwe5FIB06dMixPS0tTefOnbMtEhk3bpy9hwAAAIAT2B0At27dmmO7yWSSn5+fwsLCNGrUKHXu3NneQwAAAMAJCnQfQAAAANx7CvwouAsXLujcuXPKyMhQpUqVFBAQ4Ii6AAAA4CR2LQJJSUnRu+++q+rVq6tChQpq0qSJQkNDValSJZUtW1avvPLKHW8UDQAAANfJdwA8c+aMmjZtqjFjxig6OloVKlRQaGioQkNDVaFCBV26dEkffvihmjRpoo0bN9reFxMTwz0BAQAA3EC+AmBqaqq6du2q3377TQMGDNChQ4d09uxZRUVFKSoqSmfPntWhQ4f05JNP6tKlS3r88cd18uRJRUdHq3Xr1jp8+LCzxgEAAIA8ytc1gJ999pkOHjyoiIgIRURE5NinZs2a+s9//qMaNWooIiJCTz75pE6ePKn4+Hg1btzYIUUDAADAfvmaAVy2bJmqVauWp3v7vfXWW6pevbqioqJ048YNrVu3Tt26dbO7UAAAADhGvgLg77//rrCwMJlMprv2NZlMtr67du1Su3bt7K0RAAAADpSvAJiUlCRfX9889/fx8ZGHh4eqVauW78IAAADgHPkKgOXLl9fx48fz3D86Olrly5fPd1EAAABwnnwFwBYtWmjNmjWKjY29a9/Y2Fh99913at26td3FAQAAwPHyFQCff/55JSUlqWfPnoqPj8+1359//qmePXvq2rVrGj58eIGLBAAAgOPk6zYw7du319ChQzVnzhw9+OCDGj58uDp06KAqVapIunWT6E2bNmnOnDmKj4/XsGHDWPwBAADgZvL9LOBPPvlEPj4++uCDDzR58mRNnjw5y3ar1Sqz2azXXnst2zYAAAC4Xr4DoMVi0bRp0zRs2DAtWLBAUVFRtmsCAwIC1LJlSz3zzDOqXr26w4sFAABAweU7AGaqXr263nnnHUfWAgAAgEKQr0UgAAAAuPe5bQDcs2ePunbtqlKlSql48eJq3ry5li1bluf3R0dHa/z48XrsscdUqVIlmUwmBQcH3/E9JpMp1z+DBw8u2IAAAADchN2ngJ1py5YtCg8Pl7e3t/r376+SJUtqxYoV6tevn86cOaNXX331rvvYsWOHJkyYIIvFogcffDBP9y6UpKCgoBzDXoMGDfI5CgAAAPfkdgEwLS1NQ4cOldls1vbt223Ba9y4cQoNDdXYsWPVu3dvBQUF3XE/bdq0UVRUlOrXr6+iRYvK29s7T8cPDg7W+PHjCzgKAAAA9+V2p4A3b96s6OhoDRw4MMusm6+vr8aOHaubN28qMjLyrvsJCQlR8+bNVbRoUSdWCwAAcO9xuxnArVu3SpLCwsKybQsPD5ckbdu2zWnHv3LlimbPnq34+HiVLl1arVq1Ut26dZ12PAAAgMLmdgHw2LFjkpTjfQQDAgJUokQJWx9nOHDgQLbH13Xp0kWRkZEqX778Hd+bkpKilJQU2+vExERJUmpqqlJTUyVJZrNZFotF6enpysjIsPXNbE9LS5PVarW1WywWmc3mXNvhXnL7OWX+/DN5eHjY+uel3dPTUxkZGUpPT7e1mUwmeXh45Nqe22fMUZ89dx6T5Cm4nrN+77nzZ89dx+SGJ/wMy5mfvfxwuwCYkJAg6dYp35z4+PjY+jjaq6++ql69eqlGjRry8vLSb7/9pokTJ2rNmjXq3r27oqKiZLFYcn3/5MmTNWHChGzt69evV7FixSRJgYGBatiwoX755RedPn3a1qdmzZqqVauWdu/erYsXL9raGzRooKCgIG3fvl1Xr161tbdo0eKugRSFL7ef0/r167P8wm7fvr2KFi2q1atXZ3l/165ddf36dW3ZssXW5uHhoW7duik+Pl5RUVG29pIlS6pDhw46c+aM9u/fb2svV66cWrZsqWPHjunIkSO2dkd/9tx5TFIPwfUyPwtG+uy565ikO183j8LjzM9exYoV81yHyXr7P0XcQFhYmDZs2KBjx46pWrVq2bZXqlRJSUlJ+Q6B3t7eCggI0MmTJ/P1voyMDHXo0EHbtm3TihUr9MQTT+TaN6cZwCpVqig+Pl4+Pj6SHP+vxqEz8jUcONGckcwAusuYXpjFDKA7+ORFZgDdZUzDP2IG0B3MGencGcDk5GT5+voqISHBljty43YzgJkzf7kFvMTERPn5+RVaPWazWUOHDtW2bdv0/fff3zEAFilSREWKFMnW7unpKU/PrH8hWSyWHGcTM7/ceW2He8nt5/TXn7897WazOccp/tzac/uMOeqzdy+MCa7lrN9798Jnz93GBPfhLr/33O5TkXntX07X+cXGxiopKanQnzNctmxZSVJycnKhHhcAAMAZ3C4Atm3bVtKt6+b+at26dVn6FJZdu3ZJ0l2fJAIAAHAvcLsA2LFjR4WEhGjx4sVZLoZMSEjQpEmT5OXlpUGDBtnaY2JidPjw4QIvDPn111+zXYMhST/88IOmTp0qT09P9enTp0DHAAAAcAdud2GZh4eH5s6dq/DwcLVp0ybLo+BOnTql6dOnZ5mJGzNmjCIjIzV//vwsj3CLj4/Xa6+9Znudmpqq+Pj4LH2mT59uO7373nvv6bvvvlPr1q1VpUoVeXp66uDBg1q/fr1MJpNmzZqlBx54wNnDBwAAcDq3C4DSreXvO3fuVEREhJYuXarU1FTVrVtXU6dOVb9+/fK0j6SkpGxPDElOTs7SNn78eFsA7NGjh65cuaIDBw5ow4YNunnzpgICAtS/f3+NHDlSoaGhjhsgAACAC7llAJSk0NBQrVmz5q79FixYoAULFmRrDw4OVn7ucNOzZ0/17NkzPyUCAADck9zuGkAAAAA4FwEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBgCIAAAgMEQAAEAAAyGAAgAAGAwBEAAAACDIQACAAAYDAEQAADAYAiAAAAABkMABAAAMBi3DYB79uxR165dVapUKRUvXlzNmzfXsmXL8rWPlJQUvf3226pevbq8vb1VsWJFDRs2TBcuXMj1PYsWLVJoaKiKFy8uPz8/de/eXXv37i3ocAAAANyGWwbALVu2qFWrVtq5c6f69u2r559/XrGxserXr5/ee++9PO0jIyNDPXr0UEREhMqWLauRI0eqRYsWmjt3rlq0aKGLFy9me88777yjp556ShcuXNDzzz+vPn36aPv27WrZsqW+//57Rw8TAADAJTxcXcBfpaWlaejQoTKbzdq+fbsaNGggSRo3bpxCQ0M1duxY9e7dW0FBQXfcT2RkpNatW6cBAwZo0aJFMplMkqR///vf+vvf/6633npLn332ma3/sWPHNH78eNWoUUO7d++Wr6+vJOmFF15Q8+bNNXToUP32228ym90yMwMAAOSZ26WZzZs3Kzo6WgMHDrSFP0ny9fXV2LFjdfPmTUVGRt51P3PmzJEkTZ482Rb+JGn48OEKCQnRokWLdP36dVv7/PnzlZaWpjfffNMW/iSpQYMGGjBggA4dOqSdO3c6YIQAAACu5XYBcOvWrZKksLCwbNvCw8MlSdu2bbvjPm7cuKFdu3apZs2a2WYKTSaTOnfurOTkZP30008OPS4AAMC9wO0C4LFjxyRJ1atXz7YtICBAJUqUsPXJTXR0tDIyMnLcx+37vn0/x44dU4kSJRQQEJCn/gAAAPcqt7sGMCEhQZKynIa9nY+Pj61PQfZxe7/M/y5fvnye++ckJSVFKSkp2eq4dOmSUlNTJUlms1kWi0Xp6enKyMiw9c1sT0tLk9VqtbVbLBaZzeZc22/euGNJKESJicr155T588/k4XHrq5eWlpandk9PT2VkZCg9Pd3WZjKZ5OHhkWt7bp8xR3323HlMN294Cq7355/O+b3nzp89dx3TzRtuN99jSImJcupnLzk5WZKyfMZy43YB8F42efJkTZgwIVt71apVXVANCtv/jXF1BYB74TsBZFVY34mrV6/mOgmWye0CYGbBuc22JSYmys/Pr8D7uL1f5n/np39OxowZo1GjRtleZ2Rk6NKlSypTpkyWhSjIKjExUVWqVNGZM2dss62AkfGdALLiO5E3VqtVV69eVcWKFe/a1+0C4O3X2zVu3DjLttjYWCUlJSk0NPSO+wgJCZHZbM71mr2crjOsXr26oqKiFBsbm+06wDtdl3i7IkWKqEiRIlnaSpUqdcf34H98fHz4YgO34TsBZMV34u7uNlmVye0uCmjbtq0kaf369dm2rVu3Lkuf3BQtWlShoaE6cuSITp06lWWb1WrVhg0bVLx4cTVp0sShxwUAALgXuF0A7Nixo0JCQrR48WLt37/f1p6QkKBJkybJy8tLgwYNsrXHxMTo8OHD2U7fDhs2TNKt07K3Xwz52Wef6cSJE3ryySdVtGhRW/uQIUPk4eGhd955J8u+9u/fry+++EIPPvigWrdu7ejhAgAAFDq3OwXs4eGhuXPnKjw8XG3atFH//v1VsmRJrVixQqdOndL06dMVHBxs6z9mzBhFRkZq/vz5Gjx4sK39mWee0dKlS/XFF1/ojz/+UNu2bXX8+HF9+eWXqlq1qv71r39lOW6NGjU0fvx4vfXWW6pfv7569eqlq1evasmSJZJu3Viap4A4R5EiRRQREZHt9DlgVHwngKz4TjieyZqXtcIusHv3bkVEROiHH35Qamqq6tatq1GjRqlfv35Z+g0ePDjHACjdui3LlClT9J///EdnzpxR6dKl1b17d/3rX/+Sv79/jsddtGiRZsyYoYMHD8rLy0utWrXSxIkT1ahRI2cNFQAAoFC5bQAEAACAc3BOEwAAwGAIgAAAAAZDAAQAADAYAiAAAIDBEAABAAAMhgAIAABgMARAAHATmXflSk9Pd3ElAO533AcQhS4jI4OnqgAA4EIEQLgUYRC4Ze3atfrtt9904MABlStXTqGhoapWrZoCAwNVpkwZWSwWWa1WmUwmV5cKFIr09HRZLBZXl3HfIgCi0MTFxendd99VWFiYmjVrplKlStm2Wa1WWa1WwiAM58qVK5o8ebKmTZsmi8WS5fRv6dKl1apVK/Xs2VOPP/54lu8McL/668RAXv9+4B9I+UMARKGJiIjQxIkTFRwcrNq1a6tdu3Zq27at6tWrl+UB3xkZGbJarbJYLNq6datu3LihLl26uLBywHmmTZum8ePHKzw8XC+//LIqVqyoffv26ciRI9qzZ4927dql+Ph4NWzYUP/85z/1+OOPu7pkwKk+/fRTbd26VYMGDVLbtm1VokQJ27aMjAxJYrLAAQiAKDQNGzbU77//rkaNGmnv3r1KTU1VUFCQWrVqpfbt26tVq1aqVauWrf+1a9c0YMAAffvtt0pOTpa3t7cLqwecIzg4WHXq1FFkZKTKlCmTZdv58+e1b98+rVy5UvPmzVN6erpmz56t5557zkXVAs5XtWpVnTp1SkWKFFH9+vUVFhamrl27qlmzZllm+NLS0uTh4aFr165p9uzZql+/vtq3b+/Cyu8tBEAUijNnzqhNmzYqU6aMoqKi9PPPP2v16tVauXKlfvnlF5nNZj300ENq06aN2rRpo/DwcB05ckSPPfaYmjZtqpUrV7p6CIDDHT58WE2bNtXLL7+sd955R1LOMxw3b97Uxo0b9dJLL+nKlSv69ttv1aJFC5fUDDjTwYMHVbduXTVu3Fh+fn7auHGjJKl48eJq1aqVunbtqrCwsCyTBTt37lSbNm3UsmVL7dy501Wl33M8XF0AjCEmJkaJiYlq27atPD091bRpU4WGhmrEiBHau3evvvnmG61Zs0azZs3SvHnz1KRJE3l6eiouLk7Dhg1zdfmAU1itVpUqVUrR0dGSbs1omM1mW/jL/Pe5l5eXunbtqtTUVPXs2VM7duwgAOK+9Ouvv0qSBg4cqFdeeUVHjx7V119/rS+++ELr16/X+vXrFRAQoHbt2umRRx5R9+7dtXv3bknSmDFjXFn6PYcZQBSK48ePa/To0erVq5cGDhyYbXtqaqrOnz+vHTt2aNWqVdq4caMuX76sUqVK6dKlSy6oGCgczZs31++//66lS5fqkUceybIt86L2zIviL126pCZNmqhx48Zavny5iyoGnGf27Nl6/vnn9d1332X7PuzZs0dffPGF/vvf/+rs2bOSpOrVqysxMVHXr1/XlStXXFDxvYurKFEoqlWrpnnz5ik8PDzH7Z6engoKCtLAgQO1dOlSTZo0SZI0YMCAwiwTKDSZ//b+6KOP5OPjo27duumVV17R7t27dePGDUmyXe+UmpoqSTpy5IhSUlJUsWJF1xQNOJHValW9evU0cuRI1ahRI0u7JDVt2lTvv/++jh49qlWrVmnQoEGKi4tTXFycnn76aVeVfc9iBhBOl9PS/PT0dJlMplxXcr3xxhuaPn26fvrpJzVq1KgwygRcIj09XQsXLtSYMWMUGxur2rVrKywsTC1btlTt2rVVq1Ytmc1mnTt3Tq+//rqWL1+uXbt28b3AfSspKUleXl7y8vLKtu2vf5+MGDFCn3zyifbu3asGDRoUYpX3PgIgCkXmlzY2Nlbly5fPEvzS09NlNpttX+qzZ8+qW7duOn/+vC5evOiqkoFCdfHiRc2cOVPLli3T0aNHVaxYMVWqVEklSpRQ6dKldfjwYV28eFFDhgzRJ5984upyAZfJ/PskOjpa/fr1U0JCgo4dO+bqsu45LAKBU6Wlpen777/XvHnzdPToUZnNZhUtWlT169dXr1691LJly2x3evf29tbgwYM5zQVDsFqtysjIULly5fSPf/xDvXr10p49e/T9999r165d2rdvn8qVK6cqVarozTff1FNPPeXqkgGXypwsOHTokPbu3avXX3/dxRXdm5gBhFNNnz5dEydO1NWrV1WtWjVZLBYdOXLEtr1WrVoaOnSoBgwYoICAAFv7zZs35eHhwc0+YUgZGRm6ceOGvLy8lJCQoNjYWD300EOuLgsoFHl9okdcXJzWrl2rRx99VKVLly6Eyu4vBEA4zR9//KG6deuqUaNGioyMlJeXl/z9/RUbG6tVq1Zp+fLl2rp1qySpQ4cOevfdd7muCfe969ev6/Tp0woMDFTRokWzbMvIyJDJZLL95ffXvwh5djbuR3f6TtwNzwu2HwEQTjNu3Dh99tlnWrx4sTp27Cgp+19ov/76q6ZPn65ly5YpKChIixYtUuPGjXmmI+5bU6ZM0YoVK/TEE0+oefPmqlmzpvz9/bP8JZb5aznzO3Dx4kX5+fnJw4OrdnD/yct34q/4ThQcARBO06tXL+3fv19btmxRYGCg7bE9mdc83f7l/vDDD/XKK6/omWee0fz5811YNeBclStX1vnz52WxWOTr66uWLVsqLCxMzZo1U0hISLbHwSUnJ2v8+PH6888/NXfuXGYAcd8pyHdizpw5zADaiegMp2nYsKG++uorJSUlSZLtX2omk8n2hc2c6ft//+//aceOHdq8ebNOnDihkJAQl9UNOMvRo0eVkJCgFi1aaODAgdqwYYOioqL07bffKjAwUO3atVOnTp3UsGFDVapUSaVKldJvv/2mOXPmqF27doQ/3HcK+p0g/NmPAAinyXwo95NPPqn33ntPrVu3zvG+TpnXcNSsWVNr1qyxBUbgfnP06FHduHFDYWFhevHFF9W9e3cdOXJEUVFR2rx5s1asWKFFixapdu3a6tChg7p06aJNmzYpMTFRQ4cOdXX5gMPxnXAdTgHDadLT0zV69Gi9//77qlWrll588UX17t1b/v7+2fpevnxZI0eO1Jo1a3ThwgUXVAs433//+1/17dtXS5YsUd++fW3tqampOnXqlA4cOKAdO3Zo69atOnTokDw9PWW1WlWkSBEeiYj7Et8J1yEAwuk+++wzTZs2TSdOnFDFihXVs2dPPfLII6pSpYosFotKlSqljz/+WDNmzNALL7yg9957z9UlA05htVp1+PBheXt7q2rVqjkudkpOTtbRo0d15MgRzZ8/Xxs2bNCIESP00UcfuahqwHn4TrgOARBOZ7Vadfz4cc2ZM0dLliyxPcS7fPny8vT0VExMjDIyMjRgwABNnTpVlStXdnHFQOHL6S++l19+WTNnztTPP/+shg0buqgywDX4TjgXARCFKjk5Wbt379bKlSt1/vx5XbhwQT4+Purbt6969eolb29vV5cIuFTmvf5OnjypHj166PLlyzp9+rSrywJchu+Ec7AIBIWqePHiat++vdq3b6/U1FR5enq6uiTArWSu9D137pxSU1P1wgsvuLgiwLX4TjgHM4AA4IasVqvOnj2r0qVLq3jx4q4uB3A5vhOORQAEAAAwGO4qCgAAYDAEQAAAAIMhAAIAABgMARAAAMBgCIAAAAAGQwAEAAAwGAIgAACAwRAAAQAADIYACAAAYDD/H+OQK8g1DzLJAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(result.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "7cfef097-78ef-4c57-b5b7-187a39c94408",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2096.01x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import ZZFeatureMap, PauliFeatureMap\n",
    "num_qubits = 5\n",
    "map_zz = ZZFeatureMap(feature_dimension=num_qubits, reps=1, entanglement=\"linear\", insert_barriers=True)\n",
    "map_zz.decompose().draw(output=\"mpl\", style=\"iqp\", initial_state=True, scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "753d4a74-0ba0-413b-b552-32d3c31d698c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1089.81x225.75 with 1 Axes>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from qiskit.providers.fake_provider import FakeManilaV2, FakeAthensV2\n",
    "from qiskit_ibm_runtime.fake_provider import FakeProvider\n",
    "from qiskit import transpile\n",
    "\n",
    "backend1 = FakeProvider().get_backend(\"fake_manila\")\n",
    "\n",
    "tp_map_zz = transpile(map_zz, backend)\n",
    "tp_map_zz.decompose().draw(output=\"mpl\", style=\"iqp\", initial_state=True, scale=0.5\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "c06f7a85-53ef-49a9-8e30-65556dffae77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 674.623x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import RealAmplitudes\n",
    "\n",
    "ansatz = RealAmplitudes(5, reps=1, parameter_prefix='θ', insert_barriers=False)\n",
    "ansatz.decompose().draw(output=\"mpl\", style=\"iqp\", initial_state=True, scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "78baf1e7-7d13-4fdd-9f9c-9bd45703db47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 674.623x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
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    }
   ],
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    "tp_ansatz = transpile(ansatz, backend)\n",
    "tp_ansatz.decompose().draw(output=\"mpl\", style=\"iqp\", initial_state=True, scale=1)"
   ]
  },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Qiskit Version:  1.0.2\n",
      "Qiskit IBM Runtime Version:  0.21.2\n"
     ]
    }
   ],
   "source": [
    "import qiskit\n",
    "import qiskit_ibm_runtime\n",
    "\n",
    "print(\n",
    "\"Qiskit Version: \", qiskit.version.get_version_info())\n",
    "print(\n",
    "\"Qiskit IBM Runtime Version: \", qiskit_ibm_runtime.version.get_version_info())\n",
    "\n"
   ]
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