GHZ-on-Real-Devices.ipynb

{
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   "source": [
    "# Winning the GHZ Game on Real IBM Quantum Computer<a name=\"top\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "*Lennart Schulze, Dr. Jan-Rainer Lahmann, October 2020*\n",
    "\n",
    "updated to Qiskit v1.x by *Davide Moretti, November 2024*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The GHZ game is a serious game for quantum computing to show the quantum mechanical property of entanglement. Three players are asked for two different properties A and B of an object, an each property can be one of two conditions 1 or 0. When all are asked for property A, 1 should appear two times or zero times. When two players are asked for property B, 1 should appear three times ore one time. When the players don't know what the other two were asked, respectively, there is no strategy in classical logic that can lead to winning in all cases. Using Quantum Computing, however, there is. If you wish to find out more about this game, click [here](https://github.com/JanLahmann/Fun-with-Quantum/blob/master/GHZ-Game.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
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     "name": "#%% md\n"
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   },
   "source": [
    "The Qiskit built-in local Aer-simulator for running the Quantum circuit of the GHZ game is perfect, giving us the results that we expected from theory. In reality, however, the imperfection of real Quantum Computing hardware returns \"noisy\" output due to various sources of errors. Luckily, there is a variety of options available to mitigate these effects, some of which we will apply and inspect in this notebook."
   ]
  },
  {
   "cell_type": "markdown",
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     "name": "#%% md\n"
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   "source": [
    "In the following, we will have a closer look by:\n",
    "1. Comparing IBM Quantum devices [[Go](#devices)]\n",
    "2. Manually optimizing our circuit for a specific device [[Go](#manual)]\n",
    "3. Using the Qiskit transpiler optimization [[Go](#transpiler)]\n",
    "4. Best system ..? [[Go](#mem)]\n",
    "\n",
    "Appendix [[Go](#appendix)]\n",
    "* Running this notebook on real Quantum Computers [[Go](#appendix-b)]\n",
    "\n",
    "_____"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   },
   "source": [
    "## Setup\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   },
   "source": [
    "We'll define our global variables: 3 qubits are needed for our circuit (GHZ state), and we use a high number of shots (=times a circuit is executed per run on a device, out of which the relative result distribution is calculated) to get consistent results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
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   },
   "outputs": [],
   "source": [
    "# global vars\n",
    "n = 3 # number of qubits\n",
    "shots = 8000 # high number of shots per execution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For the remainder of this notebook, this will be our reference circuit for assessment. Note that the GHZ game uses 4 distinct circuits. These, however, only differ in their measurment base and order, but all have the same core - the GHZ state, which is the entanglement of 3 qubits (see part before the first barrier)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit   # circuit creation\n",
    "\n",
    "# basic circuit\n",
    "name = \"GHZ yyx default\" # ghz in measurement base Y,Y,X\n",
    "ghz = QuantumCircuit(n,n, name=name) # create circuit\n",
    "ghz.h(0) # h gate\n",
    "ghz.cx(0,1) # cnot gate\n",
    "ghz.cx(0,2) # cnot gate\n",
    "ghz.barrier()\n",
    "ghz.sdg([0,1]) # s dagger gate\n",
    "ghz.h(range(n)) # h gates\n",
    "ghz.barrier()\n",
    "ghz.measure(range(n), range(n)) # measurements\n",
    "ghz.draw(\"mpl\") # draw cirucit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In order to evaluate the accuracy of the results of executing the GHZ state on different devices and with different mitigation techniques, we need a metric which we will define as state accuracy. It represents the percentage of counts resulted from the experiment that belong to one of the four target states of the GHZ game ('001', '010', '100', '111'). Reaching either of them equals winning they game, therefore our metric represents the fidelity with which we win the GHZ game on our quantum computer. We will use the state accuracy to measure the effectiveness of our different optimization approaches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "expected_states = ['001', '010', '100', '111']  # target states\n",
    "\n",
    "def get_state_accuracy(counts): # funciton to calculate state accuracy\n",
    "    expected_counts = 0\n",
    "    for state in counts.keys():\n",
    "        if state in expected_states:\n",
    "            expected_counts = expected_counts + counts[state]\n",
    "    state_accuracy = expected_counts / shots\n",
    "    return str(state_accuracy*100)+\"%\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For reference, this is what the state accuracy would look like for results from a perfect backend (100%)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "state accuracy on the simulator: 100.0%\n"
     ]
    }
   ],
   "source": [
    "from qiskit_ibm_runtime import Sampler # importing primitive for execution\n",
    "from qiskit_aer import AerSimulator # importing simulator\n",
    "\n",
    "backend = AerSimulator()\n",
    "sampler = Sampler(mode=backend)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "counts = sampler.run([ghz]).result()[0].data.c.get_counts() # execution on simulator\n",
    "state_accuracy = get_state_accuracy(counts)\n",
    "\n",
    "print(f\"state accuracy on the simulator: {state_accuracy}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that the state accuracy is a custom metric designed for our needs. Depending on your research aim, other metrics such as the built-in [hellinger fidelity](https://docs.quantum.ibm.com/api/qiskit/quantum_info#qiskit.quantum_info.hellinger_fidelity) might be a better choice to assess circuit execution on different devices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Great, now we're all set to run our experiments!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 1. Comparing IBM quantum devices<a name=devices><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To start with, we need to find available quantum devices that are suitable to run our experiment. However, in case IBM Quantum devices are busy with jobs from other users, the execution of the following experiments take very long. To avoid this, we will use Qiskit built-in mock implementations of them, executed locally.\n",
    "\n",
    "(If you want to try out this notebook on real systems, execute the cell above again and read the [appendix](#appendix-b) for detailed instructions.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime.fake_provider import *     # mock devices\n",
    "\n",
    "backends = [FakeWashingtonV2(), FakeTorino(), FakeSherbrooke(), FakeQuebec(), FakeBrisbane(), FakePrague(),\n",
    "                FakeOsaka(), FakeKyiv()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now, let's compare the results from the execution of the GHZ circuit on these backends:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager # we'll talk about it at the end of chapter 3\n",
    "from qiskit_ibm_runtime import Sampler  # primitives that run the circuit\n",
    "from qiskit.visualization import plot_distribution # visualize results\n",
    "\n",
    "results_backends = []\n",
    "\n",
    "for backend in backends:\n",
    "    \n",
    "    sampler = Sampler(mode=backend)\n",
    "    sampler.options.default_shots=shots\n",
    "\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=0) # pass manager, advanced way to transpile, see end of chapter 3 for more details\n",
    "    circuit_isa = pm.run(ghz)\n",
    "\n",
    "    counts = sampler.run([circuit_isa]).result()[0].data.c.get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backends.append((backend.backend_name, counts, state_accuracy)) # store results\n",
    "    \n",
    "# plot results\n",
    "plot_distribution([counts for backend_name, counts, state_accuracy in results_backends],\n",
    "                legend=[backend_name for backend_name, counts, state_accuracy in results_backends],\n",
    "                sort=\"asc\",\n",
    "                color=[\"red\", \"orange\", \"yellow\", \"green\", \"blue\", \"violet\", \"purple\", \"black\"],\n",
    "                bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The bars represent the relative amount (probability) to read a certain state from the execution of our circuit on the respective backend over the 8000 times the experiment was executed there. Remember that ideally, only four states should be returned by our circuit: 001, 010, 100, 100. Therefore, the best devices are those with the highest probability on these states while having the lowest on all other, undesired states."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To make it easier to interpret, we use the state accuracy as indicator of the results' quality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>backend</th>\n",
       "      <th>state_accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>fake_prague</td>\n",
       "      <td>94.0375%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fake_sherbrooke</td>\n",
       "      <td>93.5875%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>fake_quebec</td>\n",
       "      <td>92.2625%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fake_brisbane</td>\n",
       "      <td>92.07499999999999%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fake_osaka</td>\n",
       "      <td>91.3625%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fake_washington</td>\n",
       "      <td>88.4875%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fake_torino</td>\n",
       "      <td>87.7%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fake_kyiv</td>\n",
       "      <td>79.05%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           backend      state_accuracy\n",
       "0      fake_prague            94.0375%\n",
       "1  fake_sherbrooke            93.5875%\n",
       "2      fake_quebec            92.2625%\n",
       "3    fake_brisbane  92.07499999999999%\n",
       "4       fake_osaka            91.3625%\n",
       "5  fake_washington            88.4875%\n",
       "6      fake_torino               87.7%\n",
       "7        fake_kyiv              79.05%"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# setup ordered table\n",
    "import pandas as pd # handy tools for calculation\n",
    "\n",
    "results_backends_table = pd.DataFrame(columns=[\"backend\", \"state_accuracy\"]) # create table\n",
    "for backend_name, counts, state_accuracy in results_backends:\n",
    "    results_backends_table.loc[len(results_backends_table)] = [backend_name, state_accuracy] # put values into table\n",
    "results_backends_table = results_backends_table.sort_values(by=[\"state_accuracy\"], ascending=False).reset_index().iloc[:, 1:] # sort values\n",
    "results_backends_table \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now we know the ranking of the devices based on their fidelity. Let's pick one with the worst state accuracy to test the optimization techniques in the remaining chapters. In addition, we will pick one system with the best accuracy to compare it against later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# high accuracy\n",
    "backend1 = FakeSherbrooke()\n",
    "\n",
    "# lower accuracy\n",
    "backend2 = FakeKyiv()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 2. Manually optimizing circuits<a name=manual><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Why is it that the IBM Quantum computer show different performances? As mentioned earlier, hardware optimization is a major research field at the moment. Essentially, our Quantum computer consist of different numbers of qubits that are connected with each other and manipulated according to our circuit. However, the way in which they are connected - the so called coupling map - as well the error rates when performing gates on single qubits, multiple qubits and when reading the state of the qubits differs across our devices due to manifacturing. Finally, the qubits posess varying coherence times (T1/T2). \n",
    "\n",
    "Let's have a closer look on how the coupling map and error rates look like on the \"worst\" among picked devices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'fake_kyiv'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend2.backend_name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "On the Configuration tab you can see the coupling map of the devices. Qubits that are connected with a line can perform a multiple qubit gate such as CNOT directly. Trying to apply CNOT on non-connected qubits would require Qiskit to internally change the circuit before execution to fit it to the coupling map of the device. \n",
    "\n",
    "On the Error Map tab you can see the quality of each qubit and each connection where a darker color indicates a lower error rate (more desirable). If you are interested in the exact error rates, you can find them on the Qubit Properties tab (U2 - single qubit error rate, readout error rate) and on the Multi-Qubit Gates tab."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Coupling Map based optimization**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The Qiskit transpiler prepares our code for execution on the real device. In case our circuit layout does not match the device's configuration, it will introduce swaps into our circuit so to make it applicable to the coupling map. Sometimes this can produce a worse accuracy than that from our original circuit. Therefore, let's try to create custom coupling map specific circuits of the GHZ state to avoid the transpiler interfering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Backend 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9Z1A9WoJlA31iYqIyMzM1fvx4hYaGau/evYqOjtaLL76oFStWaOfO43ca/Xmg79mzZ4Nj5bdt23ZG00DBe4wM1QR687Pb7YqKirLsWaR9r9yh727orNznb9bBFc/JsfpV5b81T9tuH6DK3C2KHjVNYckNf10O/2D1HvAHOTk5tf9/8nWATeVJmD+hW7f/Xky/Z88ej4+JlmXZQC8dD+fLly/X0aNHdfToUX3zzTe66aabVFZWpr179yogIEB9+vSps81ll12mL7/8snZKS0n65ptvtHv3bk2YMMHXLwENGDfcmFlmAgJsGnNuJ0OODe/Jy8vTnXfeWafHraTzjKcUde5VKsv+t/IzHlTun2/SweXPKii6k7r89hUlz/qr0SXCYFbvAX9w8sx5nt4grDlhXpI6d/7vLFEHDpzqajYYwS8/nm/dulVut1upqan1vqa66aabtGjRIl1xxRWaN2+eKisrNWfOHA0ZMkRXXHGFQRXjZBMv6qKO0aE6eLjSp8edMKKzOsc1fJMymEdpaakyMzN14403Gl1Ki2h7zsVqe87FRpfRaozo0FHHJlxzynVOt9xqrN4D/iAmJkZ9+/bVsWPHPBoOnJeX16wwL0nt27dXamqqgoODddZZLTtjFDznl4H++++/l1R/uI10/JbJa9as0ezZs3XttdfKbrfrsssu09NPP60AE866YEXBQYG6cVIP/enlb3163FunMOQKAGC88847T+edd57H28XHx+t//ud/9NVXX3kU5qXjZ+gfeughj48J3yDQN6B79+5avny5L0uCh27/VR+9vDTbZ2fpRw2O15hzmbYNAGBegYGBuu2225ScnKxx48Y1Ocyj9fPLU86nC/Ro/TpEheov9w33ybEiwux6Zd4FCgho+M54AACYRWBgoC6//HLCvMX45Rn6NWvWGF0CvGDiRcmaNiFFb7z/Q5O3OXHDqNPdgOpkz8w5V10TIz2uD61TbGysZs+erdjYWKNLAQxBDwDW45eBHtbx0gPn68ChCq36qmk3yjndjad+7v6bz9FvJvVoTmlopWJiYjR16lSjywAMQw8A1uOXQ25gHSHBgXrv/8boilGeTdvVFI/MHKgHbz3H6/uFsUpKSrR69WqVlJQYXQpgCHoAsB4CPUwvNMSud58eo2fmDFVYaOAZ769zXIRW/eUS3XvTANlsjJu3mvz8fM2dO1f5+flGlwIYgh4ArIdAD0sICLBp9q/66Lt/XKVLL2jejadCQwJ165Se+n7pVbr4PGNuXgUAAOApxtDDUlKS2mrFny/RDz+W6C9vb1fGh3uUf/DUF8D26t5eN0xM1a+vSFV0uxAfVQoAAOAdBHpYUkpSWz1x11A9cddQ5R8s08Zth5S9t1gPvbhZR8uq1a5NkN77v7E6Jy1G7SKZugsAAJgXgR6W16ljhDp1jNAESc/8vy06WlatNuFBGjk43ujSYICQkBD16NFDISF8GwP/RA8A1kOgB+BXunbtqjfffNPoMgDD0AOA9XBRLAAAAGBiBHoAfiU7O1vDhw9Xdna20aUAhqAHAOsh0APwK263W9XV1XK73UaXAhiCHgCshzH0ANAKhQZKmZcaXYVnvHBft/8KCZH97de9uEMf4CJTeFlgYKAmTZrklX0tfHGJjpaVKTIiQnffPKXR585EYKA33wTgCQI9ALRCNpsU5sfv0DabTQoNNboMwFA2m012u3feCNySXO7jf57YZ0PPwZwYcgMAAACYGB/HAPiV5ORkZWRkKCEhwehSAEPQA4D1EOgB+JXQ0FB1797d6DIAw9ADgPUw5AaAXykoKNAjjzyigoICo0sBDEEPANZDoAfgV4qLi7Vs2TIVFxcbXQpgCHoAsB4CPQAAAGBiBHoAAADAxAj0AAAAgIkR6AH4lejoaE2fPl3R0dFGlwIYgh4ArIdAD8CvBAQEKCgoSAEBvP3BP9EDgPXQzQD8isPh0OLFi+VwOIwuBTAEPQBYD4EeAAAAMDECPQAAAGBiBHoAAADAxAj0APxKZGSkxo0bp8jISKNLAQxBDwDWYze6AADwpYSEBD300ENGlwEYhh4ArIcz9AD8SlVVlfbt26eqqiqjSwEMQQ8A1kOgB+BXcnJyNGnSJOXk5BhdCmAIegCwHobctFJut1sy09mTkBDZbDajqwAsw+2WKp1GV+GZ0EDJW28DpnsPlHgf9DK32y2n01xNEBgYyL8BGIJA31pVVanmmulGV9Fk9rdfl0JDjS4DsIxKp3TBB0ZX4ZnMS6Uwb/1WMdl7oMT7oLc5nU4tXbrU6DI8MmnSJNntRCv4HkNuAAAAABMj0AMAAAAmxvdCAPxKWlqa1q1bZ3QZgGHoAcB6OEMPAAAAmBiBHoBfyc3N1YwZM5Sbm2t0KYAh6AHAegj0APxKRUWFtmzZooqKCqNLAQxBDwDWQ6AHAAAATIxADwAAAJgYgR4AAAAwMQI9AL8SHx+vefPmKT4+3uhSAEPQA4D1EOgB+JV27dopPT1d7dq1M7qUVsfxyWvKvnek0WWghdEDzZeTk6PKykqjywDq4cZSAPxKUVGRVq9erTFjxigqKsrocgCf86cecLvd2rVrl3bu3Kk9e/boxx9/VHl5udxut4KCghQfH69u3bqpe/fu6tu3r0JCQhrdV3Z2tubPn6+uXbvqnnvuUWhoqA9fCXBqfhHoHQ6HHn/8cb377rvKy8tTbGysrrrqKj366KOaNWuWXn31VS1atEgzZ840ulQALezAgQNauHCh+vbta/kw01R7F/1GRV++JbezRm5ntTZPaSNJGvD3YtkCAw2uDt7mDz1QXl6uL774QqtXr1ZeXl6j6x08eFDffvutJCkiIkIXXnihxo4dq06dOtVZ70SYr6ys1Pbt2/XPf/5Tv/jFL1r0NQCesHygz8rKUnp6ugoLCxUREaFevXopPz9fzz77rHbv3q3Dhw9LkgYMGGBsoS3kc8dBjf36Mz3Wq59+1z2twXWC339bl3aM13tDL/Bxdb5TUnpMyz/fp6Pl1ZKkyiqnampcstv9Y9SZ2+3W5xsKteWHIlVU1qhDVKjGX9BZHWPCjC4NLaCqcI8Klz6mo1u/0LGfflRAUIiCouIUfvYQdRj9a0X2G1Vn/eTfLlbybxfL8clrOrTmNfX402fGFN4CeA/0P+vWrdMrr7yi4uLiesvsdrvatm0r6fh8/CfPxV9WVqaVK1fqww8/1GWXXaarr75awcHBdcK8JPXr10+TJk3yzYsBmsjSgd7hcGjChAkqLCzUnXfeqQceeECRkZGSpMcff1z33HOP7Ha7bDab+vXrZ3C1aAk/FpRq/uJv9f9W/KDS8pra5w8VVyl53BLdfHWa7pzWV+Fh1mwFp9OlF97eoT+/tU07cur+cguyB+jqi7vqDzf0U5+zow2qEN5WtmuDdt47QjZ7kKJHTlNYUm+5jlWoKn+XSrI+UmBYZL1AD1hBeXm5Fi9erK+++qrO82lpaTr//POVkpKixMRE2e3H3+/dbrccDodycnK0YcMGff3116qurpbb7db777+vjRs3asKECXr99dfrhPm77rpLwcHBPn99wKlYM8X8x6xZs5SXl6eZM2fqiSeeqLNszpw5+vvf/65vv/1WXbt2rf3EDuvI2nFI4/53lQ4cavhuiPsPluv+P2/Sii/26YPnL1F0u8bHTppR1TGnrp3zqd5b0/Dt3atrXPr7B7v1r09ztfSpi3TJ8EQfV4iWULBknlxV5eq5IEvhXfvXW15dVGhAVUDLOnr0qObPn689e/bUPjdw4EBNmTJFSUlJDW5js9kUGxur2NhYDRkyRNddd50+/PBDvffee3I6ncrPz9eLL75Yuz5hHq2ZZccbbN++XUuWLFGHDh00f/78BtcZOHCgJKl////+0jvxAWDIkCEKCQmRzWbzSb3wrn2FpUq/tfEwf7Jvvv9JV87+WNXVLh9U5js3zfuy0TB/srKKGl11xyfatM3hg6qMFx4erqFDhyo8PNzoUlpEZf4uBUbGNBjmJSkoKs7HFaG1sVoPlJeX1wnzERERuu2223TXXXc1GuYbEhkZqauvvlqPPfZYvTH0KSkphHm0apYN9BkZGXK5XJo6daratGnT4DphYcfHD58c6H/44QctXbpUcXFxGjx4sE9q9YVyp1OOqqoG/7Oiha99r0LH6cP8CZmbDuhfn54+/JrF5u0OvfH+D01ev7yyRvf9eWMLVtR6JCUladGiRR79ojeTkLjuch49pKKv3zW6lFbF394DT8VqPfDqq6/WhvmoqCg9+OCDuuCCC5p9Qq68vLz2+roTHA6Hjh07dsa1Ai3FskNu1qxZI0kaNarxsaInrnw/OdBfeOGFKigokCQ9+OCDWrt2bQtW6TsPZW/VQ9lbjS7DJ0rLq/X6sl0eb/f8ku2afHHXFqjI9154e4fH26z8Mk978krULdHaw8+cTqcqKioUFhamQAvO4BJ/zR919NuPteexSQrpdLba9DxfEWcPVps+IxXWuafR5RnGn94DT8dKPbBhwwZ9+eWXko5/8zB37lx17ty52fv7+QWwERERKisr05EjR/TGG2/o1ltv9UrdgLdZNtDn5h4/29qlS5cGl9fU1NSG9ZMDfUCANb+0+E1SN03q1PCbXPq/P/dxNS3rwy/zVFJa7fF2n64vUKGjXHEdzP01tNvtVsbKPadfsd520turcvT7GxoeqmEVu3bt0rRp0/TGG28oLa3hWU/MrE3aMPV8cqMO/OtJFW9cqUOf/FWHPvnr8WW9LlDy7NcUEtetwW1tgUEKCLbmzEf+9B54OlbpgcrKSi1evLj28fTp070a5vv166cZM2Zo7ty5tdNgDh8+vE5mAFoLywb6srIySaozJdXJlixZIofDocjISHXt2rJnZQcNGqTCQs8uRAsLCNC2AcO8VkNKmza6KPYsr+3v51JTU1Xhah1j0EtDhkgR45u1bf+BFyjIecDLFfmWW3aVRt/XrG0fWbBIzz3woZcralmTJ0/2aP2DBw9KklauXKmNG5s2zGjixIke13WmbMFhOusZz79pkqSw5L5Knv2aJKnqYK5Kt3wux8eLVbotUz88eoV6PrlRAUH1xwLHjJyqmJFTm11zaurZch9r+lC3UzHbe6Bk3PugVXsgODi40WvgJOnLL7/UkSNHJEnnnHOOLrzwwmYfq6Ewf2LM/LRp0/SXv/xFkrRixYpTBvrU1NRWOzRn4vW3K6JNWxUUFigxMbHR52CcuLg4bdiwoVnbWjbQx8XFqaioSJs2bdKwYXV/KRQUFOjuu++WdLxpW/rC18LCQu3fv9+jbcIDA6UBLVNPS8jPz1e502l0GcdFHZIimrfpwQP5UpXZZwEJlJo5C2XZ0WKVFXr2b9VoJz68N9WJD/kVFRVN3tbT/vWGgJBweSN+hnTsopDR0xQ96jpl/+EClW1fq/Jd69Sm1/le2Htd+fn5clWVe2VfZnsPlIx7H7RqD5zqrq1ut1sfffRR7eNrrrmm2b/LTxXmpeNDcd99910dPHhQ3333nQoKChQfH9/gvvLz81XVSq/LcP3n36bL6az9+2zoOZiTZQP9mDFjtH37di1YsEBjx45VamqqJGn9+vW67rrr5HAcn9HDFzeUiovzfFaJMJMN/enUqVOrOUNfZXfKIR0fQ+LJG7y7WvEdwhSghJYqzWcKnUVyBnp+B8j24ccUkWCu1x8R4dmntxMBJiwsrMnbJhjwM7F5eeiLzWZTROpQlW1fq2OHWuYXd6dOnbx6ht5sjHoftGoPnGpGmb179+rHH3+UdHwGmuZ+0366MC8dH4o7duxY/e1vf5MkffbZZ43eJbZTp06t9gx9wH+ulwgIDKz9+2zoORinOXnxBMsG+hPzzO/bt0+9e/dWWlqaKisr9cMPPyg9PV3JyclatWqVT8bCNefrE3dlpWqumd4C1bSMnTt3yhYaanQZkiSXy60el/9DP/xY4tF210/spVcf8nzseWv06MtZuneRZ7PWtAm368ev31FkhLmmZVu/fr1H6+/YsUMZGRlKT09v8vjhZ555phmVnZmKGumCDzzfriTrY0X2HSVbYN23d1dVhUqyjp/RDOvcyxsl1rNz5y556x5tZnsPlIx7H7RqD9TU1Gjp0qUNLtu5c2ft/59/fvO+bWpKmD9h+PDhtYF+167Gh8Lt3Lmz9sZVrc2jf/6bSkrLFB8XXzspSEPPwZzMdwqkiRITE5WZmanx48crNDRUe/fuVXR0tF588UWtWLGi9s2Ai1usJyDApv+9xvMLvf73GuvMAHLDVT0UHORZe0+bcLbpwnxzpKSkaNWqVUpJSTG6lBax75U79N0NnZX7/M06uOI5OVa/qvy35mnb7QNUmbtF0aOmKSy5r9FlwkBW6IGcnJza/+/evbvH23sS5iUpOjpa0dHRtcd2tZJvpIETWufHSC/p2bOnli9fXu/50tJS7d27VwEBAerTp48BlaGlzfxFL634Yp/WrCto0vpzf9Nfg/vEtnBVvnNWTJj+ct9wzbg/s0nr9+zWXo/8dmALV9U62O12RUV5PhzJLDrPeEpHvvmXSrd/qaKvlspZdkSBEe0U1qWf4ibdo5jRvza6RBjMCj1wYriNzWZrdDa7xnga5k/o2rWrDh8+rIqKCjkcDnXs2LF5xQMtwNKBvjFbt26V2+1Wampqg3fK+8c//iFJ2rZtW53HycnJGjRokO8K9YIRHTrq2IRrTrnO6ZabUXBQoP717Fhdc9carfzy1F8j3ntjfz0803ph9vorU1VT49L//ukrOZ3uRtf7n54xWv7cxYpq2/gFaFaSl5enp59+WnfccYclZ3Voe87FanvOxUaX0Wr463vgqVihB8rLj198HRER4dHdW5sb5iWpXbt2tf/f2Ax6gFH8MtB///33khofbnP11Vc3+Hj69Ol67bXXWrQ2eE+b8CAtf+5irVqbpxfe3qHlX/wo939ybXioXb+6rLv+95qeGpAWY2yhLejGyWkaPbSTXnxnh175504dLv7v7AsXDozTrVN6auJFXRQcZO6by3iitLRUmZmZuvHGG40uBTCEFXpg3rx5qqqqktPDWYVyc3ObFeal41ng8ssvV3BwsNq2tfYN+GA+BPoGuN2Nn82EuQQE2JR+QWelX9BZR0qq9FNRpeyBATorJkzh3rp6r5Xr3rmtHv/dED3y24FKuvgtHThUqbgOYfr8r82bqx8AjHby2XJPXHzxxXI6ndq8ebNHYV6S6Ycpwdr8I9H8zOkCPaypfdsQtfeTYSUNCQ4KlD3w+IWygQEte+8FAGit0tPTdckll1j2zvDwT34Z6NesWWN0CQAAwCCEeVgN/6IB+JXY2FjNnj1bsbHWmdUI8AQ9AFiPX56hB+C/YmJiNHXqVKPLAAxDDwDWwxl6AH6lpKREq1evVkmJZ3cSBqyCHgCsh0APwK/k5+dr7ty5ys/PN7oUwBD0AGA9BHoAAADAxAj0AAAAgIkR6AEAAAATI9AD8CshISHq0aOHQkL89yZj8G/0AGA9TFsJwK907dpVb775ptFlAIahBwDr4Qw9AAAAYGIEegB+JTs7W8OHD1d2drbRpQCGoAcA6yHQA/Arbrdb1dXVcrvdRpcCGIIeAKyHMfStVUiI7G+/bnQVTcfFVYBXhQZKmZcaXYVnQgO9uDOzvQdKvA96WWBgoCZNmuS1/S18cYmOlpUpMiJCd988pd5jbwgM9GYTAE1HoG+lbDabFBpqdBkADGKzSWF+/A7NeyBsNpvsdu81gVuSy338T7vdXu8xYGYMuQEAAABMjI+kAPxKcnKyMjIylJCQYHQpgCHoAcB6CPQA/EpoaKi6d+9udBmAYegBwHoYcgPArxQUFOiRRx5RQUGB0aUAhqAHAOsh0APwK8XFxVq2bJmKi4uNLgUwBD0AWA+BHgAAADAxAj0AAABgYgR6AAAAwMQI9AD8SkBAgM455xwFBPD2B/9EDwDWQzcD8Csul0ubN2+Wy+UyuhTAEPQAYD0EegAAAMDECPQAAACAiRHoAQAAABMj0APwK5GRkRo3bpwiIyONLgUwBD0AWI/d6AIAwJcSEhL00EMPGV0GYBh6ALAeztAD8CtVVVXat2+fqqqqjC4FMAQ9AFgPgR6AX8nJydGkSZOUk5NjdCmAIegBwHoYcgMArZDb7ZbMdgY1JEQ2m83oKgBYhNvtltPpNLoMjwQGBhryPkigB4DWqKpKNddMN7oKj9jffl0KDTW6DAAW4XQ6tXTpUqPL8MikSZNkt/s+XjPkBgAAADAxAj0AAABgYgy5AeBX0tLStG7dOqPLAAxDDwDWwxl6AAAAwMQI9AD8Sm5urmbMmKHc3FyjSwEMQQ8A1sOQG8DC8g+W6ausg9q43aGsHYd18HClJOmnokpNm/u5BvXuoIG9Omho31jZ7f7x+b6iokJbtmxRRUWF0aUAhqAHAOsh0AMW43K59fHX+/X8ku1a/sU+uVzueuscq3bpzeU/6M3lP0iSEjqG66bJabpxUg/Fx4b7umQAAHAG/OOUHOAnvt95WEN+uUzj/neVln32Y4NhviH7D5brgec3qcslSzTvhU2qrna1cKUAAMBbCPSABbhcbj36cpYGXvsvbdzmaPZ+qmtcevCFzRoy9V/asuuwFysEAAAthUAPmFx1tUvXzf1c9y7aqOoa75xZz9pxWOdNW64vNhR4ZX+tSXx8vObNm6f4+HijSwEMQQ8A1kOgB0zM6XRp+h8/198/2O31fR8tq9alt32kr7894PV9G6ldu3ZKT09Xu3btjC4FMAQ9ADSfy9U6h6RyUSxgYo//9XtlrNzTYvsvq6jRFbNWa+s/r1JsdFiLHceXioqKtHr1ao0ZM0ZRUVFGlwP4HD0Af+N2u3Xo0CHt2bNH+/fv17FjxyRJYWFh6ty5s7p169akD7gFBQVauHChbr75ZvXo0aOly/YIgR4wqa0/FOnBFzZ5tM36jMsV1yFchY5yDf7FsiZt81NRpX772Nd66/HRzSmz1Tlw4IAWLlyovn37Embgl+gB+Iv8/HytXr1aa9euVXFx8SnX7dixo0aMGKHRo0c32BcFBQV66KGHVFRUpPnz5+uPf/yjUlJSWqp0j/nFkBuHw6E5c+YoJSVFoaGh6ty5s2bPnq2ysjLdcMMNstlseu6554wuE2gyt9utGfdn6piHs9HEdQhX4lkRiuvg2dSUSz7M0Xtr9nq0DVqHzx0HFfz+23pq945G1wl+/21d+U2mD6sCgJZTWFioxx57TL/73e/0wQcfnDbMS9LBgwf1zjvvaObMmXr++edVUlJSu+zkMC8dD/8dO3Zssfqbw/Jn6LOyspSenq7CwkJFRESoV69eys/P17PPPqvdu3fr8OHjM3kMGDDA2EIBD3y6rkDrtvzk02MuePU7XTk62afHBACgqVwul1atWqWMjIzaYTWSFBQUpJ49e6pbt25KTk5WRESE3G63SkpKlJOTo927dys7O1tut1tOp1NffPGFsrKydMMNNygpKalOmE9KStIf//hHtW3b1qiX2SBLB3qHw6EJEyaosLBQd955px544AFFRkZKkh5//HHdc889stvtstls6tevn8HVAk33/JLtPj/mv7/7SZu2OfQ/vTr4/NgAAJxKdXW1Fi1apHXr1tU+FxMTo3HjxmnkyJG1+e/nzj//fEnHM+Mnn3yijz76SGVlZSopKdHTTz+tkJAQVVVVSWq9YV6y+JCbWbNmKS8vTzNnztQTTzxR5y9zzpw56t+/v2pqapScnNwq/3KAhhw8VKH3Ps015NgvL8025LjeFB4erqFDhyo8nDviwj/RA7CampoaPfXUU3XC/MUXX6wnn3xSEyZMaDTMn6xDhw6aMmWKnnzySQ0ePLj2+RNhvnPnzq02zEsWDvTbt2/XkiVL1KFDB82fP7/BdQYOHChJ6t+/f+1z//jHPzRp0iR16dJF4eHhSktL07333qvS0lKf1A2czjff/ySns2l3gPW2tVnmn8IyKSlJixYtUlJSktGl+FS50ylHVVWD/8G/+GsPwLpeffVVbd68WZIUEhKie+65RzNmzFBoaKjH+2rfvr1+8Ytf1PvAO2TIkFYb5iULD7nJyMiQy+XS1KlT1aZNmwbXCQs7Pg3fyYH+iSeeUFJSkh599FElJiYqKytL8+bN0+eff64vvvhCAQGW/QwEkziTO8GeqW17jqi8okbhYeZ963A6naqoqFBYWJgCAwONLsdnHsreqoeytxpdBloBf+0BWNOmTZu0Zs0aScfHyt9zzz3q1atXs/dXUFCghx9+WOXl5XWe/9e//qVzzz1XnTt3PqN6W4p5fyufxom/3FGjRjW6Tl5enqS6gf79999XbGxs7eMRI0YoNjZWU6dO1ZdffqkLL7ywhSoGmmbzjkOGHdvpdGvLD0Ua0jf29Cu3Urt27dK0adP0xhtvKC0tzehyfOY3Sd00qVPDv4jS//25j6uBkfy1B2A9ZWVlevnll2sfX3/99Wcc5n9+AWxaWpo++ugj1dTU6IUXXtDDDz/cKj8IWzbQ5+YeH2PcpUuXBpfX1NRo7dq1kuoG+pPD/AmDBg2SJO3fv79ZtQwaNEiFhYXN2hb4uZ8ir5eCkhtcdmKe+cbEdQir/XPfx9ee8jiNzVV/6YTJCq3x/p1pm2vy5MkerX/w4EFJ0sqVK7Vx48YmbTNx4kSP6zpTYQEB2jZgmNf2l9KmjS6KPctr+2tIamqqKlrpXRStzKo94G0Tr79dEW3aqqCwQImJifUeW11Dr7e1/wyCg4MbHTYtSR999FFt+O7fv/8pT+KeTkNh/o9//KNCQ0O1ZcsW5efna8+ePVq/fr3OPffcRveTmppaZ4YdT8TFxWnDhg3N2taygb6srEySVFFR0eDyJUuWyOFwKDIyUl27dj3lvj799FNJUs+ePZtVS2FhYbM/DAD1dKuWghpedGKe+dOxBwY0ab2GHDpcJB1tPf+eT/R6U514T6ioqGjytkb0b3hgoDTA54c9I/n5+Sp3Oo0uw+9YtQe8zfWff5sup1P79++v99jqGnq9rf1nEBIS0ugyp9Op1atXS5JsNpuuv/562Wy2Zh2nsTB/Ysz89OnTaz9YfPzxx6cM9Pn5+bUX0vqSZQN9XFycioqKtGnTJg0bVvcsV0FBge6++25JUr9+/U75D2D//v267777NG7cuGbPVR8XF9es7YCGOIID1NhbRaGjvJElx8V1CJM9MEA1TpcKHQ1/2D3dvjpEt1VI24SmlOoTERGefTA5EWDCwsKavG1Cgu9fb5gJr9fp1KkTZ+gNYNUe8LaA/wyTCAgMVEJCQr3HVtfQ623tP4Pg4OBGl23evFmHDh0fgnrOOec0O2udLsxLUt++fRUfH6+CggJt3bpV+/fvb/Tn1alTpzM6Q99clg30Y8aM0fbt27VgwQKNHTtWqampkqT169fruuuuk8Nx/MLCU4X00tJSXXHFFQoODtarr77a7Fqa+/UJ0JBbHl6rF99p+K6fDQ2ROdm+j69V4lkRKnRUqPPYt5p1/E3//lCd4xq+0NwI69ev92j9HTt2KCMjQ+np6U0eP/zMM880o7Iz466sVM01031+3DOxc+dO2ZoxqwTOjFV7wNse/fPfVFJapvi4eOXl5dV7bHUNvd7W/jOoqanR0qVLG1z23Xff1f7/RRdd1Kz9NyXMS1JAQIBGjx6tv/3tb7XHbizQ79y5U3a77+O1+U4BNdGcOXMUExOjffv2qXfv3urbt6/OPvtsDRkyRN26ddPo0aMl1R0/f7KKigpNmDBBOTk5+uijjxQfH+/L8oFGDewZY9ixY6NCmz1Up7VISUnRqlWrlJKSYnQpgCHoAVjBnj17av+/OUOimxrmTzj5YtucnByPj9fSLBvoExMTlZmZqfHjxys0NFR79+5VdHS0XnzxRa1YsUI7d+6U1HCgr66u1uTJk7VhwwatXLnyjK6YBrxtUG/j7tQ6sFeHZo9RbC3sdruioqIMOYMCtAb0AMzO6XTWTn4SFxfn8U3SPA3z0vEbS52Y3ebkDxOthaW7uWfPnlq+fHm950tLS7V3714FBASoT58+dZadmLv+k08+0QcffKAhQ4b4qlygSfr3iFH3zpHave+oz4999cWnvoDcDPLy8vT000/rjjvuaJWzOnjbiA4ddWzCNadc53TLYS3+1gOwnrKyMlVXV0uSxyMomhPmpePj+WNjY1VYWKgjR440q+6WZOlA35itW7fK7XYrNTW13qe62267Te+8845+//vfKzw8XP/+979rl3Xv3r3BaS0BXwoIsOl/r+mpu55cd/qVvah9ZLCuHdfNp8dsCaWlpcrMzNSNN95odCmAIegBmF1QUJCmTJmiY8eOeRTo3W63Fi1a5HGYP2HMmDEqLy+vvTFpa+KXgf7777+X1PBwm5UrV0qSHnvsMT322GN1lv31r3/Vr3/96xavDzid669M1X1/3qiKSt9NEThjYqqp7xALALCGsLCwZt0bwWazaebMmXr44YcVGRnpUZiXpMsuu8zjY/qKX/52PlWg37t3r4+rATwX3S5Ef/rtIP1u4Tc+OV58bLj+eNMAnxwLAICW0qlTJ91///2KiIjwKMy3dpa9KPZUThXoAbOY9cteGn5Oy97584SX7h+uqLaN3+ADAACziI+Pt1SYl/z0DP2aNWuMLgE4Y4GBAXrt4Qt17q+W6dCRpt2V7sTNok53A6qT3Tqlpy4bkdSsGluj2NhYzZ49m+th4LfoAcB6/DLQA1aRktRWH75wicbe9KGOHD39nelOd+Opn/vlpd317O8bv8W1GcXExGjq1KlGlwEYhh4ArMcvh9wAVjKod6w+/+t4dY7z7g2fbru2p97404UKDLTW20RJSYlWr16tkpISo0sBDEEPANZjrd/UgJ/qlxqt75depd9clXrG++rUMVwr/nyxnpt7nuXCvCTl5+dr7ty5ys/PN7oUwBD0AGA91vttDfipdpHBevnBC/TxS+N00dBOHm8f0z5Ec67vq63vXqVLL+jcAhUCAICWwBh6wGLGnJugMecmaEfOES1emq0vNx9QVvZhVR2rP2d94lkRGtgrRpPGJOvqi7sqNIS3BAAAzIbf3oBFpXVtryfuGipJqq52KXvvERWVHFN1jUthoYHqnthWHWNa393uAACAZwj0gB8ICgpQn7OjjS6jVQgJCVGPHj0UEsK8+vBP9ABgPQR6AH6la9euevPNN40uAzAMPQBYDxfFAgAAACZGoAfgV7KzszV8+HBlZ2cbXQpgCHoAsB4CPQC/4na7VV1dLbfbbXQpgCHoAcB6GEMPAK1RSIjsb79udBWe4SJLAF4UGBioSZMmeW1/C19coqNlZYqMiNDdN0+p99gbAgMDvbIfTxHoAaAVstlsUmio0WUAgGFsNpvsdu9FVbckl/v4n3a7vd5jM2PIDQAAAGBi5v44AgAeSk5OVkZGhhISEowuBTAEPQBYD4EegF8JDQ1V9+7djS4DMAw9AFgPQ24A+JWCggI98sgjKigoMLoUwBD0AGA9BHoAfqW4uFjLli1TcXGx0aUAhqAHAOsh0AMAAAAmRqAHAAAATIxADwAAAJgYgR6AXwkICNA555yjgADe/uCf6AHAeuhmAH7F5XJp8+bNcrlcRpcCGIIeAKyHQA8AAACYGIEeAAAAMDECPQAAAGBiBHoAfiUyMlLjxo1TZGSk0aUAhqAHAOuxG10AAPhSQkKCHnroIaPLAAxDDwDWwxl6AH6lqqpK+/btU1VVldGlAIagBwDrIdAD8Cs5OTmaNGmScnJyjC4FMAQ9AFgPgR4AAAAwMQI9AAAAYGIEegAAAMDECPQAAACAiTFtJQC/kpaWpnXr1hldBmAYegCwHs7QAwAAACZGoAfgV3JzczVjxgzl5uYaXQpgCHoAsB4CPQC/UlFRoS1btqiiosLoUgBD0AOA9RDoAQAAABMj0AMAAAAmRqAHAAAATIxAD8CvxMfHa968eYqPjze6FMAQ9ABgPcxDD8CvtGvXTunp6UaXARiGHgCshzP0APxKUVGR3nnnHRUVFRldCmAIegCwHgI9AL9y4MABLVy4UAcOHDC6FMAQ9ABgPX4R6B0Oh+bMmaOUlBSFhoaqc+fOmj17tsrKynTDDTfIZrPpueeeM7pMAAAAwGOWH0OflZWl9PR0FRYWKiIiQr169VJ+fr6effZZ7d69W4cPH5YkDRgwwNhCAQAAgGaw9Bl6h8OhCRMmqLCwUHfeeacKCgq0adMmFRYWasGCBVqxYoXWr18vm82mfv36GV0uAAAA4DFLB/pZs2YpLy9PM2fO1BNPPKHIyMjaZXPmzFH//v1VU1Oj5ORktW3b1sBKAfhKeHi4hg4dqvDwcKNLAQxBDwDWY9lAv337di1ZskQdOnTQ/PnzG1xn4MCBkqT+/fvXPpeZmakxY8YoPj5eISEhSkxM1JQpU7R9+3af1A2gZSUlJWnRokVKSkoyuhTAEPQAYD2WHUOfkZEhl8ulqVOnqk2bNg2uExYWJqluoC8qKlLfvn118803q2PHjsrLy9P8+fM1bNgwbdmyRYmJiT6pH0DLcDqdqqioUFhYmAIDA40uB/A5egCwHsueoV+zZo0kadSoUY2uk5eXJ6luoL/88sv19NNP6+qrr9aIESM0depUvfvuuyouLtbSpUtbtmgALW7Xrl0aPXq0du3aZXQpgCHoAcB6LBvoc3NzJUldunRpcHlNTY3Wrl0rqW6gb0hMTIwkyW637BcaAAAAMCnLJtSysjJJUkVFRYPLlyxZIofDocjISHXt2rXecqfTKZfLpdzcXP3hD39QXFycrrnmmmbVMmjQIBUWFjZrWwCnNnnyZI/WP3jwoCRp5cqV2rhxY5O2mThxosd1Ab5CDzTNxOtvV0SbtiooLFBiYmK9x1bX0Ov1959Ba3v9cXFx2rBhQ7O2tWygj4uLU1FRkTZt2qRhw4bVWVZQUKC7775bktSvXz/ZbLZ6248YMaL2DH5KSorWrFmj2NjYZtVSWFio/fv3N2tbAKd24sN7U534kF9RUdHkbelftGb0QNO4nM7aP/fv31/vsdU19Hr9/Wdgpddv2UA/ZswYbd++XQsWLNDYsWOVmpoqSVq/fr2uu+46ORwOSY3fUOqVV17RkSNHlJOTo4ULF+riiy/W2rVrmzUrQFxcXLNfB4BTi4iI8Gj9EwEmLCysydsmJCR4XBfgK/RA0wT85wLggMBAJSQk1HtsdQ29Xn//GbS2138medHmdrvdXqyl1cjLy9OAAQN06NAh2e12paWlqbKyUj/88IPS09Plcrm0atUqvfTSS7rxxhtPua8jR44oOTlZv/rVr/Tcc8/56BUAaIr169d7tH5NTY2OHj2qyMjIJl8XM3jw4OaUBvgEPdA0j/75byopLVPbNhGae9vUeo+trqHX6+8/Ayu9fsteFJuYmKjMzEyNHz9eoaGh2rt3r6Kjo/Xiiy9qxYoV2rlzp6TTXxArSe3bt1dKSop++OGHli4bQAuz2+2KioriInf4LXoAsB7LBnpJ6tmzp5YvX66jR4/q6NGj+uabb3TTTTeprKxMe/fuVUBAgPr06XPa/Rw8eFDZ2dnq3r27D6oG0JLy8vJ055131k5bC/gbegCwHr/8eL5161a53W6lpqbWu/X1r371K6WkpGjAgAFq3769du3apaefflp2u1133HGHQRUD8JbS0lJlZmaedqgdYFX0AGA9fhnov//+e0kND7c599xz9cYbb+j//u//VFlZqc6dO2vUqFGaO3duo3PaAwAAAEYh0P/MzJkzNXPmTF+XBAAAADSLpcfQN+ZUgR4AAAAwE788Q79mzRqjSwBgkNjYWM2ePbvZN4oDzI4eAKzHLwM9AP8VExOjqVPNPd8wcCboAcB6/HLIDQD/VVJSotWrV6ukpMToUgBD0AOA9RDoAfiV/Px8zZ07V/n5+UaXAhiCHgCsh0APAAAAmBiBHgAAADAxAj0AAABgYgR6AH4lJCREPXr0UEhIiNGlAIagBwDrYdpKAH6la9euevPNN40uAzAMPQBYD2foAQAAABMj0APwK9nZ2Ro+fLiys7ONLgUwBD0AWA+BHoBfcbvdqq6ultvtNroUwBD0AGA9BHoAAADAxAj0AAAAgIkR6AEAAAATY9pKAH4lOTlZGRkZSkhIMLoUwBD0AGA9BHoAfiU0NFTdu3c3ugzAMPQAYD0MuQHgVwoKCvTII4+ooKDA6FIAQ9ADgPUQ6AH4leLiYi1btkzFxcVGlwIYgh4ArIdADwAAAJgYgR4AAAAwMQI9AAAAYGIEegB+JTo6WtOnT1d0dLTRpQCGoAcA6yHQA/ArAQEBCgoKUkAAb3/wT/QAYD10MwC/4nA4tHjxYjkcDqNLAQxBDwDWQ6AHAAAATIxADwAAAJgYgR4AAAAwMQI9AL8SGRmpcePGKTIy0uhSAEPQA4D12I0uAAB8KSEhQQ899JDRZQCGoQcA6+EMPQC/UlVVpX379qmqqsroUgBD0AOA9RDoAfiVnJwcTZo0STk5OUaXAhiCHgCsh0APAAAAmBiBHgAAADAxAj0AAABgYgR6AAAAwMSYthKAX0lLS9O6deuMLgMwDD0AWA9n6AEAAAATI9AD8Cu5ubmaMWOGcnNzjS4FMAQ9AFgPgR6AX6moqNCWLVtUUVFhdCmAIegBwHoI9AAAAICJEegBAAAAEyPQAwAAACZGoAfgV+Lj4zVv3jzFx8cbXQpgCHoAsB7moQfgV9q1a6f09HSjywAMQw8A1sMZegB+paioSO+8846KioqMLgUwBD0AWA+BHoBfOXDggBYuXKgDBw4YXQpgCHoAsB7LB3qHw6E5c+YoJSVFoaGh6ty5s2bPnq2ysjLdcMMNstlseu6554wuEwAAAGgWS4+hz8rKUnp6ugoLCxUREaFevXopPz9fzz77rHbv3q3Dhw9LkgYMGGBsoQAAAEAzWfYMvcPh0IQJE1RYWKg777xTBQUF2rRpkwoLC7VgwQKtWLFC69evl81mU79+/YwuFwAAAGgWywb6WbNmKS8vTzNnztQTTzyhyMjI2mVz5sxR//79VVNTo+TkZLVt29bASgH4Unh4uIYOHarw8HCjSwEMQQ8A1mPJQL99+3YtWbJEHTp00Pz58xtcZ+DAgZKk/v37N7qf9PR02Ww2Pfjggy1RJgADJCUladGiRUpKSjK6FMAQ9ABgPZYM9BkZGXK5XJo6daratGnT4DphYWGSGg/0b7/9trKyslqqRAAGcTqdKi0tldPpNLoUwBD0AGA9lgz0a9askSSNGjWq0XXy8vIkNRzoS0pKdPvtt+uJJ55omQIBGGbXrl0aPXq0du3aZXQpgCHoAcB6LDnLTW5uriSpS5cuDS6vqanR2rVrJTUc6O+9916lpqZq6tSp+tWvfnXG9QwaNEiFhYVnvB8A9U2ePNmj9Q8ePChJWrlypTZu3NikbSZOnOhxXYCv0ANNM/H62xXRpq0KCguUmJhY77HVNfR6/f1n0Npef1xcnDZs2NCsbS0Z6MvKyiRJFRUVDS5fsmSJHA6HIiMj1bVr1zrLNmzYoJdffrnJb3JNUVhYqP3793ttfwD+60S/N9WJ94WKioomb0v/ojWjB5rG9Z8hRi6nU/v376/32Ooaer3+/jOw0uu3ZKCPi4tTUVGRNm3apGHDhtVZVlBQoLvvvluS1K9fP9lsttplTqdTN998s2bOnKnevXt7tR4ALSMiIsKj9U8EmLCwsCZvm5CQ4HFdgK/QA00TEBhY+2dCQkK9x1bX0Ov1959Ba3v9Z5IXLRnox4wZo+3bt2vBggUaO3asUlNTJUnr16/XddddJ4fDIan+DaWee+45HThwwOuz2jT36xMAp7d+/XqP1t+xY4cyMjKUnp6utLS0Jm3zzDPPNKMywDfogaZ59M9/U0lpmeLj4pWXl1fvsdU19Hr9/WdgpddvyYti58yZo5iYGO3bt0+9e/dW3759dfbZZ2vIkCHq1q2bRo8eLanu+HmHw6H77rtP999/v2pqanTkyBEdOXJEklRZWakjR47I5XIZ8XIAeFFKSopWrVqllJQUo0sBDEEPANZjyUCfmJiozMxMjR8/XqGhodq7d6+io6P14osvasWKFdq5c6ekuoE+Ly9PR48e1c0336yoqKja/yRpwYIFioqK0o8//mjI6wHgPXa7XVFRUbLbLfkFJXBa9ABgPZbt5p49e2r58uX1ni8tLdXevXsVEBCgPn361D6fkpKiTz/9tN76o0aN0vTp0/XrX/+asfCABeTl5enpp5/WHXfc0SpmNQB8jR4ArMeygb4xW7duldvtVmpqap3bXrdp00YjR45scJvk5ORGlwEwl9LSUmVmZurGG280uhTAEPQAYD2WHHJzKt9//72kxu8QCwAAAJiJ352h9zTQu93uliwHAAAAOCOcoQcAAABMzO/O0K9Zs8boEgAYKDY2VrNnz1ZsbKzRpQCGoAcA6/G7QA/Av8XExGjq1KlGlwEYhh4ArMfvhtwA8G8lJSVavXq1SkpKjC4FMAQ9AFgPgR6AX8nPz9fcuXOVn59vdCmAIegBwHoI9AAAAICJEegBAAAAEyPQAwAAACZGoAfgV0JCQtSjRw+FhIQYXQpgCHoAsB6mrQTgV7p27ao333zT6DIAw9ADgPVwhh4AAAAwMQI9AL+SnZ2t4cOHKzs72+hSAEPQA4D1EOgB+BW3263q6mq53W6jSwEMQQ8A1kOgBwAAAEyMQA8AAACYGIEeAAAAMDGmrQTgV5KTk5WRkaGEhASjSwEMQQ8A1kOgB+BXQkND1b17d6PLAAxDDwDWw5AbAH6loKBAjzzyiAoKCowuBTAEPQBYD4EegF8pLi7WsmXLVFxcbHQpgCHoAcB6CPQAAACAiRHoAQAAABMj0AMAAAAmxiw3AExt8ODBHq2fmJioBx54QGPGjFF8fHwLVQX4Dj0AgEAPwK/Ex8frwQcfNLoMwDD0AGA9DLkBAAAATIxADwAAAJgYgR4AAAAwMQI9AAAAYGIEegAAAMDECPQAAACAiRHoAQAAABMj0AMAAAAmRqAHAAAATIxADwAAAJgYgR4AAAAwMQJ9K/Dmm29q4MCBioqKUlhYmHr27KmnnnpKbrfb6NIAAEAjPvjgAw0YMEAhISFKTk7WU089ZXRJPvXFF1/oiiuuUJcuXWSz2fTII48YXZJPLVy4UMOGDVNUVJTat2+v888/Xx9++KEhtdgNOSrq6Nixo+677z716NFDISEhyszM1K233qrAwEDNnj3b6PIAAMDPbNiwQVdccYXuuusuZWRk6JtvvtEtt9yi8PBw3XLLLUaX5xOlpaXq1auXfvnLX+r22283uhyfW7NmjWbMmKHBgwcrPDxcixcv1mWXXabPP/9cw4cP92ktBPpW4JJLLqnzuFu3bnrvvff02WefEegBAGiFnnrqKQ0ePFjz58+XJPXs2VNbt27VY4895jeB/tJLL9Wll14qSbrnnnsMrsb3Vq5cWefx448/rg8//FDvvvuuzwM9Q25aGbfbrXXr1mnt2rUaNWqU0eUAAIAGrF27VuPGjavz3Lhx45Sbm6u8vDyDqoKRXC6XSkpKFBER4fNjc4a+lSguLlZCQoKOHTsml8ulBx54QLNmzTK6LAAATKW6pkY5+wrrPV/jdNb+uTMnr97jk8VGt1NUu8hTHqegoEBxcXF1njvxuKCgQImJic1+DWcqr+AnlVdW1Xmuodfb2M8gJMiuLol1X5uZlJSWq/Cnw/We9+TfQFKnjgoNCfbouI8++qiOHDmim266qZmVNx+BvpWIjIxUVlaWysvL9dVXX+kPf/iDOnXqpBtuuMHo0gAAMA17YKDWZW3Xlp05DS4vr6jUq29/0OjjiPBQ3THj6havsyWVllfotX80fHHmz19vQ89NTh9h6kAfEmTXex9l6vCRow0uP92/ga6d43XjteM9Oubzzz+vRx99VMuWLTPkwxxDblqJgIAApaSkqF+/frrllls0Z84c3XvvvUaXBQCAqdhsNk285AK1iQhr1vaTxl3YpG3j4+NVWFj3m4ADBw7ULjNSWvckDemf1qxte52drIF9U71ckW+FhATrmvGjZLPZPN82OEjXjB+pgICmR+QnnnhCd999t5YtW6YxY8Z4fExvINC3Ui6XS5WVlUaXAQCA6USEh2py+giPtxvUr4d6nZ3cpHWHDx+uVatW1Xnuww8/VJcuXQwdbnPC+NHDFNO+rUfbtAkP01XjLmhWEG5tkhPjNGJof4+3u3zM8NMOtzrZ/fffr3nz5umDDz4wLMxLBPpW4YEHHtDq1au1Z88eZWdn6+WXX9aCBQs0ffp0o0sDAMCU0ronaeiAnk1eP7pdpCaMHtbk9e+44w6tW7dO9957r3bs2KHXX39dixYt0u9///vmlOt1IcFBuuYyz85SX5V+odqEN/2bjdLSUmVlZSkrK0vHjh1TYWGhsrKy9MMPPzSnZK8bc/5AxXeMafL6vVOT9T99zm7y+rfffrsWLlyoN998Uz169FBhYaEKCwtVXFzcnHLPiM3N3YsMd8cdd+j999/X/v37FRoaqm7dumnGjBm65ZZbFBgYaHR5AACYUtWxaj372lIdKio55Xo2STdPvVzJHo4bX7FihebOnasdO3YoLi5Os2fP1u9+97szqNj7Vn2xXp9+vfm06w3ul6ZJ6Rd6tO/PPvuswRn5RowYoc8++8yjfbWUwp8O67nX/1l7AWxj2kSE6fYZkz36QNPYh6Xp06frtdde86TMM0agBwAAlvXj/gN64W/LTnn39RFD+yt95FAfVuU7NU6nnn/zPeUfONToOtHtIzX715MU4uGsLmaRue47rfj036dc59eTxymte5KPKvI+htyYzL6Cg/WmogIAAA1LSjhLo84d0Ojy+I4xGnv+IN8V5GP2wEBNuWy07I1842+z2XTN+FGWDfOSNHxwX3VL6tTo8iH900wd5iUCvanUOJ36f//8WAte+Lt+3H/A6HIAADCFi4YPVMJZHeo9HxgYoCmXjZLdbu3hrWd1iNK4EUMaXDZiaH+PhxqZTYDNpmvGj1RIcFC9ZTHt22q8B9dOtFYE+p9xOp168803dfHFFys2NlYhISFKSkrSuHHjtHjxYjlPMwarJW38PlvFR8sUHBzk0UUeAAD4s8DAAF3TQHC/5MIhiouNNqgq3zpvUB9171L3LHV8xxiNOX+gQRX5Vvu2bXTF2OF1nrOdIuibDYH+JCUlJRo7dqymTZumjz/+WMHBwerfv79cLpc++ugj3XjjjTp6tOGbFLS0GqdTa746flHLyKEDFBTEPcEAAGiqn5+l7to5XucP7mtgRb4VYLPp6ktH1t799PhQnFGNDsWxonN6n60+qV1rH488t7+pb6B1MgL9SW644QZ9+umnSkxM1Jo1a7R//36tW7dOeXl5Kigo0J/+9CcFBRnzKe7E2fnINuHNvlkEAAD+7LyBfZTSJeG/Nw+ywHzrnjj5LPUlFw72m28nTjhx07HIiDB1OitGFw23zrcTzHLzHxs3btSgQYNkt9u1efNm9enTx2v7XvT6uzpaWnEGe3DraFmF3G63QkOCFWzQhwoAAMzO5XLJ6XIpyO6f33S73W4dq65RcJDdEjeQao6amhrZAgIU6MHdYH0hsk2Yfjv9qmZt65//mhvw3nvvSZLGjx/v1TAvSUdLK1RSWuaVfVVWHVNl1TGv7AsAAH9VIf+eMa7qGFnCSgj0/7Ft2zZJ0rBh3r/SObJN029SUB9n5wEAAKzuTPIigf4/SkqO30WuXbt2Xt93c78+kaRvsrbrn6syFdkmXHNuupaLYQEAAFAH6fA/2rZtK0kqLi72+r6bP4b++Nl5SaqurtHCl5Z4tzAAAAC0Coyh94LevXvr3Xff1ddff+31fXtjDD1j5wEAANAQAv1/TJw4UQ8//LA++OADbdu2Tb169fLavps3Joqx8wAAAP7iTMbQM23lSaZMmaK3335bSUlJeuONNzRixIjaZQcOHNCrr76qWbNmKSIiosVrYew8AAAAmoJAf5KSkhJdccUV+uyzzyRJCQkJ6tSpkwoKCrR//3653W4VFRWpffv2LVpHjdOpJ15aoiMlpZpw0XkaPsi702gCAADAOlrXjPoGa9u2rVavXq1XXnlFI0eOVHl5ub799lsFBATokksu0SuvvKLIyMgWr2Pj9zt1pKSUu8ICAADgtDhD3wpt3rpLKz9bpxFD+3N2HgAAAKdEoG+lqmtqZJNNdnug0aUAAACgFSPQAwAAACbGGHoAAADAxAj0AAAAgIkR6AEAAAATI9ADAAAAJkagBwAAAEyMQA8AAACYGIEeAAAAMDECPQAAAGBiBHoAAADAxAj0AAAAgIkR6AEAAAATI9ADAAAAJkagBwAAAEyMQA8AAACYGIEeAAAAMDECPQAAAGBiBHoAAADAxAj0AAAAgIkR6AEAAAATI9ADAAAAJkagBwAAAEyMQA8AAACYGIEeAAAAMDECPQAAAGBiBHoAAADAxAj0AAAAgIkR6AEAAAATI9ADAAAAJkagBwAAAEyMQA8AAACYGIEeAAAAMDECPQAAAGBiBHoAAADAxAj0AAAAgIkR6AEAAAATI9ADAAAAJkagBwAAAEyMQA8AAACYGIEeAAAAMLH/D4J61VZ9+v6/AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 956.385x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend2: create coupling map optimised circuit\n",
    "\n",
    "# map: qubit 0 -> qubit 1\n",
    "# qubit 1 -> qubit 0\n",
    "# qubit 2 -> qubit 2\n",
    "\n",
    "ghz_backend2 = QuantumCircuit(5,3, name=f\"GHZ yyx {backend2.backend_name} optimized\") # note that we use 5 qubits here to match the configuration of the device\n",
    "ghz_backend2.h(1) # we map qubit 0 to qubit 1 and qubit 1 to qubit 0 ..\n",
    "ghz_backend2.cx(1,0) # .. to ensure that all logical CNOT gates are performed on physical connections\n",
    "ghz_backend2.cx(1,2)\n",
    "ghz_backend2.barrier()\n",
    "ghz_backend2.sdg([1,0]) \n",
    "ghz_backend2.h(range(n))\n",
    "ghz_backend2.barrier()\n",
    "ghz_backend2.measure([1,0,2], range(n))\n",
    "ghz_backend2.draw('mpl', idle_wires=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's compare the two circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "GHZ yyx default: 78.525%\n",
      "GHZ yyx fake_kyiv optimized: 90.4%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results between original and coupling map optimized circuit on backend1\n",
    "from qiskit import transpile\n",
    "\n",
    "results_backend2_coupling = []\n",
    "\n",
    "sampler = Sampler(mode=backend2)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "circuits = [ghz, ghz_backend2]\n",
    "\n",
    "for circuit in circuits:\n",
    "    \n",
    "    transpiled_circuit = transpile(circuit, backend=backend2, optimization_level=0)\n",
    "\n",
    "    counts = sampler.run([transpiled_circuit]).result()[0].data.c.get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend2_coupling.append((circuit.name, counts, state_accuracy)) # store\n",
    "    \n",
    "\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(circuit_name)+': '+str(state_accuracy) \n",
    "                 for circuit_name, counts, state_accuracy in results_backend2_coupling]))\n",
    "\n",
    "plot_distribution([counts for circuit_name, counts, state_accuracy in results_backend2_coupling],\n",
    "               legend=[circuit_name for circuit_name, counts, state_accuracy in results_backend2_coupling],\n",
    "               title=backend2.backend_name,\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As you can see, the state accuracy improved by around 5-12% (depending on runs) on our system!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Error Map based optimization**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As mentioned, this was one of two ways we are considering to manually optimize the circuits. The second builds off of the results from the coupling map based optimization and additionally takes into account the error rates. For this, we have another look on the error map and pick qubits that have the least single qubit gate, multiple qubit gate and readout error rate (see colors for intuition). Sometimes you need to trade off between these as for instance some qubits have excellent read out error rates while not as good single qubit gate error rates. Though, as this approach is manual, you don not need to try out each possible configuration to find the best one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Backend 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 956.385x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend2: create coupling map + error rate optimised circuit\n",
    "\n",
    "# map: qubit 0 -> qubit 3\n",
    "# qubit 1 -> qubit 1\n",
    "# qubit 2 -> qubit 4\n",
    "\n",
    "ghz_backend2_error = QuantumCircuit(5,3, name=f\"GHZ yyx {backend2.backend_name} error rate optimised\") # note that we use 5 qubits here to match the configuration of the device\n",
    "ghz_backend2_error.h(3) # qubit with best adjacent multi-qubit gates error rates (cnot)\n",
    "ghz_backend2_error.cx(3,1)\n",
    "ghz_backend2_error.cx(3,4) \n",
    "ghz_backend2_error.barrier()\n",
    "ghz_backend2_error.sdg([3,1]) # avoid 4 as it has a worse single qubit error rate\n",
    "ghz_backend2_error.h([3,1,4]) # best readout error rates\n",
    "ghz_backend2_error.barrier()\n",
    "ghz_backend2_error.measure([3,1,4], range(n)) # readout still in same order\n",
    "ghz_backend2_error.draw(\"mpl\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "GHZ yyx default: 78.525%\n",
      "GHZ yyx fake_kyiv optimized: 90.4%\n",
      "GHZ yyx fake_kyiv error rate optimised: 94.9375%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results between original, coupling map, and error rates optimized circuit on backend2\n",
    "results_backend2_error = []\n",
    "\n",
    "sampler = Sampler(mode=backend2)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "circuits = [ghz_backend2_error]\n",
    "\n",
    "for circuit in circuits:\n",
    "    transpiled_circuit = transpile(circuit, backend=backend2, optimization_level=0)\n",
    "    counts = sampler.run([transpiled_circuit]).result()[0].data.c.get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend2_error.append((circuit.name, counts, state_accuracy)) # store\n",
    "    \n",
    "\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(circuit_name)+': '+str(state_accuracy) \n",
    "                 for circuit_name, counts, state_accuracy in results_backend2_coupling+results_backend2_error]))\n",
    "\n",
    "plot_distribution([counts for circuit_name, counts, state_accuracy in results_backend2_coupling+results_backend2_error],\n",
    "               legend=[circuit_name for circuit_name, counts, state_accuracy in results_backend2_coupling+results_backend2_error],\n",
    "               title=backend2.backend_name,\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As can be seen, the results from the coupling map and error rate optimised circuit are around the same as those from the circuit only optimised for its coupling map. This is because while the new circuit uses qubits with improved CNOT error rates, the old one natively had good readout error rates so that effects of swapping qubit mappings do not produce a significantly better result. However, there might be still a better circuit layout than the one found here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 3. Qiskit Transpiler Optimization<a name=transpiler><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Qiskit comes with a built-in transpiler to translate logical circuits into circuits that are executable on the target backend. In addition, the transpile function (and execute function calling it) has four different levels of optimization available that can be set as parameter. See an extract of the [documentation](https://docs.quantum.ibm.com/api/qiskit/transpiler_preset) here to understand their differences:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Optimization Levels\n",
    "\n",
    "* Level 0: no explicit optimization other than **mapping to backend**.\n",
    "\n",
    "* level 1: light optimization by simple **adjacent gate collapsing**.\n",
    "\n",
    "* level 2: medium optimization by **initial layout selection** and **gate cancellation** using commutativity rules.\n",
    "\n",
    "* level 3: heavy optimization by **noise adaptive qubit mapping** and gate cancellation using commutativity rules and **unitary synthesis**.m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Next to other actions taken such as combining gates and mapping to the device's coupling map (which takes place necessarily on every level), note that only optimization level 3 applies noise adaptive mapping, which we attempted to do manually in the previous chapter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To separately view the effects from each chapter, we will now again use the basic GHZ YYX circuit and compare the different transpiler optimization levels on backend 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "optimization_level_0: 78.3125%\n",
      "optimization_level_1: 97.82499999999999%\n",
      "optimization_level_2: 98.02499999999999%\n",
      "optimization_level_3: 98.575%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results from different optimization levels on backend 2\n",
    "results_backend2_transpiler = []\n",
    "\n",
    "optimization_levels = [0,1,2,3]\n",
    "\n",
    "sampler=Sampler(mode=backend2)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "for optim_level in optimization_levels:\n",
    "\n",
    "    transpiled_circuit = transpile(ghz, backend=backend2, optimization_level=optim_level)\n",
    "\n",
    "    counts = sampler.run([transpiled_circuit]).result()[0].data.c.get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend2_transpiler.append((optim_level, counts, state_accuracy)) # store\n",
    "    \n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([\"optimization_level_\"+str(optim_level)+': '+str(state_accuracy) \n",
    "                 for optim_level, counts, state_accuracy in results_backend2_transpiler]))\n",
    "\n",
    "# plot results\n",
    "plot_distribution([counts for optim_level, counts, state_accuracy in results_backend2_transpiler],\n",
    "               legend=[\"optimization_level_\"+str(optim_level) for optim_level, counts, state_accuracy in results_backend2_transpiler],\n",
    "               title=backend2.backend_name,\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Did you notice? Counterintuively, there was only a visible improvement from optimization level 0 to 1, while level 1, 2 and 3 produce similar results on the backend. But why is there no improvement on each level? To understand this phenomenon better, let's see what happens under the hood by inspecting the transpiled circuits that the transpiler produces to execute them on our backend:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original circuit\n"
     ]
    },
    {
     "data": {
      "image/png": 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QnZ2NgIAAfPLJJ9i8eTMyMzMB1A30cXFxVsfKp6Wl2XXSIGHM/UsCWmrq/7j2dt07BmL8kKjmK8jJ+iQEY+ygps8x7aGU4/Wn727GilyHUqmEv7+/ZHvRLq18Hv+b0Ro5Hz+FK5s/hH7n59B+uxBpz3VDWc5pBAyaCnWUtG6iRraRQhuoGaptnR/e1jAPAHK5vHqSjStXrqCoqMiOqomaj2QDPXArnP/0008oKipCUVERDh06hCeffBIlJSXIzs6GXC5H586da20zevRo/PLLL9VTWgLAoUOHcOHCBYwZM8bZL4HsFBPph03Lh6CFb+OhPr5dS2z+aCi8VOL943Y7mUyGr98eiIG9rN/uvCYPpRxfLxqI++52jxsO5ebm4oUXXqjVxqWk9fRl8L/nYZRk/AZt8j+R89GTuPLTB/AICEObZ1ciavYXQpdIApNCGygouHWllFqttnrdW33sCfNVwsLCqr+39kk+kZCkk2BscObMGVgsFsTGxta59fWTTz6J5cuXY+zYsVi4cCHKysowd+5c9O7dG2PHjhWoYvsNCGqFijETGlynseVidd/dITj43zFY8PFxfL8rG0ZT7dumttB4YtqYGCycdTda+jU8m4IY+Xh7YNu/h2HRypP4z7qz0OnrXqw49N5w/OOp7ujXvXln/3AlxcXFSElJwRNPPCF0Kc3Cr/tQ+HUfKnQZLsOdz4H1kUIbGD58OG7cuAG5jRdPr1u3zq4wDwDdu3dHy5Yt4enpCY1GY3PNRM3JLQP9qVOnANQdbgPculp+9+7dmDNnDiZNmgSlUonRo0fjvffes/nEQcKLa9sSa5cOhvZKCdZtz8LfPzyG4lIjWmo8kbtjkiRuItUQlacCC/56N+Y93hUb9/yO6f/Yj6JSI/x8PHD027Fo36aF0CUSEdls6FD73rSOHz8e58+fR25urk1hHgD69OmDPn362HVcoubGQG9Fu3bt8NNPPzmzJGpmYa18MOfRzliy6hSKS43wUSslH+Zr8vRQYPzQaDz3zm8oKjVC4+PBME9EbketVuOVV17B1atXa91Akkjs3LLLubFAT0RERNKkVqsZ5kly3LKHfvfu3UKXQEQCCQ4Oxpw5cxAcHCx0KUSCYBsgkh63DPRE5L4CAwMxefJkocsgEgzbAJH0uOWQGyJyX4WFhdi5cycKCwuFLoVIEGwDRNLDQE9EbkWr1WL+/PnQarVCl0IkCLYBIulhoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6InIrKpUKHTp0gEqlEroUIkGwDRBJD6etJCK3Eh0djdWrVwtdBpFg2AaIpIc99EREREREIsZAT0RuJSMjA/369UNGRobQpRAJgm2ASHoY6InIrVgsFlRWVsJisQhdCpEg2AaIpIdj6F2VSgXl2i+FrqLpeHEVkUN5KYCUkUJXYRsvhQN3JrZzIMDzoIMpFAokJSU5bH9LPlmDopISaHx88NJTE+s8dgSFwpGNgKjpGOhdlEwmA7y8hC6DiAQikwFqNz5D8xxIMpkMSqXjGoEFgNly66tSqazzmEjMOOSGiIiIiEjE+JaUiNxKVFQUkpOTER4eLnQpRIJgGyCSHgZ6InIrXl5eaNeundBlEAmGbYBIejjkhojcSn5+Pt58803k5+cLXQqRINgGiKSHgZ6I3MrNmzexceNG3Lx5U+hSiATBNkAkPQz0REREREQixkBPRERERCRiDPRERERERCLGQE9EbkUul6N79+6Qy3n6I/fENkAkPWzNRORWzGYzTpw4AbPZLHQpRIJgGyCSHgZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCcit6LRaDB8+HBoNBqhSyESBNsAkfQohS6AiMiZwsPD8frrrwtdBpFg2AaIpIc99ETkVsrLy3Hp0iWUl5cLXQqRINgGiKSHgZ6I3EpWVhaSkpKQlZUldClEgmAbIJIeBnoiIiIiIhHjGHoiIhdksQBlJqGrsI2XApDJHLMvi8UCiG1IiEoFmaN+AES41Q5MJvGcCBQKBduAQBjoiYhcUJkJ6L9F6CpskzISUDvqr0p5OYwTpjloZ86hXPsl4OUldBkkISaTCevXrxe6jCZLSkqCUsloKQQOuSEiIiIiEjG+jSIit9KxY0ccPnxY6DKIBMM2QCQ97KEnIiIiIhIxBnoicis5OTmYPn06cnJyhC6FSBBsA0TSwyE3JHmlBiNOZl5DRvZNFJdW3nquzIhTmdcR17YllEq+r3UnBoMBp0+fhsFgELoUIkGwDRBJDwM9SdKVawas/D4TyVsvIO3iDZhMllrLCworkDD+e6i9FOjVKRjTH4rFhGHRUHuxSRAREZG4ML2QpORfLcUr7x/Bt9suoqLS3Oj6hjIT9h/TYf8xHf629BCemRSPeY8nwEvFpkFERETiwLEGJAkWiwVfbz6PTuPW46tN55sU5m93/WY5Xv/kBHpM+hGHT11thiqJiIiIHI+BnkTPaDRj+j9S8Oi8fSgorLjj/aVduIG+UzbhP2vTHVAduZrQ0FAsXLgQoaGhQpdCJAi2ASLp4bgCEjWTyYzJ8/Zi7c9ZDt2v2WzBX9/8FeUVJsx5tLND903CatGiBUaMGCF0GUSCYRsgkh720JOoPb/kkMPDfE3PvXMIa3++2Gz7J+crKCjAunXrUFBQIHQpLke/axUyXh0odBnUzNgG3FdFRQX0ej3y8/Nx9epVlJeX27R9fn4+9uzZ00zV0Z1gDz2J1o6DeVj+TZpN2xxJfhAhQd7Q6UvR608bm7TNzDcOoP/dIQgN9ranTHIxly9fxpIlS9ClSxf4+/sLXQ6R07ENuA+j0YijR48iNTUVWVlZyM3Nhclkql4uk8kQHh6O6OhodOnSBffccw88PT2t7is/Px9vvPEGrl+/joqKCgwbNsxZL4OawC166PV6PebOnYuYmBh4eXmhdevWmDNnDkpKSjBjxgzIZDJ8+OGHQpdJNigsrsDj/0yxebuQIG9E3OWDkKCmh/OCwgrMfOMALBZL4ysTiVD28sdxYqIvfv/3TBSnpeDERF+cmOgLS40//EQkHsXFxVi3bh2effZZvP/++9i7dy9ycnJqhXng1oQSubm5SElJwccff4ynn34aX3/9dZ1Pb2qGeQDYtWsXKisrnfZ6qHGS76FPTU3FiBEjoNPp4OPjg/j4eGi1WnzwwQe4cOFC9S9nt27dhC2UbLL8mzT8nl/itONt3Ps7Uo7pcH9PXkRGrq9cdxG69YtQdGY/Kq7+DrmHCh7+IfBu3xtBgx+DJmFQrfWjnl2BqGdXQL9rFa7tXoUO/9orTOHNYJ/+CoYc3ItF8Qn4W7uOVtfx3LQWI1uF4oc+/Z1cHZHjHTt2DJ999hlu3LhR63mZTIaIiAiEhobC09MTRqMROp0Oly5dqg76RUVF2LRpE3bv3o3HHnsM9913H3Q6Xa0wHxkZib///e/w8PBw9kujBkg60Ov1eowZMwY6nQ4vvPACFixYAI1GAwB455138PLLL0OpVEImkyEhIUHgaqmpjEYzPvnurNOP+++1ZxnoyeWVnDuKzFcHQKb0QMDAqVBHdoK5woBy7TkUpm6HQq2pE+iJSPyMRiNWrFiBvXv3Vj8nl8vRs2dPPPDAA+jYsSNUKlWd7SoqKnD+/Hns3r0bv/32G4xGI0pKSvDRRx9h//79yM3Nre6xrwrzfn5+znpZ1ESSDvSzZ89Gbm4unnnmGSxdurTWsrlz5+Kbb77ByZMnER0dzV9OEdmccgmXdM7rna+yfmc2dPpSm4brkOvx9vZGnz594O0tzf/H/DULYS4vRdziVHhHd62zvLJAJ0BV5Eqk3gbcUWVlJZYtW4YTJ05UP9e9e3fMmDEDQUFBDW7r6emJ+Ph4xMfH49FHH8Xq1atx4MABAMCpU6eq12OYd22SHUOfnp6ONWvWICgoCG+//bbVdXr06AEA6Nr1//7oVb0B6N27N1QqFWQymVPqpab7ad/vghy30mjGjoN5ghybHCcyMhLLly9HZGSk0KU0izLtOSg0gVbDPAB4+Ic4uSJyNVJvA+7GbDZj+fLl1WHew8MDM2fOxNy5cxsN87dr2bIlnn32WfzlL3+plX9UKhVeeeUVhnkXJtlAn5ycDLPZjMmTJ8PX19fqOmq1GkDtQH/+/HmsX78eISEh6NWrl1NqJdscS7vmlscmxzCZTCguLq5zcZhUqELawVR0DQUHNwhdikspNZmgLy+3+s/dSL0NuJudO3fi8OHDAG4F73nz5mHgwIF2d0jm5+fjxx9/rDURRHl5OXbt2uWQeql5SDbQ7969GwAwaFD9Y0Vzc3MB1A70999/P/Lz87Fx40YkJiY2b5Fks/IKE06fF27u5GNpesGOTY5x7tw5DB48GOfOnRO6lGYROuHvkCk9cHFREk7/NRbZH0zH1a3/huGSe9/5+PWMMwjb/qPVf+5G6m3AnVy5cgVff/119eM5c+YgPj7e7v3dPpvNXXfdVf3G4IcffkB2dvYd1UvNR7Jj6HNycgAAbdq0sbrcaDRWjxGrGejlcsm+x5EEnb4UlUazYMf/XVcs2LGJmsK3Y1/EvXsMl398FzePbcW1XV/g2q4vbi2L74+oOaugCmlrdVuZwgNyT7Uzy3WaxyPbIimstdVlI37b5+RqiBzjyy+/rL45VGJiIu6++26793V7mK8aM79t2zZs2LABJpMJK1euxBtvvOGQ2smxJBvoS0puXTRpMBisLl+zZg30ej00Gg2io6ObtZaePXtCp+OFaI5QKQ8EWs6ud3nVjaPqExKkrv56aceketer78ZTuXmXERERYUPFriW/5d8AeQvk6/JF/TpqGj9+vE3rX7lyBQCwdetWHDt2rEnbjBs3zua67pTMU4273revB1Ud1QVRc1YBAMqv5KD49D7od6xAcVoKzr81FnHvHoPco+7NYwIHTkbgwMl21xwb2x6WCuvnXFup5XKkdevrkH0BQIyvLx4Ivsth+7MmNjYWBrPzOxyk2gYcbdxfnoOPr1/1+e/2x67I09Oz3usAr1y5guPHjwMA/P39MXmy/W23vjDv5+eHhx9+GIcOHUJeXh7OnTuHCxcuoF27dlb3Exsbi4qKCrvrcHchISE4evSoXdtKNtCHhISgoKAAx48fR9++tf8o5Ofn46WXXgIAJCQkNPuFrzqdDnl5vJjSITzKgZb1L666cVRjlAp5k9a7ndlYIe7/S40JkANmk0ncr6OGqjfvTVX1Jt9gMDR5WyF+VnKVNxwRP1Wt2kA1eCoCBk1Bxrz+KEk/gNJzh+Ebf58D9l6bVquFubzUIfvyViiAbg7ZldNotVqUCjAuXaptwNHMf/zfVJ3/bn/siqxNM1ll586d1ePchw4dWn1doK0aCvMAoFQqMWrUKHz66acAgB07dtQb6LVabfUnBuRckg30iYmJSE9Px+LFizFkyBDExsYCAI4cOYIpU6ZAr781FtoZN5QKCeGsEo5ihifyG1iu0zccJkKC1FAq5DCazNDp6+9JrG8/HvIytAoPb0qpLilfoYAZgFyhQKiIX0dNPj62vTGrCjBqtbrJ24YL8LOSOXjoi0wmg09sH5SkH0DFteYJL2FhYQ7toRebsLAwQXropdoGHE2uUFR/DQ8Pr/PYFXl61v0krcqvv/4KAFAoFA1eL9iQxsJ8lXvvvRf//e9/UVpaioMHD+KJJ56A4o+fX01hYWHsob8Dd5IXJRvoq+aZv3TpEjp16oSOHTuirKwM58+fx4gRIxAVFYWff/651vj55mLvxydkXYcx3yEz56bVZdaGydR0acckRNzlA53egNZDvrX52NMmDMRn/3zN5u1cRURiMvKulCI0JBS5p3OFLschjhw5YtP6RqMRjz32GDQaDZTKpp0C33//fTsquzMGI9B/i+3bFabugKbLIMgUtV+budyAwtTtAAB1a/svmmtIZuY5qB30V8VSVgbjhGmO2ZmTZGZmQubl5fTjSrUNONpbH32NwuKSW+e/3Nw6j12R0WjE+vXr6zx/8+bN6o7J2NhYtGzZ0uZ9NzXMA4CXlxcSEhLw22+/oby8HFqtFq1b170mJTMzs8m/U+RY4usCaaKIiAikpKRg1KhR8PLyQnZ2NgICAvDJJ59g8+bNyMzMBACnBHpyrB7xgQIe27Y5fcn1KJVK+Pv7S/aPzqWVz+N/M1oj5+OncGXzh9Dv/Bzabxci7bluKMs5jYBBU6GO6iJ0mSQgqbcBd3Dx4sXq79u2tX6Re0NsCfNVal5vWPP45Bok3Zrj4uLw008/1Xm+uLgY2dnZkMvl6Ny5swCV0Z0Y1CsUyVuFOZkM7BUqyHHJcXJzc/Hee+/h+eefd9kL4e5E6+nLcOPQjyhO/wUFv66HqeQGFD4toG6TgJCklxE4+DGhSySBSb0NuAOtVlv9fX2z+dXHnjAPAFFRUdXfu+o1B+5M0oG+PmfOnIHFYkFsbKzVW19/9913AIC0tLRaj6OiotCzZ0/nFUpW/WlkO7zw7mEUlVQ69bgDe4WiY3RLpx6THK+4uBgpKSl44oknhC6lWfh1Hwq/7kOFLsNlDAhqhYoxExpcp7HlUiP1NuAOPD09ERwcjIqKCpvu3nrlyhW7wjwAaDQatGjRAh4eHnZfgEvNxy0D/alTpwDUP9zmkUcesfp42rRpWLVqVbPWRo3z9fbAtAfb48PkNKced9bEOKcej4iIyJohQ4ZgyJAhNm/n5+eH4OBgXL9+3aYwD9wa2vPJJ5/YfExyDgZ6K2re7phc0wtTO+OLHzJRYjA65XgJsQF4aJBtH2sSERG5Ei8vL8ybNw9fffUVJk2aZFPvPrk2yV4U25DGAj25vqhwDd55vpdTjqVUyrDqjf7w8HDL5kJERBLi5eWFJ598kmFeYtyyh3737t1Cl0AOMHNCHL7fnYOdv2kbX/kPVfPLNzZffU2vPt4N3eM4u41UBAcHY86cOQgODha6FCJBsA0QSY9bBnqSBrlchrVLB2Pg9C34X+b1Jm3T2Dz1t5syOgb/mNndnvLIRQUGBt7RLdKJxI5tgEh6OIaARM3fT4Vdn41olvnh//JQe3z+en/I5TKH75uEU1hYiJ07d6KwsFDoUogEwTZAJD0M9CR6Qf5e2Pf5SDzzJ8fc/dJHrcRH8/tixT/7Q6lkE5EarVaL+fPn15rHmcidsA0QSQ/TCkmCj7cHls/riz0rR6JDVAu79zP03nCcWv8wZk2KZ888ERERiQLH0JOkDOwVirQfkrDztzx8vCYdm/Zdgtnc8DSkvt4emDK6Hf46IQ5dYgOcVCkRERGRYzDQk+TI5TIMvTcCQ++NQFFJBVLPXsfRND3OZt1AaZkRCrkcGh8PdI0NQI/4QHSK8Yenh0LosomIiIjswkBPkqbx8UT/HiHo3yNE6FLIRahUKnTo0AEqlUroUogEwTZAJD0M9ETkVqKjo7F69WqhyyASDNsAkfTwolgiIiIiIhFjoCcit5KRkYF+/fohIyND6FKIBME2QCQ9DPRE5FYsFgsqKythsTQ8+xGRVLENEEkPAz0RERERkYjxolgiIhfkpQBSRgpdhW28HDn7q0oF5dovHbhDJ+CsMeRgCoUCSUlJDtnXkk/WoKikBBofH7z01MR6n7sTCgWngBYKAz0RkQuSyQC1G5+hZTIZ4OUldBlEgpLJZFAqHXMisAAwW259rdqntedInPi/R0RuJSoqCsnJyQgPDxe6FCJBsA0QSQ8DPRG5FS8vL7Rr107oMogEwzZAJD28KJaI3Ep+fj7efPNN5OfnC10KkSDYBoikh4GeiNzKzZs3sXHjRty8eVPoUogEwTZAJD0M9EREREREIsZAT0REREQkYgz0REREREQixkBPRG4lICAA06ZNQ0BAgNClEAmCbYBIehjoicityOVyeHh4QC7n6Y/cE9sAkfSwNRORW9Hr9VixYgX0er3QpRAJgm2ASHoY6ImIiIiIRIyBnoiIiIhIxBjoiYiIiIhEjIGeiNyKRqPB8OHDodFohC6FSBBsA0TSoxS6ACIiZwoPD8frr78udBlEgmEbIJIe9tATkVspLy/HpUuXUF5eLnQpRIJgGyCSHgZ6InIrWVlZSEpKQlZWltClEAmCbYBIejjkhojIBVksFkBsPagqFWQymdBVEJFEWCwWmEwmocuwiUKhEOQ8yEBPROSKysthnDBN6Cpsolz7JeDlJXQZRCQRJpMJ69evF7oMmyQlJUGpdH685pAbIiIiIiIRY6AnIiIiIhIxDrkhIrfSsWNHHD58WOgyiATDNkAkPeyhJyIiIiISMQZ6IjdhsVhuzZzyx/fuKicnB9OnT0dOTo7QpRAJgm2ASHo45IZIoioqTdi453ekHNfhWPo1pJ69hhKDEQCgvWpA9PA16NkpCD3igzBucBt0iG4pbMFOYjAYcPr0aRgMBqFLIRIE2wCR9DDQE0mM9koJPvo2HSs2ZODK9bJ618vWFiNbW4zvdmRj3v87igf6hOHpSXF4aHAbziVOREQkIgz0RBJhsViwckMm/rb0EIpKKm3eftchLXYd0uKBPmFYufA+tAnTNEOVRERE5GgcQ08kAddvlmPkrO14YuEvdoX5mnYd0qLzw9/jvz+dd1B1RERE1JzYQ08kcpevGZD4xFacPl/gsH0Wl1Ziyvx90BeU4bkpnR22X1cQGhqKhQsXIjQ0VOhSiATBNkAkPQz0RCJ2s6gCw2Zuc2iYr+n5JYfgo1biifEdm2X/QmjRogVGjBghdBlEgmEbILLf1atXERwcLHQZdTDQE4nY7EUHcTLjerMe4+m3DuKehFboEhvQrMdxloKCAuzcuROJiYnw9/cXuhwip2MbIHej1Wpx8eJFXLx4EXl5eSgvL4dMJoNarUbr1q3Rtm1bxMTEIDAwsMH9HDt2DO+99x6mTJmCYcOGOan6pmGgJxKpTXt/x1ebbBvnfiT5QYQEeUOnL0WvP21s0jaVRjMee20/fvvvg/DwEP9lN5cvX8aSJUvQpUsXhhlyS2wD5A7Ky8tx8OBBbN++HRcvXqx3vePHj1d/36VLFwwZMgQ9evSAQqGotd6xY8ewbNkymEwmfPHFFwgJCUHXrl2brX5bif+vcxPo9XrMnTsXMTEx8PLyQuvWrTFnzhyUlJRgxowZkMlk+PDDD4Uuk6jJyitMmPnmAZu3CwnyRsRdPggJ8rZpu+Pp1/Dht2k2H4+Et09/BZ6b1mLZhbP1ruO5aS0eOpTixKqIiJrPwYMH8eyzz+I///lPg2H+dqdOncKyZcvwwgsvID09vfr5mmEeAPr164fOnV3r+jLJ99CnpqZixIgR0Ol08PHxQXx8PLRaLT744ANcuHAB16/fGq7QrVs3YQslssF3O7KgvVLq1GMu/yYNs/8cD4XCLfoBiIhIZAoLC7Fy5UocOnSo1vNRUVHo06cPoqOjERUVBR8fH1gsFhQWFiI7OxsXLlzAr7/+isuXLwMAdDodXn/9dQwbNgxxcXH44IMPaoX5WbNm1enBF5qkA71er8eYMWOg0+nwwgsvYMGCBdBobs2t/c477+Dll1+GUqmETCZDQkKCwNUSNd1H36Y3vpKDZeUVYduBXIy6P9LpxyYiImqIXq/Hv/71L+Tn51c/16NHDzz00EOIiYmxesPEoKAgBAUFoWfPnnjkkUdw6tQpfPfddzh37hwsFgu2bduGbdu2Va/vqmEekPiQm9mzZyM3NxfPPPMMli5dWh3mAWDu3Lno2rUrjEYjoqKi4OfnJ2ClRE134VIhDp68IsixbR2z74q8vb3Rp08feHvbNuyISCrYBkhqCgoK8MYbb1SHeY1Gg9mzZ+PFF19E+/btm3T3c7lcjq5du2LhwoWYMmVKndDet29flw3zgIQDfXp6OtasWYOgoCC8/fbbVtfp0aMHANS6qOG7775DUlIS2rRpA29vb3Ts2BGvvvoqiouLnVI3UWMOn7oq2LGPnNYLdmxHiYyMxPLlyxEZ6V6fNJSaTNCXl1v9R+7FXdsASZPZbMZ7771XPVwmJCQEb731Fu69994mBfnbyeVyhISE1HleqVS6bJgHJDzkJjk5GWazGZMnT4avr6/VddRqNYDagX7p0qWIjIzEW2+9hYiICKSmpmLhwoXYt28f9u/fD7lcsu+BSCSOpgkXqrPyinDtRhkCW3oJVsOdMplMMBgMUKvVLn1ydrTXM87g9YwzQpdBLsBd2wBJ05YtW5CZmQng1hCa1157rdHpJxty+wWwCoUCJpMJKSkpuOeee6o7g12NZAP97t27AQCDBg2qd53c3FwAtQP9pk2bat0wYMCAAQgODsbkyZPxyy+/4P7772+mioma5kwz3USqqdIu3ED/HnV7L8Ti3LlzmDp1Kr766it07CidG2Y15vHItkgKa2112Yjf9jm5GhKSu7YBkh6dToc1a9YAAGQyGZ555hmHhvl+/fqhU6dO+PTTTwEAK1asQFxcnEsOV5NsoM/JyQEAtGnTxupyo9GIAwduTftXM9Bbu/tXz549AQB5eXl21dKzZ0/odDq7tiW63VXNdMDD+u911Tzz9QkJUld/vbRjUoPHqW+u+nHjJ8Gr0nXG0o8fP96m9a9cuXX9wdatW3Hs2LEmbTNu3Dib67pTarkcad36Omx/Mb6+eCD4Loftz5rY2FgYzOZmPQbVJdU24Gjj/vIcfHz9kK/LR0RERJ3HUmft9br6z8DT07PeYdPArd75yspKAMDw4cPv6A2qtTA/a9YsyOVyHD58GKmpqSgoKMD+/fsxfPjwevcTGxuLiooKu2oICQnB0aNH7dpWsoG+pKQEAGAwGKwuX7NmDfR6PTQaDaKjoxvc1549ewAAcXFxdtWi0+nsfjNAVEfbcsDD+qKqeeYbo1TIm7SeNdf0eqDYdX6fq9p6U1WdEwwGQ5O3FaL9eisUQDenH/aOaLValP7xx5CcR6ptwNHMf/xumk0m5OXl1XksddZer6v/DFQqVb3LDAYDUlJSqtez9Y1tTfWF+aohaZMnT0ZqaioAYPv27Rg2bFi94/O1Wi3KBbg2SbKBPiQkBAUFBTh+/Dj69q3dy5Wfn4+XXnoJAJCQkNDgRRN5eXl47bXXMHz4cLvnqrd2cQWRvfQeMtR3qtDpG56bPiRIDaVCDqPJDJ3e+pvdxvYVFOgHVYvwppTqFD4+tr0xqQowarW6yduGhzv/9apFeL1OWFgYe+gFINU24GjyP8KZXKFAeHh4ncdSZ+31uvrPwNPTs95lBw8erH5z2q9fP5vbQZXGwjwAtG7dGnFxcUhPT4dWq8XZs2fr7eQNCwu7ox56e0k20CcmJiI9PR2LFy/GkCFDEBsbCwA4cuQIpkyZAr3+1oWFDYX04uJijB07Fp6envj888/trsXej0+IrHlx6SG8+9Vpq8usDZGp6dKOSYi4ywc6vQGth3xr1/EzTu5BQIv6e02c7ciRIzatf/bsWSQnJ2PEiBFN/nj2/ffft6OyO2MpK4NxwjSnH/dOZGZmQuYl3gumxUqqbcDR3vroaxQWlyA0JBS5ubl1Hkudtdfr6j8Do9GI9evXW1129uz/3f16wIABdu2/KWG+5jGq7h7bUKDPzMyEUun8eC2+LqAmmjt3LgIDA3Hp0iV06tQJXbp0Qfv27dG7d2+0bdsWgwcPBlB7/HxNBoMBY8aMQVZWFrZv347Q0FBnlk9Urx7xQYIdOzpc41Jh3h4xMTH4+eefERMTI3QpRIJgGyApuHjxIoBbs9A0NnTaGlvCPAC0b9+++vusrCw7Km5ekg30ERERSElJwahRo+Dl5YXs7GwEBATgk08+webNm6unOLIW6CsrKzF+/HgcPXoUW7duRXx8vLPLJ6pXn4S6F247S+8uwr2ZcBSlUgl/f39BelCIXAHbAIldRUVF9Zj/1q1bNzg0xxpbwzwAhIaGwuuPTyCzs7PtK7wZSbo1x8XF4aeffqrzfHFxMbKzsyGXy9G5c+day6rmrt+1axe2bNmC3r17O6tcoiZpG+GHft3vwoETl51+7Glj2je+kovLzc3Fe++9h+eff94lZ3VwtAFBrVAxZkKD6zS2nKTF3doASU9paSksFgsA2DxNpT1hHrh1w6mAgABotVqXvNmopAN9fc6cOQOLxYLY2Ng6c4k+/fTTWLduHV555RV4e3vjt99+q17Wrl07q9NaEjnbrAlxTg/0bSM0GNZP/H/8i4uLkZKSgieeeELoUogEwTZAYufj44MFCxagoqKi3puHWmOxWLBlyxabw3yVxx9/HEajscHZd4TiloH+1KlTAKwPt9m6dSsAYNGiRVi0aFGtZV988QUee+yxZq+PqDFJQ6Lw8vs+yL1s23R1d2L2n+Mhl9t+G20iIiJH8vDwsGsqcZlMhhdffBGLFi1CUFCQTWEegEsPwWagv40rjosiup3KU4FP/9EPI5/e7pTj9eochKcnue6JjIiIqCnUajXmzZsHDw8Pm8K8q5PsRbENaSjQE4nFiP6t8ZeHbBvTrtOXIvdySaPz1dfk6SHHqjfuh1LplqcLIiKSGC8vL0mFecBNe+h3794tdAlEDvH+3HtwMuM6jqdfa9L6jc1Tb81/XuuH+Hb+Nm/nqoKDgzFnzhxeD0Nui22ASHrY5UYkYn6+ntj272Ho2iGgWfa/fF5f/OWh2GbZt1ACAwMxefJkm2dGIJIKtgEi6WGgJxK54AA19q4cidH3t3bYPv18PZC8eCCe+ZP0xs0XFhZi586dKCwsFLoUIkGwDRBJDwM9kQS09FNh4/Ih+PLN+9FSY9sNNm43vF8EzmxIwqQR7RxUnWvRarWYP38+tFqt0KUQCYJtgEh63HIMPZEUyWQyTH2wPYb1i8B/1qbj0/UZ0F5p2sWvMtmtID9rYhxG3d8aMhmnpyQiIhILBnoiibkrUI0Ff70b8x/vhi2/XMIvxy/jWJoeJ85ew42iCgCAQiFDuwg/9IgPRI/4IDw0uA3atfYTuHIiIiKyBwM9kUR5eMgxdlAbjB3Upvo5s9kCk8kCDw+OtiMiIpIKBnoiNyKXy9z+bq8qlQodOnRwyVt3EzkD2wCR9DDQE5FbiY6OxurVq4Uug0gwbANE0sPP3YmIiIiIRIyBnojcSkZGBvr164eMjAyhSyESBNsAkfQw0BORW7FYLKisrITFYhG6FCJBsA0QSQ/H0BMRuSKVCsq1XwpdhW14kSUROZBCoUBSUpLD9rfkkzUoKimBxscHLz01sc5jR1AoFA7Zj60Y6ImIXJBMJgO8vIQug4hIMDKZDEql46KqBYDZcuurUqms81jMOOSGiIiIiEjExP12hIjIRlFRUUhOTkZ4eLjQpRAJgm2ASHoY6InIrXh5eaFdu3ZCl0EkGLYBIunhkBsiciv5+fl48803kZ+fL3QpRIJgGyCSHgZ6InIrN2/exMaNG3Hz5k2hSyESBNsAkfQw0BMRERERiRgDPRERERGRiDHQExERERGJGGe5ISJR69Wrl03rR0REYMGCBUhMTERoaGgzVUXkPGwDRMRAT0RuJTQ0FP/85z+FLoNIMGwDRNLDITdERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkDvAlavXo0ePXrA398farUacXFxWLZsGSwWi9ClERERUT22bNmCbt26QaVSISoqCsuWLRO6JKfav38/xo4dizZt2kAmk+HNN98UuiSnWrJkCfr27Qt/f3+0bNkS9913H7Zt2yZILUpBjkq1tGrVCq+99ho6dOgAlUqFlJQUzJo1CwqFAnPmzBG6PCIiIrrN0aNHMXbsWLz44otITk7GoUOHMHPmTHh7e2PmzJlCl+cUxcXFiI+Px5///Gc899xzQpfjdLt378b06dPRq1cveHt7Y8WKFRg9ejT27duHfv36ObUWBnoXMGzYsFqP27Ztix9++AF79+5loCciInJBy5YtQ69evfD2228DAOLi4nDmzBksWrTIbQL9yJEjMXLkSADAyy+/LHA1zrd169Zaj9955x1s27YNGzZscHqg55AbF2OxWHD48GEcOHAAgwYNErocIiIisuLAgQMYPnx4reeGDx+OnJwc5ObmClQVCclsNqOwsBA+Pj5OPzZ76F3EzZs3ER4ejoqKCpjNZixYsACzZ88WuiwiIiJRqTQakXVJV+d5o8lU/TUzK7fO45qCA1rAv4WmwePk5+cjJCSk1nNVj/Pz8xEREWH3a7hTuflXUVpWXus5a6+3vp+BykOJNhG1X5uYFBaXQnf1ep3nbfkdiAxrBS+Vp03Hfeutt3Djxg08+eSTdlZuPwZ6F6HRaJCamorS0lL8+uuvmDdvHsLCwjBjxgyhSyMiIhINpUKBw6npOJ2ZZXV5qaEMn6/dUu9jH28vPD/9kWavszkVlxqw6jvrF2fe/nqtPTd+xABRB3qVhxI/bE/B9RtFVpc39jsQ3ToUT0waZdMxP/74Y7z11lvYuHGjIG/mOOTGRcjlcsTExCAhIQEzZ87E3Llz8eqrrwpdFhERkajIZDKMG9Yfvj5qu7ZPGn5/k7YNDQ2FTlf7k4DLly9XLxNSx3aR6N21o13bxrePQo8usQ6uyLlUKk9MGDUIMpnM9m09PTBh1EDI5U2PyEuXLsVLL72EjRs3IjEx0eZjOgIDvYsym80oKysTugwiIiLR8fH2wvgRA2zermdCB8S3j2rSuv369cPPP/9c67lt27ahTZs2gg63qTJqcF8EtvSzaRtfbzUeHt7friDsaqIiQjCgT1ebt3swsV+jw61q+sc//oGFCxdiy5YtgoV5gIHeJSxYsAA7d+7ExYsXkZGRgc8++wyLFy/GtGnThC6NiIhIlDq2i0SfbnFNXj+ghQZjBvdt8vrPP/88Dh8+jFdffRVnz57Fl19+ieXLl+OVV16xp1yHU3l6YMJo23qpHx5xP3y9m/7JRnFxMVJTU5GamoqKigrodDqkpqbi/Pnz9pTscIn39UBoq8Amr98pNgp3d27f5PWfe+45LFmyBKtXr0aHDh2g0+mg0+lw8+ZNe8q9IzIL714kuOeffx6bNm1CXl4evLy80LZtW0yfPh0zZ86EQqEQujwiIiJRKq+oxAer1uNaQWGD68kAPDX5QUTZOG588+bNmD9/Ps6ePYuQkBDMmTMHf/vb3+6gYsf7ef8R7Dl4otH1eiV0RNKI+23a9969e63OyDdgwADs3bvXpn01F93V6/jwy++rL4Ctj6+PGs9NH2/TG5r63ixNmzYNq1atsqXMO8ZAT0RERJL1e95l/PvrjQ3efX1An64YMbCPE6tyHqPJhI9X/wDt5Wv1rhPQUoM5jyVBZeOsLmKRcvh/2LzntwbXeWz8cHRsF+mkihyPQ25E5lL+lTpTUREREZF1keF3YdA93epdHtoqEEPu6+m8gpxMqVBg4ujBUNbzib9MJsOEUYMkG+YBoF+vLmgbGVbv8t5dO4o6zAMM9KJiNJnw3+93YPG/v8HveZeFLoeIiEgUHujXA+F3BdV5XqGQY+LoQVAqpT289a4gfwwf0NvqsgF9uto81Ehs5DIZJowaCJWnR51lgS39MMqGaydcFQP9bUwmE1avXo2hQ4ciODgYKpUKkZGRGD58OFasWAFTI2OwmtOxUxm4WVQCT08Pmy7yICIicmcKhRwTrAT3Yff3RkhwgEBVOde9PTujXZvavdShrQKReF8PgSpyrpZ+vhg7pF+t52QNBH2xYaCvobCwEEOGDMHUqVOxY8cOeHp6omvXrjCbzdi+fTueeOIJFBVZv0lBczOaTNj9662LWgb26QYPD94TjIiIqKlu76WObh2K+3p1EbAi55LLZHhk5MDqu5/eGoozqN6hOFLUvVN7dI6Nrn488J6uor6BVk0M9DXMmDEDe/bsQUREBHbv3o28vDwcPnwYubm5yM/Px7/+9S94eAjzLq6qd17j6233zSKIiIjc2b09OiOmTfj/3TxIAvOt26JmL/Ww+3u5zacTVapuOqbxUSPsrkA80E86n05wlps/HDt2DD179oRSqcSJEyfQuXNnh+17+ZcbUFRsuIM9WFBUYoDFYoGXyhOeAr2pICIiEjuz2QyT2QwPpXt+0m2xWFBRaYSnh1ISN5Cyh9FohEwuh8KGu8E6g8ZXjWenPWzXtu7522zFDz/8AAAYNWqUQ8M8ABQVG1BYXOKQfZWVV6CsvMIh+yIiInJXBrj3jHHlFcwSUsJA/4e0tDQAQN++jr/SWePb9JsU1MXeeSIiIiKpu5O8yED/h8LCW3eRa9GihcP3be/HJwBwKDUd3/+cAo2vN+Y+OYkXwxIRERFRLUyHf/Dz8wMA3Lx50+H7tn8M/a3eeQCorDRiyadrHFsYEREREbkEjqF3gE6dOmHDhg04ePCgw/ftiDH0HDtPRERERNYw0P9h3LhxeOONN7BlyxakpaUhPj7eYfu2b0wUx84TERERuYs7GUPPaStrmDhxItauXYvIyEh89dVXGDBgQPWyy5cv4/PPP8fs2bPh4+PT7LVw7DwRERERNQUDfQ2FhYUYO3Ys9u7dCwAIDw9HWFgY8vPzkZeXB4vFgoKCArRs2bJZ6zCaTFj66RrcKCzGmAfuRb+ejp1Gk4iIiIikw7Vm1BeYn58fdu7ciZUrV2LgwIEoLS3FyZMnIZfLMWzYMKxcuRIajabZ6zh2KhM3Cot5V1giIiIiahR76F3QiTPnsHXvYQzo05W980RERETUIAZ6F1VpNEIGGZRKhdClEBEREZELY6AnIiIiIhIxjqEnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIiIiIhIxBnoiIiIiIhFjoCciIiIiErH/D0oMrBQ3gULaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare transpiled circuits for different optimization levels on backend 2\n",
    "\n",
    "optimization_levels = [0,1,2,3]\n",
    "print(\"original circuit\")\n",
    "ghz.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimization level: 0 \n",
      "\n",
      "optimization level: 1 \n",
      "\n",
      "optimization level: 2 \n",
      "\n",
      "optimization level: 3 \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2263.23x785.944 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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BeXh76dS+I+r4yHClLFyns4cuvl959u3fJ+8A5z2xsrrbgLPPv+TcNgDA3Cq7D2RuPaDI+M4Ku7y1jq//fY59T19vhV4WpWO/GDvvvrPuB/QF6AvQF7CfIwMz9uzZo9mzZ2vAgAFq27at3fu9/vrrVYjs0rhaG3D2+XckD9SGHCA5Nw+Y/T7gCEcHZ1UlDxiRA4DCwkLNmzev3HXbtm2z/f+1115bpePbU+yVJG9vb/Xp00eLFi1SUVGRdu3apauuuqrcY+7bt09eXjWfCGp1KSI8PFxZWVnavHmzevToUWpdenq6nnzySUlSx44dZbFYKjzO0aNH9cwzz6h///7q3LlzdYYsSZo0aZIOHDigoUOHavbs2Yac2Kq6MF/v/v37dejQoXJH+S5fvlySLukph7VR/YRRqp9Q9SH/tc2R7zaqab9uyk7NVEH2xT9Vjr17oCJ6XqZNL/5PR77doBuWT1HP1x7Qt8Mm1kC0xnO38w/APJK/XqeODw9Tu3sGlSr4th7ZV94Bfkqa7xrPEKgN3O1eQF/AMe52/u3VqlUrLVu2rMojodyJu7UBcoDj3K0N2Is8AHeQnJwsqWTah+jo6Crtb0+x94LY2FgtWrTItm9FBV+jVP3pZTWgb9++kqSXX35Z+/btsy1PTExUQkKCMjMzJanSIm52draGDBkiHx8fffDBB1WOpU+fPho+fLhdX2944403NGnSJM2ZM8elir1SyXQNDRs2VEFBgW6++eZSv/ecnByNHz9eK1eulCSNHj3aqDBhhyPLN6rp9XFqHN9JaT9tr3TboBbh6jLhDv22Zb9+nfGVTu1L1dZpXyi8R3vF3j2whiIGAFTFqT2HtefDbxU16EolvP+kWt9xreImjlb358YoY91OJc1fY3SIMAh9AdjDy8tL9erVc7m/W3Bx5ADYizwAV3f27Fn99lvJPOVRUVHy8HCs3OlosVdSqaJyUlJSFaKuXrW64Dt+/HjVr19fR44cUfv27dWhQwe1bt1a3bt3V3R0tK655hpJpefv/aOcnBzdcMMNSk5O1vLlyxUREVHlWCZNmqS5c+eWOz/wn/n7++vZZ5+Vt7d3ld/vj9auXauwsDDbv1dffVWS9Pnnn5dafmE+40vZLzAwUJ999pkCAwOVmJio2NhYRUdHq1OnTgoLC9OUKVMkSQ8++KCGDBnilJ8P1ePY+t0Kjo5Q8wHd9Vvi3oo3tFjU6/WH5OHhoTXjZshaXDLH1q//+VqZWw+oy4Q7FNS8Ko9HAADUlA3PzlLicx8pJKaJrpz8F7UY0lO7P1iqFaNevOT5F+G66AvAHqmpqXr88cdtD8OG+yAHwF7kAbi6U6dO2f7f0dpfVYq9klSvXj35+/uXef/aolYXfJs0aaLVq1dr0KBB8vPzU0pKikJDQzVz5kwtXrzYNvq0vIJvQUGBRowYoY0bN2rp0qVq165dTYfvNAUFBTpx4oTt34U5jfPy8kotLygocMp+ffv21fbt2/XQQw8pJiZGGRkZ2r17t+rWrashQ4Zo0aJFmjFjRs388Kgya1Gxjq4qmcPmQqetPO3vu0GNurfVlilzdHr/7w81tBYXa824GfLw9FTP1x6o9ngBAFVnLS7WzpnfaEHvcfok6nZ92eWvSnzuIxWer9p8+3AP9AVgj+zsbK1evVrZ2dlGhwInIwfAXuQBuLqgoCDdcsstuummm9SlSxe79yssLNRrr73mcLH3gkGDBmnYsGHq169fleKuTrV+vP4f58T4o+zsbKWkpMjDw0OXXXZZqXXFxcUaOXKkVq5cqSVLlqh79+41FW61iI+Pl7UKo3Oqup9UMjR9+vTpVdoXtcfhpRsqHdlVt3Wkuoy/Tcc37tXO/35TZv2Fr3J1nTBSsXcP1O73q/kpCQAAwKnoCwDmRg4AYAYhISEaNmyYw/t5eXlp3LhxeuGFF9S0aVOHir2SNGLECIffs6bU+oJvRXbu3Cmr1aqYmBgFBASUWvfggw/qyy+/1D/+8Q8FBATol19+sa1r2bKlXdMyAO7g0KKfK11/ev9RfdLijkq32TF9gXZMX+DMsAAAQA2hLwCYGzkAACrXsmVLPffcc2rYsKFDxd7azmULvjt27JBU/nQOS5culSS99NJLeumll0qt+/DDDzV27Nhqjw+uLWvtXJ3euFiF57KUe2SXPHz85VW3oZrd/7b8IloZHR4AAHCirLVzdWb7SjW9+zUlTb2Ne78J0QZAGzA3zj9gbs2aNTM6BKdzy4JvSkpKDUcDd3PqlwWq1+sWWTy9Fdx1gCwWi44vnqFDM/6iNi+sMjo8AADgRKd+WaDQhNGSpAbX38u934TM3AYaNGigcePGmf5bkGZuA+D8kwcA9+OWBV+gMoXZp7Tr4ctUnJ8jn7CmshbkKS8jSaHxoxT1t/dkLSxQ9p61iho3SxYvb9t+gTFX6thXUw2MHNXpYu0CAOC6Ksvxze9/u9R9v27cQNt+3PvdB22gYvXr19fIkSONDqPa0QbMjfNfObPkAcBMXLbg+/333xsdAlyUV50QhV59hzz9gxRx6zM6vXmZMuZOthX1zu74QYFtrypV7JWk44veUEj3IUaEjBpwsXYBAHBdleX4M1uWl3vfl7j3uxPaQMXOnDmjDRs2qHv37goODjY6nGpDGzA3zn/lzJIHADNx2YIvUJE943soN21/uevavbZFPg2a6nzyVjUc/LAk6fzBTQqIvty2zan1X6nelUNL7Zf+5WTlpR9Q83+trL7AUa0utV0AAFxbRTm+vPu+xL3fHdEGypeWlqYJEybo448/dvtCD23A3Dj/FTNTHgDMgoIv3E7bVyp/Eq0k5SRvtd3gzx/cpJDuN0qSrFarTm9Zpsgxr9i2zVgwVad+nq/Wz6+Qh29A9QSNancp7QIA4PrKy/Hl3fcl7v3uijYA2oC5cf4BmImH0QEANS3/xFFJFvnUj5Qk5aRsl3/zDpKk8/s2yL9JrDz960iSjn39qrJWz1br57+TV50QgyJGTaisXQAAXFtFOf7P932Je7+7og2ANmBunH8AZsMIX5jO+aQtpb6q7xkYouNL3lLU395T1i8LFHLFTZKk/MxUpX7wuHzCo7Xv6QRJksXLV7FT1xsRNqpZZe0CAODaKsrxXsFhtvu+xL3fndEGQBswN84/ALOh4AvTCek2WCHdBttex05LtP3/6cRv1OjfP0iSfMKaqOvX1hqPD8aorF0AAFxbRTl+50Ptbfd9iXu/O6MNVMzX11dt2rSRr6+v0aFUK9qAuXH+K2eWPACYCQVf4A/az9hpdAgAAKCGcN8HbUBq0aKFPvnkE6PDMAxtwNw4/yXMngcAd8QcvgAAAAAAAADgJij4AgAAAIBJ7d27Vz179tTevXuNDgWAQcgDgPuh4AsAAAAAJmW1WlVQUCCr1XzzlgIoQR4A3A9z+MIl+HlKqwcaHYVj/Dyddywvf1+NPPip8w5YA7z8nTvhv9nbAACYndnvA/QFaANwvTbg7PNv9jzgaudfIgcAzubp6anhw4c77XhTZs7R2XPnFBQYqCf/emuZ187g6WlMIqDgC5dgsUj+Jm6tFotF3gF+RodhKLO3AQAwO7PfB+gL0AZAGzB7HjD7+QdQkge9vJyXCKySiq0l//Xy8irz2pUxpQMAAAAAAAAAuAnXLlcDAADAbuE92qv//EkVri8uLNLHTZ3z9TUAriEqKkqzZ89WZGSk0aEAMAh5AHA/FHwBAABMJmn+aqV+v7nMcmsxD2sBzMbPz08tW7Y0OgwABiIPAO6Hgi8AAIDJnNiRrKR5q6vt+F4Bfio8n1ttxwfgPOnp6Xr//fd19913KyIiwuhwABiAPAC4H+bwBQAAQLmaD7pC/edN0h17PtKdSZ9p6Oo31P1fd8nDu2TMQHiP9hqbPletbolX27H9ddOPr2lUymxddv+NBkcOwF6nT5/WwoULdfr0aaNDAWAQ8gDgfhjhCwAAYDJe/j7yDQ0qs7w4v1AF2TmSpMv/cbs6jRuurL1HtPOdRco5nqWg5uFqPugKbZ3yufILCm37tbtnkHzrBWnfZyuU89spnUs7UWM/CwAAAIDSKPgCAACYzOXjb9Pl428rs/zId5u0cvSLCuvcSp3GDVf6mh1acedkFeUV2LbZ9MKnZfYLjAzTgt7jlHviTLXGDQAAAODiKPgCAACYzN5Plivlm5/LLL9QsI0e3luStGny/0oVeytycO6PFHsBAACAWoKCLwAAgMmcScpQ+uodFa4PbhEha3Gxsnal2HW80wfTnRQZgJrm4eGhyy+/XB4ePN4FMCvyAOB+uJoBAABQhtVqldVqtWvbopy8ao4GQHUpLi7Wli1bVFxcbHQoAAxCHgDcDwVfAAAAlHImKU0enp4KbRdldCgAAAAAHETBFwAAAKUkzV8jSery1B3y8GYGMAAAAMCV0IMHAAAwmfodWtgezPZnh5cmKnPrAe2YvkAd/jZUNyx/RckL1ynn+CkFNWuo5oOu1OKB/1D+mfM1HDUAAAAAe1DwBQAAMJnoYb0VPaz8gu+8Hg/pbEqGNk3+TCd3pajt/w1QhweGSB4WnU87oaPfb1ZhTn4NRwygugQFBal///4KCgoyOhQABiEPAO6Hgi8AAIBJZPy8U7MiRti9ffJXa5X81VqnHQ9A7RMZGannn3/e6DAAGIg8ALgf5vAFAAAAAJPKy8vTkSNHlJeXZ3QoAAxCHgDcDwVfAAAAADCp5ORkDR8+XMnJyUaHAsAg5AHA/VDwBQAAAAAAAAA3wRy+cAlWq5RbZHQUjvHzlCwW5xzLarWqMMe1vl7j5e8ri7N+ASbniuf/Ame2A1fLA87MAZJrtgMzn3/J+W3A7MzeBsyeAyTaAFzvOuAa4BqAc1mtVhUVudZF4Onpyd/FMAQFX7iE3CKp9xKjo3DM6oGSv5OusMKcPH3W8k7nHKyGjDz4qbwD/IwOwy244vm/wJntwNXygDNzgOSa7cDM519yfhswO7O3AbPnAIk2ANe7DrgGuAbgXEVFRZo3b57RYThk+PDh8vLiIkDNY0oHAAAAAAAAAHATfMwAAAAAACbVtm1bbdiwwegwABiIPAC4H0b4AgAAAAAAAICboOALAAAAACZ16NAh3XXXXTp06JDRoQAwCHkAcD8UfAEAAADApHJycvTrr78qJyfH6FAAGIQ8ALgfCr4AAAAAAAAA4CYo+AIAAAAAAACAm/AyOgCgOp3dsUr7nk4otczDL1C+jWNUP36UGg7+myyeXAaAuyIHgDYA2oC5cf4BrgMAMCOyOkyh3tW3q27XgZLVqoKsDJ1Y9bFSP3hMuam71fzBd4wOD0A1IweANgDagLlx/isWERGhSZMmKSIiwuhQUM24DlAR8gDgfij4whQCoruofvydttcNBj6gnQ+0VeZ376nxnS/Iu24DA6MDUN3IAaANgDZgbpz/itWtW1cDBgwwOgzUAK4DVIQ8ALgfCr4uICUlRStXrlRiYqISExO1Y8cOFRQUaMyYMZo1a5bT95Ok3377TVOmTNE333yjlJQU+fn5qUOHDrrvvvt0xx13OPcHNICnX6AC21ypU+vmKi/joOk6N2PT5zrtWLMiRjjtWEBNIQeQA8zeBkAbMHseMPv5/6OsrCytWLFCffv2Vb169YwOp8aY/RqQuA7wO7PmAavVqrNnzyonJ0dWq1V+fn6qW7euLBaL3fsvW7ZM3bt3V2hoaDVHCziGgq8LeP311/XGG2/U2H67d+9W3759lZaWJm9vb1122WXKzc3VmjVrtHr1aq1cuVLvv/++w8etbfIyDkqSvOqYKzEHRoZpw8RZ2vXOIqNDAQxFDiAHmLUN4HdmbQPkgRJmPf9/duzYMU2ZMkUdOnQwTaGHa+B3XAeQzJUHjh8/rtWrV+vAgQNKSkrS6dOnS60PDAxUixYtFB0drV69eqlZs2blHsdqtWru3LmaN2+eli1bpmeffdbtf3dwLRR8XUBYWJgGDhyobt26KS4uTkuXLtVbb71VLfsVFRVp+PDhSktLU69evfTll18qPDxckrRjxw4NHjxYH3zwga688krdc889Tvn5akJx3nkVnsmU1WpVYVaGfvv2v8pJ2qKA1t3lFxljdHg1qul1cTqyfKPRYQA1ihzwO7PmANoAaAO/M2Me4Pzjj8x4DUhcBzC3nTt3avHixdqyZYusVmuF2507d06//vqrfv31Vy1cuFBt27ZV//79dcUVV9hG/v6x2CtJ6enp2r59u/r06VMjPwtgDwq+LuDpp58u9fqXX36ptv2WLFmi3bt3y9fXV5988omt2CtJHTp00H/+8x/dcMMNeu6553TXXXfJ09PTrliMlj57otJnTyy1LKTHMDX7638Misg4wdHh2jMrw+gw4GwWi9rdM0htRl2nOk0aKPfEGSV/s05bX5mjwpw8o6MzHDngd2bNAe7eBjr8bajqd4hW/Y7RCmreSNlHjmtu9weMDqtWcfc24Agz5gHOP/7IjNeAxHUAczp37pw++eQTrVq1qsy6C6N5g4ODZbFYdO7cOaWkpOjUqVO2bfbs2aM9e/aoc+fOuueeexQaGlqq2CtJY8aModiLWsdlCr6ZmZl65ZVXNH/+fKWmpqpBgwYaNmyYJk+erIcfflgffPCBpk+froceesjoUCWVfOJj77wvtcmaNWskSXFxcYqKiiqzfvDgwQoMDFRaWppWr16t+Pj4mg2wisL63at6V90sa1GBcg7tUMb8l5WfmSqLt59tm7M7V+vA82UnqrcW5staXKSuC4pqMuRq4RXgp4LsXKPDQDXo/vxYtfvLIB1asl6//vcbhbSOVLu7B6r+ZS207JbnpUo+xTYDckAJM+cAd28DXSeMVO7Jszq5I0k+wQFGh1MruXsbsJdZ8wDnHxeY9RqQuA5gPvv379drr72mkydP2pbVr19fffv2VY8ePdSoUaNy6zYnT57Uhg0btGLFCqWmpkqStm7dqieeeEKdOnUqNZhuzJgxPPAOtZJLFHy3bt2qAQMGKCMjQ4GBgWrXrp3S0tL05ptv6uDBg7aLt3PnztUWQ3x8vH788UclJyeXWwj9o+3bt2v06NGaO3euWrVqVW0xVYcLv8vIyMgKt4mMjNS+ffu0bt06lyn4+ka0VnDnvpKkul0HqE5sL+19qpcOv32fop/8XJIU1L63Lp+TXWq//BNp2vN4nBoMqh0fJFyqxn066uiP24wOA04WEtNEsXcNUMriX7TqL1Nty88ePq4rX7hbLW7qqeQFawyM0HjkgBJmzgHu3gbmXvGAsg8flyQN+eFVeQf6XWQP83H3NmAvs+YBzn/FAgICdMUVVyggwBwfFpn1GpC4DlAxd8wDO3fu1CuvvKK8vJJvO/r7+2vkyJFKSEi46DeVQ0ND1b9/f/Xr10+bNm3S+++/r6ysLOXk5FDshcvwMDqAi8nMzNQNN9ygjIwMPf7440pPT9fmzZuVkZGhl19+WYsXL1ZiYqIsFos6duxodLiSpA8//FDbtm1TQkKCkpKSjA7HISEhIZKko0ePVrjNhXV79+6tiZCqRZ3YqxQaP0pZa+Yoe/e6crcpLshT0kvDVKddL0XcPKGGI6weDbu11W+Jpc9bl6fu0Nj0uWp12zXl7tN/3iSNSpmtkDZNayJEVEGLob1k8fDQrncXl1q+/7MVKjifq5bDrzYostqLHPA7s+YAd2sDF4q9sJ+7tQF7kQdKmPX8l6dZs2aaPn16hQ8mcjdcA7/jOsAF7pYHkpKSShV727ZtqylTpqhv374OTUtpsVgUFxenV155pcyguGuuuYZiL2q1Wl/wffjhh5WamqqHHnpIU6dOVVBQkG3d+PHj1alTJxUWFioqKkrBwcEGRvq7adOmadSoUUpNTVVCQoJSUlKMDslu3bp1kyRt3LhRhw4dKrN+yZIlOnfunCQpKyurRmNztohbn5E8PJX2v2fLXX/4rftUXJCrqHGzajaw6mKxSBbJWlxcavHWqV8oa/chdX9ujAIiSj+dt929gxV+VXttnTpHp/Yeqclo4YCwzq1UXFSkzC37Sy0vyivQyV9TFNa5pUGR1W7kgBJmzgGmawMow3RtgDxQiunOfwWKioqUnZ2toiITfFWfa6AMrgNI7pUH8vLy9Oabb9qKvV26dNGECRMUFhZWpeNZrVZ9++23ZQbFrV+/vtRUEUBtU6sLvrt379acOXMUFhamF198sdxtunbtKknq1KlTqeXJycm68cYbFRQUpHr16mn06NE6ceLEJceUmpqqlJSUSv8dPnxYzz33nK655hodPnxYCQkJOnz48CW/d00YMmSImjRpory8PN122206cuT3Tk1iYqLuu+8+2+vz588bEaLT+EW0Umjv23R2+0qd3bm61Lrj37yp0xsXqeVTX8nD1z2+1tLg8lbK3HKgzPLigkKtHjdDXgG+6vnq7w/4CW7ZWF3+cbt+27RPv761sCZDhYMCGtVT3smzKs4vLLPufMZJ+dWvKw9vl5jBp0aRA0qYOQeYrQ2gLLO1AfJAaWY7/xXZv3+/rrnmGu3fv//iG7s4roGyuA4guVce+OKLL5SRUfJQxpYtW+qRRx6Rj49PlY5ltVrLPKCtefPmkkoeBvfee+/JavJnpaD2qtUF39mzZ6u4uFgjR45UnTp1yt3G399fUumC79mzZ5WQkKDU1FTNnj1b77zzjlavXq3Bgwer+E+f5jqqd+/eatGixUX/tWzZUt9//70kKSUlRXfeeeclvW9N8fX11RdffKG6devql19+UYsWLRQbG6sWLVqoe/fuOn/+vIYNGyZJpUZbu6rwm/8peXiU+kT77PYflPrx3xU9/kv5NooyLrhL0OjKWFk8S1/ekQmX6+gPW8vd/uSOZG2fvkCR8Z0Vc2dfWTw81PvNv0mSVo+bUWYUBGoXT39fFeUXlLuuKK9kuZd/1To57o4cUMLMOcBd2wDs565tgDxgH3c9/+AacATXAdzFkSNHtGTJEkmSt7e3HnjgAacWe8eMGaOnn35adevWlSRt3rxZmzZtuvTAgWpQq4d8XSiYJiQkVLjNhScm/rHg+8477+jo0aP66aefbHPQNGnSRFdddZUWLlyom266qcoxdejQwe6EceLECdt0DrGxsVV+z5rWo0cPbdmyRS+99JKWLVumpKQk1atXT2PHjtXzzz+vyZMnS5LCw8OrdPy4uDjbJ272svj4q9Hrjn/aGNQhXl2/rvgTN/+msaWeNJt3LEVJU25Rk7FTFNQh3uH3+6OYmNay5udc0jEu8LZ6aKK627Vt1I1Xqee0+7VyzEvKWLfz92MEB6jgbMWjsre9NlfNro9T3LOjFdo+Sg26tNaG52bpzMG0KsUc0zpGBRb37RjXpIud/6KcPHkH1i13naevtySpMCe/WmK7GGe2g6rkAXfJAZL9eaC25ADJ+PMvuU8bcOQ+UNs4qx3QBugLuNp9QHL+vcBeI0aMsHvb48dL5gBfunSpQ4WLoUOHOhzXpXK1e2FtuAYk98mDsJ8jOUCqWh4wIgf4+PhU+O1vSVq+fLltxO3w4cMrfRh9ZSoq9l6Ys/euu+7Sa6+9JklatmyZ4uLiKjxWTEyM8vON+VsMFzf0/x5RYJ1gpWekq0mTJmVeGy08PFwbN26s0r61uuB7YQ7ZC0Pm/6ywsFBr166VVLrgu2jRIvXq1avUhOM9evRQdHS0vvnmm0sq+C5cuFBRUVEX3S41NVV9+vSRJN1666166623qvyeRmjRooVmzpxZ7rqdO0s6TZUltcpkZGRU+lC48nj4BqhRld7NfsV553XwxZtUt/uNauiEJ9CmpaWpOM850174WDxl7y8gZeE6BbcIV9N+3Wwd3MDIMJ1L/a3S/ayFRVo9boYGL31Jbcf217H1u7XrncWV7lOZtPQ05Vtdfw6o2uBi5//8sSzVjWkiDx+vMtM6BISHKvfEaRUXlJ3uoSY4sx1Udx6ozTlAsj8P1JYcILnW+Zdqdxtw5D5Q2zirHdAG6Au42n1Acv69wF4Xnrlhj5ycHNt/HdnP0f68M7javdDVrgGpdudB2M+Ra1mqWh4wIgf4+vpWuO78+fNavXq1bbvrr7++Su9xsWKvVPLso/DwcGVkZGjHjh1KS0tT48aNyz1eWlqabT5h1D7F/3/e6uKiIh09erTMa1dWqwu+FxLNheTzZ3PmzFFmZqaCgoLUokUL2/Jdu3bp5ptvLrN9+/bttWvXruoJ9g+OHj2qhIQEJSUlacSIEfr0008dehJkbZaZmamff/5ZXl5eGjhwYJWOUZWRwRYf/yq9lyOy1s1TTvI25R7dp6w1c8qsbz9jl3wa2P/U0saNGzt1VI8cGBxwaOkGXTvr70qcOEuS1PS6OB1ZfvFPhQrOnFdxfqE8fbyVunKzdAnzETWOaMwIXye52PnP3HpAkfGdFXZ5ax1fv9u23NPXW6GXRenYL7sr3rmaObMdVHceqM05QHIsD9SGHCC51vmXancbcPQ+UJs4qx3QBugLuNp9QHL+vcBegYGBdm974W8uf39/h/ar6si5S+Fq90JXuwak2p0HYT9HrmWpannAiBxQ2betN2/erNzcXEklU3EGBDg+77Q9xV5J8vDw0HXXXadPPvlEkrR27dpya1BSyTXACN/ay+P/1+o8PD0VGRlZ5rXRqvrNeqmWF3zDw8OVlZWlzZs3q0ePHqXWpaen68knn5QkdezYURaLxbYuKytLISEhZY4XGhqqvXv3VmvMkjRp0iQdOHBAQ4cO1ezZs+XlVat/zQ55+umnVVhYqJEjRyoiIqJKx6jKcPScQqn3kiq9nd3qJ4xS/YRRTjvevn375e+kU19wPleftbR/HujT+1IlqxQS00Sn9qUqqEW4zs46dtH9er7+oDy8vXRq3xF1fGS4Uhau09lDF9+vPPv275N3gF+V9kVpFzv/yV+vU8eHh6ndPYNKFXxbj+wr7wA/Jc3/qSbCLJcz20F154HanAMkx/JAbcgBkmudf6l2twFH7wO1ibPaAW2AvoCr3Qck598L7JWYmGj3toWFhRo7dqyCgoIc+rvl9ddfr0Jkl8bV7oWudg1ItTsPwn6O5ACpannAiBxQWFhYqhj7RwcPHrT9f1W+jWxvsfeCrl272gq+SUlJFR533759blUTcjeT//OZzmSfU0R4hFJTU8u8dmW1+qFtffv2lSS9/PLL2rdvn215YmKiEhISlJmZKUnq3LlztcfSp08fDR8+3K5Pu9544w1NmjRJc+bMcckLe8mSJbapMi44deqUHnnkEc2cOVMNGjTQtGnTDIoO9jry3UY17ddNXgF+Ksi++KfqsXcPVETPy7T11S+16p5p8vD0VM/XHrjofjDeqT2HtefDbxU16EolvP+kWt9xreImjlb358YoY91OJc1fY3SIMAA5wFyiR1ytjo8MV8dHhsuvfrC8gwJsr6NHXG10eDAIeQD28PLyUr169Vzy75aL4RoA7OMOeSA5Odn2/9HR0Q7t62ixV5IaNWpkqw/98b2B2qJWF3zHjx+v+vXr68iRI2rfvr06dOig1q1bq3v37oqOjtY111wjqfT8vZJUr149nTp1qszxTp48qdDQ0CrFMmnSJM2dO1cNGjS46Lb+/v569tln5e3tXaX3+rO1a9cqLCzM9u/VV1+VJH3++eellv+5SFvV/ZYvX65evXqpbt266tSpkzp16qRGjRrpjTfeUGRkpFauXKlGjVx0IkETObJ8o5peH6fG8Z2U9tP2SrcNahGuLhPu0G9b9uvXGV/p1L5UbZ32hcJ7tFfs3VWbugM1a8Ozs5T43EcKiWmiKyf/RS2G9NTuD5ZqxagXL/lr+XBN5ABzibn9WnX5++3q8vfb5d8gRL4hdWyvY26/1ujwYBDyAOyRmpqqxx9/3OVHMpWHawCwjzvkgbS0kocr1qtXT8HBwXbvV5ViryRZLBbb86ZOnTrl8LzJQHWr1R/fNGnSRKtXr9aTTz6pH3/8USkpKWrXrp1mzpype+65Ry1btpRUtuAbGxtb7ly9u3bt0tVXu94ol4KCAp04caLM8ry8vFKTfxcUFDhlv5tuuknHjh3Thg0btH//fnl5ealdu3YaNmyYHnnkEQUFBV3qj4QacGz9bgVHR6j5gO5aM+4/FW9osajX6w/Jw8NDa8bNkLW4ZJ6xX//ztZoPvEJdJtyh1BWbLulr3ah+1uJi7Zz5jXbO/MboUFBLkAPM5dvhE40OAbUQeQD2yM7O1urVq3XPPfcYHYrTcQ0A9nGHPHBhhLI9g/T+aP78+Q4Xey+oX7++6tWrJx8fHxUV8cBy1C61uuArlRRvFy1aVGZ5dna2UlJS5OHhocsuu6zUusGDB2vChAlKTU1VkyZNJEnr16/XwYMHNWXKlBqJ25ni4+NlrcIIvUvZLz4+3uH9ULtYi4p1dNW2kv8vrvhhEe3vu0GNurfVxn99otP7f38KpbW4WGvGzdANy6eo52sP6NthFBMAV0IOAEAegNlxDQDm8fLLL1dpv+bNm8vT01NFRUUOFXsl6cEHH6zSewI1oVZP6VCZnTt3ymq1qnXr1mWevnjvvfcqIiJCQ4YM0aJFizR37lzdfvvt6t69u4YMGWJQxEDNO7x0gw5/W/GE/XVbR6rL+Nt0fONe7fxv2ZGhfJUNcG3kAADkAZgd1wCAysTFxenRRx/V2LFjHSr2ArVdrR/hW5EdO3ZIKjudgyQFBwfr+++/17hx43TbbbfJy8tLgwcP1muvvSYPD5etcaOaZK2dqzPbV6rp3a8paeptyj2ySx4+/vKq21DN7n9bfhGtjA6xyg4t+rnS9af3H9UnLe6odJsd0xdox/QFzgwLQA0hB9jHne8DqLqstXN1euNiFZ7Lcuk2QR6wD3nAfXEN2IdrAGYWFxdndAiA07llwVeSWrZsWe5UEMCfnfplgUITRkuSGlx/r4K7DpDFYtHxxTN0aMZf1OaFVcYGCACoVtwHUJ5TvyxQvV63yOLpTZswATPngQYNGmjcuHEOz3sJ92LmawDkAcAduW3BF7igMPuUdj18mYrzc+QT1lTWgjzlZSQpNH6Umt//trL3rFXUuFmyeHmrbtzvX9MKjLlSx76aamDkAGpKZXki6m/vGR0eLhH3AfzZxa55a2FBqXZxAW3CdZEHKla/fn2NHDnS6DBQzbgGUBnyAOB+XLbg+/333xsdAlyEV50QhV59hzz9gxRx6zM6vXmZMuZOVtTf3tOZLcsV2PaqUn/MXXB80RsK6c6cz4AZVJYn4Pq4D+DPLnbNn93xQ7ntgjbhusgDFTtz5ow2bNig7t27Kzg42OhwUE24BlAZ8gDgfly24As44nzyVjUc/HDJ/x/cpIDoyyVJp9Z/pXpXDi2zffqXk5WXfkDN/7WyRuMEUD32jO+h3LT95a5r99oW+TRoWmGegHvgPmAul3rNl9cuaBOujzxQvrS0NE2YMEEff/wxhR43xzWAipAHAPdDwRemkJO81dahOX9wk0K63yir1arTW5YpcswrpbbNWDBVp36er9bPr5CHb4AR4QJwsravVP7AFqn8PAH3wX3AXC7lmi+vXdAm3AN5AGbHNQAA5uFhdABAdcs/cVSSRT71IyVJOSnb5d+8g87v2yD/JrHy9K9j2/bY168qa/VstX7+O3nVCTEmYAA1rqI8AffAfQB/Vtk1/+d2QZtwD+QBmB3XAACYCyN84fbOJ20p9TVNz8AQHV/ylryCwxRyxU225fmZqUr94HH5hEdr39MJkiSLl69ip66v6ZAB1LCK8gRz+LoH7gP4s8qu+axfFtjaBW3CfZAHYHZcAwBgLhR84fZCug1WSLfBttex0xIlSTsfaq9G//7BttwnrIm6fm2t8fgAGK+iPAH3wH0Af1bZNX868Rtbu6BNuA/yQMV8fX3Vpk0b+fr6Gh0KqhHXACpDHgDcDwVfmFb7GTuNDgEAYCDuAygP7cJcON9SixYt9MknnxgdBgzCNQCJPAC4I+bwBQAAAAAAAAA3QcEXAAAAAExq79696tmzp/bu3Wt0KAAMQh4A3A8FXwAAAAAwKavVqoKCAlmtzNsKmBV5AHA/FHwBAAAAAAAAwE3w0Da4BD9PafVAo6NwjJ+n847l5e+rkQc/dd4Ba4CXP094hXO5Wh5wZg6QyAOudv4l7gMXOKsd0AZcrw04uy9g9jYA17sOuAa4BuBcnp6eGj58uNOON2XmHJ09d05BgYF68q+3lnntDJ6eXAQwBgVfuASLRfI3cWu1WCzyDvAzOgzAUOQBc+cBzr+5z79EG6AN0AbAdcA1ALOzWCzy8nLeRWCVVGwt+a+Xl1eZ14ArowUDAAAAgElFRUVp9uzZioyMNDoUAAYhDwDuh4IvAJhIeI/26j9/UoXriwuL9HFT53x9CQAA1H5+fn5q2bKl0WEAMBB5AHA/FHwBwISS5q9W6vebyyy3FvNkXgAAzCQ9PV3vv/++7r77bkVERBgdDgADkAcA90PBFwBM6MSOZCXNW11tx/cK8FPh+dxqOz4AAHCO06dPa+HChRoxYgSFHsCkyAOA+6HgCwCoUPNBVyj2roEKbR8lDx8vnTuaqaOrtmnj8x+ruKDQNkXEmnEz5BXgp7b/109BzcO1Y/oCbZ32hdHhAwAAAABgOhR8AcCEvPx95BsaVGZ5cX6hCrJzJEmX/+N2dRo3XFl7j2jnO4uUczxLQc3D1XzQFdo65XPlFxTa9mt3zyD51gvSvs9WKOe3UzqXdqLGfhYAAAAAAPA7Cr4AYEKXj79Nl4+/rczyI99t0srRLyqscyt1Gjdc6Wt2aMWdk1WUV2DbZtMLn5bZLzAyTAt6j1PuiTPVGjcAAAAAAKgcBV8AMKG9nyxXyjc/l1l+oWAbPby3JGnT5P+VKvZW5ODcHyn2AgDggkJDQzVmzBiFhoYaHQoAg5AHAPdDwRcATOhMUobSV++ocH1wiwhZi4uVtSvFruOdPpjupMgAAEBN8vDwkLe3tzw8PIwOBYBByAOA++FqBgCUy2q1ymq12rVtUU5eNUcDAACqQ2Zmpt577z1lZmYaHQoAg5AHAPdDwRcAUMaZpDR5eHoqtF2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      "text/plain": [
       "<Figure size 1797.83x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1965.05x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 1965.05x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "for optim_level in optimization_levels:\n",
    "    print(f\"optimization level: {optim_level} \\n\")\n",
    "    transpiled_circuit = transpile(ghz, backend=backend2, optimization_level=optim_level)\n",
    "    transpiled_circuit.draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The circuits of level 2 and 3 are identical! Also circuits 0 and 1 behave similarly, even though the compiler picks different qubits to map our circuit. This implies that the circuit with optimization level 2 is already the best the transpiler can do for us. The small deviation between optimization level 2 and 3 only comes due to probabilistic quantum readout randomness."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Remember that the compiler is supposed to follow the idea from our manual optimization in a more sophisticated manner. Therefore let's compare its output again with what we produced in chapter 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "manual optimization\n",
      "State Accuracy\n",
      "manual optimization:  94.5875%\n",
      "transpiler optimization: 98.3375%\n"
     ]
    },
    {
     "data": {
      "image/png": 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CgpavIyNNX+TeEXPCfLNrrzcsKChAQgI7BhyJZAM9AMTHx+Prr79u83xVVRXOnTsHuVyOvn37ClAZdcWk0eFY9/Epux/Xy8MFY2/jOFKxKy4uxhtvvIF58+ZJcsainjPW4Oqh/6Aq578o+2EL9NVXofDsBvdeSQhKfwb+ox4SukQSmNTbgDMoKytr+To4ONisbS0J89cf59rjk2OQdKBvT3Z2NoxGI2JiYkyOAfv8888BAKdOnWr1ODw8HAMHDrRfoWTSsAFB6BPVHdlnr9r1uNPujoKPV/sXKJE4VFVVITMzEzNnzhS6FJvwueVO+Nxyp9BlOIwRATehYfzkDte50XKpkXobcAaxsbG4//770dDQYNYFy+fPn7cozANAYGAg7rnnHri6urZcl0iOwykD/YkTJwC0P9zm/vvvN/l4+vTp2Lhxo01roxuTyWT48wMJeOKVH+x63D9Njr/xSkRERDYWGxuL2NhYs7cLCwvD9OnT8eGHH5oV5gEgICAAf/jDH8w+JtkHA70JRqPRnuWQBR69Lxb/3JKL46ftc+fWJ6bEIzHGzy7HIiIispW0tDRERUWhd+/eNp+2m+xHsrPcdORGgZ4cn4uLHBuXDYeL0vZ/wuEhXlgxb5DNj0NERGQPMTExDPMS45Q99Pv27RO6BLKCpBg/rJw3CPNWHer0Ns03jLrRDaiaqVwV2LR8BLw8XCyqkRxPYGAg5s6di8DAQKFLIRIE2wCR9DhloCfpeGpaX1wur8ey97I6tf6Nbjx1LVcXOT5bPQq3/453+pUSf39/TJ06VegyiATDNkAkPU455Iak5eXZA7By3iDI5db7+LC7tyu+WjcG40eGWW2f5BgqKiqwd+9eVFRUCF0KkSDYBoikh4GeJGHBw0n48f/GIyGqe5f3dffwnsj+93248zbOzyxFarUaixYtglqtFroUIkGwDRBJDwM9ScagvoE49skEvDp3IHoGeZq9/YCEAGSsGImt68Yg5CbztyciIiISAsfQk6S4qZR49pF+eHp6IrZlXkDGjrM4mq3F2QuVbdZVKmXoE+WLW5NuwiMTYzCoLy8QIyIiIvFhoCdJUirlmJDSCxNSegEArlbUI/dcOe6evRvaq/UI9HXD+d1T4KZiEyAiIiJx45AbcgrdfVQYknQTVK4KAE0z2DDMOyeVSoXY2FioVCqhSyESBNsAkfQw0RCRU4mIiMCmTZuELoNIMGwDRNLDHnoiIiIiIhFjoCcip5Kbm4vk5GTk5uYKXQqRINgGiKSHgZ6InIrRaERjYyOMRqPQpRAJgm2ASHo4hp6IyAG5KYDMu4SuwjxuCivuTKWC8tMPrbhDO+BFpmRlCoUC6enpVtnXqnc3o7K6Gt6enljw+JR2n+sKhcKaJwEyBwM9EZEDkskAdyc+Q8tkMsDNTegyiAQlk8mgVFrnRGAEYDA2/d+8T1PPkThxyA0RERERkYjx7RgROZXw8HBkZGSgR48eQpdCJAi2ASLpYaAnIqfi5uaGqKgoocsgEgzbAJH0cMgNETmVkpISLFu2DCUlJUKXQiQItgEi6WGgJyKnUl5ejq1bt6K8vFzoUogEwTZAJD0M9EREREREIsZAT0REREQkYgz0REREREQixkBPRE5FLpfjlltugVzO0x85J7YBIulhayYip2IwGHD8+HEYDAahSyESBNsAkfQw0BMRERERiRgDPRERERGRiDHQExERERGJGAM9ETkVb29vpKamwtvbW+hSiATBNkAkPUqhCyAisqcePXpg6dKlQpdBJBi2ASLpYQ89ETmV+vp6XLhwAfX19UKXQiQItgEi6WGgJyKnUlhYiPT0dBQWFgpdCpEg2AaIpIeBnoiIiIhIxDiG3kEZjUZATB+HqlSQyWRCV0EkGUYjUKcXugrzuCkAa50GRHcOBHgetDKj0Qi9XlyNQKFQ8G+ABMFA76jq66GbPF3oKjpN+emHgJub0GUQSUadHhi2XegqzJN5F+BurVcVkZ0DAZ4HrU2v12PLli1Cl2GW9PR0KJWMVmR/HHJDRERERCRifBtJRE4lLi4Ohw8fFroMIsGwDRBJD3voiYiIiIhEjIGeiJxKUVERZsyYgaKiIqFLIRIE2wCR9DDQE5FTqa2txcmTJ1FbWyt0KUSCYBsgkh4GeiIiIiIiEWOgJyIiIiISMQZ6IiIiIiIRY6AnIqcSHByMJUuWIDg4WOhSiATBNkAkPZyHnoicSrdu3ZCWliZ0GUSCYRsgkh720BORUykrK8Nnn32GsrIyoUtxONpvNiL3+ZFCl0E25sxtoKqqCpcuXYJGo8GVK1dgMBjM2v7bb79FSUmJjaojshx76InIqZSWlmLVqlVITEyEr6+v0OUQ2Z0ztYGysjJkZmYiLy8PBQUFuHLlSqvl7u7uCA8PR2RkJIYOHYqoqCjIZDKT+9q1axc++OAD+Pn54YUXXuCQJXIoThHotVotVq5ciS+++ALFxcUIDAzEfffdh+XLl2POnDl4//33sW7dOsyePVvoUomI7O7cukdR9t9PYNTrYNQ34vgULwBA/4/LIVMoBK6OyHxnzpzB119/jSNHjkCv17e7Xm1tLXJycpCTk4Nt27YhMjISd955J4YPHw65/H+DGJrDPABcuXIFR48exfjx423+fRB1luQDfVZWFtLS0qDRaODp6YmEhASo1WqsXbsWZ8+ebXm33r9/f2ELtZH92ksYc/A7vJaQhL9ExZlcx/WrT3HXTcH4csgwO1dnH0ajEZnHNPh4RwEuX60HAJRXNSDvXDliwrsJXJ19XCytxoZ/5+HkmTLU1evh312F++4Ix13DQqFQcOSd1NRrCqDZ8hoqs79Hw6/nIXdRwcU3CB69ByNg1EPwTkpptX74k+sR/uR6aL/ZiMv7NiL2le+EKdwGeA50LvX19di8eTN27NgBo9HYallzb7yvry9kMhlqa2tx/vx5aLXalnUKCgrwzjvv4Ntvv8WsWbMQHBzcKswDwMSJE3H33Xfb7Xsi6gxJB3qtVovx48dDo9Fg/vz5WLx4Mby9vQEAK1euxDPPPAOlUgmZTIakpCSBqyVb2HWgGPNXH0L22autnq+q0SH2ns8xZmgI3n4+GdFhPsIUaGPasjr8efkP2LL3HPT61i9uG/+Tj14hXlj6xO/w4D29BaqQrK06/yjynh8BmdIFfiMfhHtYHxgaalGvzkdF1m4o3L3bBHoiKbhw4QJef/11aDSalue6deuGlJQUDBs2DMHBwa163ZtVVFTg6NGj2LNnDwoLCwEAubm5WLhwIQYPHowDBw60rDtx4kRMnjy53WE5REKRdKCfM2cOiouLMXv2bKxevbrVsoULF+Ljjz/Gzz//jIiICPj4SDPQObOM7Wcx7fn9bYLstfYcVGPotK+w759pSIzxs2N1tlfyaw2GP7wNZ85XtLtOkboK0//6PS5eqsFzj/azY3XC8fDwwJAhQ+Dh4SF0KTZRsnkJDPU1iF+RBY+Itr/TxjKNia3ImUixDRQWFuKVV15BVVUVAMDFxQWTJ09GWloalMqOo46Pjw9GjRqFlJQUZGdn47333sOlS5fQ2NjIME+iIdnP2nNycrB582YEBATg1VdfNbnOgAEDAAD9+v3vRS8zMxOjR49GcHAwVCoVQkNDMWXKFOTk5NilbrKOwyd+xfS/ft9hmG+mLavDXX/ejfLKBjtUZh8GgxHjn9zTYZi/1qK1R/H57kIbV+UYwsLCsG7dOoSFhQldik3UqfOh8PY3GeYBwMU3yM4VkaORWhsoKSnB8uXLW8J8eHg4XnvtNYwfP/6GYf5aMpkMffv2xcqVKxEbG9tq2S233MIwTw5NsoE+IyMDBoMBU6dOhZeXl8l13N3dAbQO9GVlZUhMTMTatWuxe/durFixAtnZ2Rg6dCiKi4vtUrst1Oj10NbXm/wnRas2/oJGXeenIysurcZHX+XbsCL72nmgGMdOaW+84jVeWZ/VZsypFOn1elRVVXV4oZyYqYKioK+8jLKDXwhdikNxtnNgR6TUBvR6Pd566y1UVlYCAGJjY/Hiiy+iR48eFu9z//79yM3NbfXciRMnoFaru1QrkS1JdsjNvn37AAApKe2PFW0O6NcG+nvuuQf33HNPq/UGDRqE2NhYbNmyBXPnzrVBtba3NDcbS3OzhS7DLtSXqvHvfUVmb/f25hzM/n2CJHpg3t5s/idKWaev4MdfLmFov5ttUJHjyM/Px4MPPoiPPvoIcXGmL5IUs+DJf0Xlz3tQ8Fo6VCG94RV/Ozx7D4JX35Fw7xkvdHmCcaZz4I1IqQ1s27YNZ8+eBdB0B9yFCxd2aSjR9RfARkREoLCwEDqdDu+88w6WLFlichw+kdAkG+iLipoCXa9evUwu1+l0LWPjrg30pvj7+wOAWR/dOZpHwyKRHtLT5LK0H/fbuRrb2vujulNDba53urAcReoqhPfwtkFV9mM0GrHrB8s+Tdrx32LJB3qp84obivjXj6H0P6+j/NgOXP7mA1z+pimgeCUMQ/jcjVAFRZrcVqZwgdzV3Z7l2o0znQOdxZUrV/DZZ58BaBou86c//Qmenp4W78/UbDYTJkzAs88+C41Gg/z8fHz77be44447ulw7kbWJN6HeQHV1NYCmOWZN2bx5M7RaLby9vREREdFmuV6vh8FgQFFREZ577jkEBQVh8uTJFtUycODAVlfdd4a7XI5T/YdadDxTor28cEeg7YJaTEwMas28456tVKmGAJ53WbTt4NtS4KoX90WDBrhA5/dXi7Zd87d38P6rO6xckW1NmjTJrPUvXboEANixYweOHTvWqW0mTpxodl1dJXN1x81vWjYMzD08EeFzNwIA6i8Voerkfmj3rEfVqUycWT4B8a8fg9zFtc12/iOnwn/kVItrjonpDWOD6XOuucR2DgSEOw9KtQ24urq2ew0c0PRJfGNjIwAgNTUVMTExFh/LVJhvHjM/a9YsvPTSSy3rjRo1qt1PcmNiYtDQ4JjXY018+Cl4evmgRFOC0NDQdp8j4QQFBeHo0aMWbSvZQB8UFISysjL89NNPGDq09YtCSUkJFixYAABISkoy2TBHjBjR0oMfHR2Nffv2ITAw0KJaNBoNLl68aNY2HgoF0N+iwwlCrVajxlHGY/qWAhZ20vyquQA0XLJuPXYnAyycsKe64jKqS837WxVa85v3zmp+k19bW9vpbc1tv9YgV3nAGvFTdVMvqEY9CL+Uach9bhiqcw6gJv8wvBJut8LeW1Or1TDU11hlX2I7BwLCnQel2gZUKlW7y3Q6Hb755hsAgFwu79K88B2FeQCIi4tDTEwM8vLycP78eZw+fRrx8aaHr6nVatQ76HUZht/+Ng16fcvv09RzJE6SDfSjR49GTk4OVqxYgTFjxrS8cz9y5AimTZvWciOJ9m4otWHDBly9ehWFhYVYtWoV7rzzThw4cMCiWQGCgsyfVcJdZGP0QkJCHKaHvlFRg0sAYDQCZoyHlxuqEBToBhksv5jKUVzSXUSj0vzvw8+9Au5duJhMCOZ+xN4cYNzd3Tu9bVcusLOUzMpDX2QyGTxjhqA65wAaLtvmhTskJMSqPfRiI9R5UKptwNW17adIzXJyclBWVgagaca65qGx5rpRmG925513Ii8vDwBw4MCBdgN9SEiIw/bQy3+767NcoWj5fZp6joRjSV5sJtlA3zzP/IULF9CnTx/ExcWhrq4OZ86cQVpaGsLDw7Fr1652x883T1k1ZMgQpKamIjw8HCtXrsRbb71ldi2WfHxirKuDbvJ0s7cTSl5eHmRubkKX0WLY9K/x3+OlZm3z7GPJeGWOOC96vt4HX+ZhxouZZm0TerMnCn/aDaVSXEHqyJEjZq2v0+nw0EMPwdvbu9PXxbz55psWVNY1tTpg2Hbzt6vI2gPvxBTIFK2/N0N9LSqydgMA3HsmWKPENvLy8uFupVcVsZ0DAeHOg1JtAzqdDlu2bDG5rKCgoOXrgQMHWrT/zoZ5APjd735n8tjXy8vLc9jr7Zb//V+oqKpGcFBwy6Qgpp4jcRLXK7cZQkNDkZmZiXHjxsHNzQ3nzp2Dn58f3n33XWzbtq3lnfaNLogFgO7duyM6OhpnzpyxddlkJU/9sY9Z67upFHhsUuyNVxSJKWMjcbO/eT28T/4+QXRh3hJKpRK+vr4O+6LbVRc2zMMvj/RE0duP49K2t6Dd+z7UnyzBqaf6o67oJPxSHoR7eKLQZZKApNAGmu/oCgCRkaYv8u6IOWEeaLoZV0hICADg/Pnz0Ol0Zh+TyJYk/eodHx+Pr7/+GpWVlaisrMShQ4fw2GOPobq6GufOnYNcLkffvn1vuJ9Lly4hNzcXUVFRdqiarCF9TATmP3jj3y0AyOUy/OvVkegVIu7Zba7l4a7E1rVj4NnJ7tL77gjH/Omd+3mJXXFxMebPny/Z3qieM9bA99b7UJ37I9QZL6Ho74/h0tdr4eIXgl5PbkD4nA9uvBOSNCm0geY54ZVKpdlDRcwN882aZ83T6XQtFxYTOQrxvj3vguzsbBiNRsTExLSZr/aPf/wjoqOj0b9/f3Tv3h35+fl44403oFQqMW/ePIEqttyIgJvQML7j2XlutFysVs0fDF8fFZa+exwNjabHtQb4umHjy8Mwbrg07ph4rcGJgdj/wThM+ss3OKeuMrmOXC7D45Ni8bdnhkKhkPT7+xZVVVXIzMzEzJkzhS7FJnxuuRM+t9wpdBkOw5nPge2RQhvw8fGBn58fVCqVWfPC79mzx6IwDwB+fn7w9fWFi4uLU9yEj8TFKQP9iRMnAJgebnPrrbfio48+wt/+9jfU1dWhZ8+eSElJwaJFi9qd054ck0wmw/OP9cfj98fhgy/z8K/tZ6HR1kKpkCGqpw9mpsdi0phwuKmk2wwGJATgzLb7sT2zGO98loNdBy5CbzBCqZDhmRlJeGxSHMKCTd9JmYjIUf31r5ZNzRsaGgqVSoX6+nqzwjwATJs2DdOmTbPouES2Jt0k04GOAv3s2bMxe/Zse5dENhTg64YFDydhwcNJQpciCIVCjvEjwzB+ZBhCR2fg4qUa3OzvjmVPWnYhGRGRWMXHx+PZZ5/FqVOncN9990nizuBEAAO9wJUQERGRPcXHx7c77SSRWDlloN+3b5/QJRCRQAIDAzF37lyLbxRHJHZsA0TS45SBnoicl7+/P6ZOnSp0GUSCYRsgkh7nmNaCiOg3FRUV2Lt3LyoqKoQuhUgQbANE0sNAT0RORa1WY9GiRS3zWBM5G7YBIulhoCciIiIiEjEGeiIiIiIiEWOgJyIiIiISMQZ6InIqKpUKsbGxUKlUQpdCJAi2ASLp4bSVRORUIiIisGnTJqHLIBIM2wCR9LCHnoiIiIhIxBjoicip5ObmIjk5Gbm5uUKXQiQItgEi6WGgJyKnYjQa0djYCKPRKHQpRIJgGyCSHgZ6IiIiIiIR40WxjkqlgvLTD4WuovM4WwKRVbkpgMy7hK7CPG4KK+5MbOdAgOdBK1MoFEhPT7fa/la9uxmV1dXw9vTEgsentHlsDQqFNRsBUecx0DsomUwGuLkJXQYRCUQmA9yd+AzNcyDJZDIoldZrBEYABmPT/0qlss1jIjHjXzAROZXw8HBkZGSgR48eQpdCJAi2ASLpYaAnIqfi5uaGqKgoocsgEgzbAJH08KJYInIqJSUlWLZsGUpKSoQuhUgQbANE0sNAT0ROpby8HFu3bkV5ebnQpRAJgm2ASHoY6ImIiIiIRIyBnoiIiIhIxBjoiYiIiIhEjIGeiJyKn58fpk+fDj8/P6FLIRIE2wCR9DDQE5FTkcvlcHFxgVzO0x85J7YBIulhayYip6LVarF+/XpotVqhSyESBNsAkfQw0BMRERERiRgDPRERERGRiDHQExERERGJGAM9ETkVb29vpKamwtvbW+hSiATBNkAkPUqhCyAisqcePXpg6dKlQpdBJBi2ASLpYQ89ETmV+vp6XLhwAfX19UKXQiQItgEi6WGgJyKnUlhYiPT0dBQWFgpdCpEg2AaIpIdDboiIHJDRaATE1oOqUkEmkwldBRFJhNFohF6vF7oMsygUCkHOgwz0RESOqL4eusnTha7CLMpPPwTc3IQug4gkQq/XY8uWLUKXYZb09HQolfaP1xxyQ0REREQkYgz0REREREQixiE3RORU4uLicPjwYaHLIBIM2wCR9LCHnoiIiIhIxBjoiZyE0Whsmjnlt6+dVVFREWbMmIGioiKhSyESBNsAkfRwyA2RRDU06rH12/PI/EmDYzmXkXX6MqprdQAA9a+1iEjdjIF9AjAgIQATR/VCbER3YQu2k9raWpw8eRK1tbVCl0IkCLYBIulhoCeSGPWlavz9kxys/yIXl67UtbveOXUVzqmr8Pmec3jub0dxx5AQ/PmBeNw7qhfnEiciIhIRBnoiiTAajdjwRR7+svoQKqsbzd7+m0NqfHNIjTuGhGDDktvRK8TbBlUSERGRtXEMPZEEXCmvx11P7MbMJf+1KMxf65tDavS979/4v6/PWKk6IiIisiX20BOJXOnlWoyeuQMnz5RZbZ9VNY2Ytmg/tGV1eGpaX6vt1xEEBwdjyZIlCA4OFroUIkGwDRBJDwM9kYiVVzZg7KydVg3z15q36hA83ZWYOSnOJvsXQrdu3ZCWliZ0GUSCYRsgstyvv/6KwMBAoctog4GeSMTmvHYQP+desekx/rz8IG5NugmJMX42PY69lJWVYe/evRg9ejR8fX2FLofI7tgGyNmo1WoUFBSgoKAAFy9eRH19PWQyGdzd3dGzZ09ERkYiOjoa/v7+He7n2LFjeOONNzBt2jSMHTvWTtV3DgM9kUh99d15fPSVeePcj2Tcg6AAD2i0NRj0+62d2qZRZ8BDL3yPH//vHri4iP+ym9LSUqxatQqJiYkMM+SU2AbIGdTX1+PgwYPYvXs3CgoK2l3vp59+avk6MTERY8aMwYABA6BQKFqtd+zYMaxZswZ6vR4ffPABgoKC0K9fP5vVby7xvzrfgFarxcKFCxEdHQ03Nzf07NkTc+fORXV1NR555BHIZDK89dZbQpdJZJb6Bj1mLTtg9nZBAR4IvdkTQQEeZm33U85lvPXJKbOPR8Lbr70E168+xZqzp9tdx/WrT3HvoUw7VkVEZDsHDx7Ek08+iXfeeafDMH+9EydOYM2aNZg/fz5ycnJanr82zANAcnIy+vZ1rOvLJN1Dn5WVhbS0NGg0Gnh6eiIhIQFqtRpr167F2bNnceVK01CF/v37C1sokZk+31MI9aUaux5z3cenMOcPCVAoJN8PQEREIlRRUYENGzbg0KFDrZ4PDw/HkCFDEBERgfDwcHh6esJoNKKiogLnzp3D2bNn8cMPP6C0tBQAoNFosHTpUowdOxbx8fFYu3ZtqzD/xBNPtOnBF5pkA71Wq8X48eOh0Wgwf/58LF68GN7eTfNqr1y5Es888wyUSiVkMhmSkpIErpbIPH//JOfGK1lZ4cVK7DxQjHHDw+x+bCIioo5otVq88sorKCkpaXluwIABuPfeexEdHW3yhokBAQEICAjAwIEDcf/99+PEiRP4/PPPkZ+fD6PRiJ07d2Lnzp0t6ztqmAckPORmzpw5KC4uxuzZs7F69eqWMA8ACxcuRL9+/aDT6RAeHg4fHx8BKyUyz9kLFTj48yVBjm3umH1H5OHhgSFDhsDDw7xhR0RSwTZAUlNWVoaXX365Jcx7e3tjzpw5ePrpp9G7d+9O3f1cLpejX79+WLJkCaZNm9YmtA8dOtRhwzwg0UCfk5ODzZs3IyAgAK+++qrJdQYMGAAAHV7QkJaWBplMhpdeeskWZRJZ5PCJXwU79pGTWsGObS1hYWFYt24dwsKc65OGGr0e2vp6k//IuThrGyBpMhgMeOONN1qGywQFBWH58uW47bbbOhXkryeXyxEUFNTmeaVS6bBhHpDokJuMjAwYDAZMnToVXl5eJtdxd3cH0H6g//TTT5GVlWWrEoksdvSUcKG68GIlLl+tg393N8Fq6Cq9Xo/a2lq4u7s79MnZ2pbmZmNpbrbQZZADcNY2QNK0fft25OXlAWgaQvPCCy/ccPrJjlx/AaxCoYBer0dmZiZuvfXWlg5hRyPJHvp9+/YBAFJSUtpdp7i4GIDpQF9RUYGnnnoKq1evtk2BRF2QbaObSHXWqbNXBT1+V+Xn52PUqFHIz88XuhS7ejQsEjtuHWHyHzkXZ20DJD0ajQabN28GAMhkMsyePduqYT45ORmPPPJIy/L169ejpsa+E1J0liR76IuKigAAvXr1Mrlcp9PhwIGmKf9MBfrnn38eMTExmDp1Kv74xz92uZ6BAwdCo9F0eT9EAPCr9wzAxfTfdvM88+0JCnBv+f/Cngc6PE57c9VPnPQA3BodZyz9pEmTzFr/0qWm6w927NiBY8eOdWqbiRMnml1XV7nL5TjVf6jV9hft5YU7Am+22v5MiYmJQa3BYNNjUFtSbQPWNvHhp+Dp5YMSTQlCQ0PbPJY6U9+vo/8MXF1d2x06DTT1zjc2NgIAUlNTERdn+V3NTYX5J554AnK5HIcPH0ZWVhbKysrw/fffIzU1td39xMTEoKGhwaIagoKCcPToUYu2lWSgr66uBgDU1taaXL5582ZotVp4e3sjIiKi1bKjR4/in//8Z6dPcp2h0Whw8eJFq+2PnFxkPeBielHzPPM3olTIO7WeKZe1WqDKcf6em9t7ZzWfF2prazu9rRDt10OhAPrb/bBdolarUfPbiyHZj1TbgLUZfvvbNOj1uHjxYpvHUmfq+3X0n4FKpWp3WW1tLTIzM1vWM/eN7bXaC/PNQ9KmTp3aMgx79+7dGDt2bLvj89VqNeoFuDZJkoE+KCgIZWVl+OmnnzB0aOserpKSEixYsAAAkJSU1OoXotfr8fjjj2P27Nno06ePVeshshatiwztnSo02o4/CgwKcIdSIYdOb4BGa/oN7432FeDvA1W3Hp0p1S48Pc17Y9IcYNzd3Tu9bY8e9v9+3eXiGxEZEhLCHnoBSLUNWJv8t3AmVyjQo0ePNo+lztT36+g/A1dX13aXHTx4sOXNaXJystntoNmNwjwA9OzZE/Hx8cjJyYFarcbp06cRHx9vcn8hISFd6qG3lCQD/ejRo5GTk4MVK1ZgzJgxiImJAQAcOXIE06ZNg1bbdFHh9TeUeuutt1BaWmr1WW0s/fiEyJSnVx/C6x+dNLnM1BCZa13Y8wBCb/aERluLnmM+sej4uT9/C79u7fea2NuRI0fMWv/06dPIyMhAWlpapz+effPNNy2orGuMdXXQTZ5u9+N2RV5eHmRu4r1gWqyk2gasbfnf/4WKqmoEBwWjuLi4zWOpM/X9OvrPQKfTYcuWLSaXnT79v7tfjxhh2bVAnQnz1x6j+e6xHQX6vLw8KJX2j9fi6wLqhIULF8Lf3x8XLlxAnz59kJiYiN69e2Pw4MGIjIzEqFGjALQeP6/VavHCCy/gxRdfhE6nw9WrV3H16lUAQF1dHa5evQoDe57IAQxICBDs2BE9vB0qzFsiOjoau3btQnR0tNClEAmCbYCkoKCgAEDTLDTXD5/uDHPCPAD07t275evCwkILKrYtSQb60NBQZGZmYty4cXBzc8O5c+fg5+eHd999F9u2bWuZ3ujaQF9cXIzKyko8/vjj8PX1bfkHACtWrICvry/Onz8vyPdDdK0hSYGCHXtwonBvJqxFqVTC19dXkB4UIkfANkBi19DQ0DLmv2fPnh0OzTHF3DAPAMHBwXD77RPIc+fOWVa4DUm2NcfHx+Prr79u83xVVRXOnTsHuVyOvn37tjwfHR2Nb7/9ts36KSkpmD59Oh566CGOhSeHEBnqg+RbbsaB46V2P/b08b1vvJKDKy4uxhtvvIF58+Y55KwO1jYi4CY0jJ/c4To3Wk7S4mxtgKSnpqYGRqMRAMyeptKSMA803XDKz88ParUaVVVVlhVuQ5IN9O3Jzs6G0WhETExMq9tee3l5YeTIkSa3CQ8Pb3cZkRCemBxv90AfGeqNscnif/GvqqpCZmYmZs6cKXQpRIJgGyCx8/T0xOLFi9HQ0NDuDURNMRqN2L59u9lhvtmjjz4KnU7X4ew7QnG6QH/ixAkA7d8hlkgM0seE45k3PVFcat50dV0x5w8JkMvNv402ERGRNbm4uLR7UWpHZDIZnn76abz22msICAgwK8wDQEJCgtnHtBcG+hto/kiHyJGoXBV478Vk3PXn3XY53qC+AfjzA457IiMiIuoMd3d3PPfcc3BxcTErzDs6SV4U2xH20JNUpA3riYfvNW9Mu0Zbg+LS6hvOV38tVxc5Nr48HEql050uiIhIgtzc3CQV5gEn7KHft2+f0CUQWc2bC2/Fz7lX8FPO5U6tf6N56k1554VkJET5mr2dowoMDMTcuXMRGCjcbEFEQmIbIJIedrkRiZiPlyt2/mMs+sX62WT/654biofvjbHJvoXi7++PqVOnmj0zApFUsA0QSQ8DPZHIBfq547sNd+Hu4T2ttk8fLxdkrBiJ2b+X3rj5iooK7N27FxUVFUKXQiQItgEi6WGgJ5KA7j4qbF03Bh8uG47u3ubdYON6qcmhyP4iHQ+kRVmpOseiVquxaNEiqNVqoUshEgTbAJH0ON0YeiKpkslkePCe3hibHIp3Ps3Be1tyob7UuYtfZbKmIP/ElHiMG94TMhmnpyQiIhILBnoiibnZ3x2L//Q7LHq0P7b/9wL++1Mpjp3S4vjpy7ha2QAAUChkiAr1wYAEfwxICMC9o3ohqqePwJUTERGRJRjoiSTKxUWOCSm9MCGlV8tzBoMRer0RLi4cbUdERCQVDPRETkQulzn93V5VKhViY2Md8tbdRPbANkAkPQz0RORUIiIisGnTJqHLIBIM2wCR9PBzdyIiIiIiEWOgJyKnkpubi+TkZOTm5gpdCpEg2AaIpIeBnoicitFoRGNjI4xGo9ClEAmCbYBIejiGnojIEalUUH76odBVmIcXWRKRFSkUCqSnp1ttf6ve3YzK6mp4e3piweNT2jy2BoVCYZX9mIuBnojIAclkMsDNTegyiIgEI5PJoFRaL6oaARiMTf8rlco2j8WMQ26IiIiIiERM3G9HiIjMFB4ejoyMDPTo0UPoUogEwTZAJD0M9ETkVNzc3BAVFSV0GUSCYRsgkh4OuSEip1JSUoJly5ahpKRE6FKIBME2QCQ9DPRE5FTKy8uxdetWlJeXC10KkSDYBoikh4GeiIiIiEjEGOiJiIiIiESMgZ6IiIiISMQ4yw0RidqgQYPMWj80NBSLFy/G6NGjERwcbKOqiOyHbYCIGOiJyKkEBwfjpZdeEroMIsGwDRBJD4fcEBERERGJGAM9EREREZGIMdATEREREYkYAz0RERERkYgx0BMRERERiRgDPRERERGRiDHQExERERGJGAM9EREREZGIMdATEREREYkYAz0RERERkYgx0BMRERERiRgDvQPYtGkTBgwYAF9fX7i7uyM+Ph5r1qyB0WgUujQiIiJqx/bt29G/f3+oVCqEh4djzZo1QpdkV99//z0mTJiAXr16QSaTYdmyZUKXZFerVq3C0KFD4evri+7du+P222/Hzp07BalFKchRqZWbbroJL7zwAmJjY6FSqZCZmYknnngCCoUCc+fOFbo8IiIius7Ro0cxYcIEPP3008jIyMChQ4cwa9YseHh4YNasWUKXZxdVVVVISEjAH/7wBzz11FNCl2N3+/btw4wZMzBo0CB4eHhg/fr1uPvuu7F//34kJyfbtRYGegcwduzYVo8jIyPx5Zdf4rvvvmOgJyIickBr1qzBoEGD8OqrrwIA4uPjkZ2djddee81pAv1dd92Fu+66CwDwzDPPCFyN/e3YsaPV45UrV2Lnzp344osv7B7oOeTGwRiNRhw+fBgHDhxASkqK0OUQERGRCQcOHEBqamqr51JTU1FUVITi4mKBqiIhGQwGVFRUwNPT0+7HZg+9gygvL0ePHj3Q0NAAg8GAxYsXY86cOUKXRUREJCqNOh0KL2jaPK/T61v+zyssbvP4WoF+3eDbzbvD45SUlCAoKKjVc82PS0pKEBoaavH30FXFJb+ipq6+1XOmvt/2fgYqFyV6hbb+3sSkoqoGml+vtHnenL+BsJCb4KZyNeu4y5cvx9WrV/HYY49ZWLnlGOgdhLe3N7KyslBTU4MffvgBzz33HEJCQvDII48IXRoREZFoKBUKHM7Kwcm8QpPLa2rr8P6n29t97Onhhnkz7rd5nbZUVVOLjZ+bvjjz+u/X1HOT0kaIOtCrXJT4cncmrlytNLn8Rn8DET2DMfOBcWYd8+2338by5cuxdetWQd7McciNg5DL5YiOjkZSUhJmzZqFhQsX4vnnnxe6LCIiIlGRyWSYOHYYvDzdLdo+PXV4p7YNDg6GRtP6k4DS0tKWZUKKiwrD4H5xFm2b0DscAxJjrFyRfalUrpg8LgUymcz8bV1dMHncSMjlnY/Iq1evxoIFC7B161aMHj3a7GNaAwO9gzIYDKirqxO6DCIiItHx9HDDpLQRZm83MCkWCb3DO7VucnIydu3a1eq5nTt3olevXoIOt2k2btRQ+Hf3MWsbLw933Jc6zKIg7GjCQ4MwYkg/s7e7Z3TyDYdbXevFF1/EkiVLsH37dsHCPMBA7xAWL16MvXv3oqCgALm5ufjnP/+JFStWYPr06UKXRkREJEpxUWEY0j++0+v7dfPG+FFDO73+vHnzcPjwYTz//PM4ffo0PvzwQ6xbtw7PPvusJeVancrVBZPvNq+X+r604fDy6PwnG1VVVcjKykJWVhYaGhqg0WiQlZWFM2fOWFKy1Y2+fQCCb/Lv9Pp9YsLxu769O73+U089hVWrVmHTpk2IjY2FRqOBRqNBeXm5JeV2iczIuxcJbt68efjqq69w8eJFuLm5ITIyEjNmzMCsWbOgUCiELo+IiEiU6hsasXbjFlwuq+hwPRmAx6feg3Azx41v27YNixYtwunTpxEUFIS5c+fiL3/5Sxcqtr5d3x/BtweP33C9QUlxSE8bbta+v/vuO5Mz8o0YMQLfffedWfuyFc2vV/DWh/9uuQC2PV6e7nhqxiSz3tC092Zp+vTp2LhxozlldhkDPREREUnW+Yul+Me/tnZ49/URQ/ohbeQQO1ZlPzq9Hm9v+hLq0svtruPX3RtzH0qHysxZXcQi8/Av2Pbtjx2u89CkVMRFhdmpIuvjkBuRuVByqc1UVERERGRaWI+bkXJr/3aXB9/kjzG3D7RfQXamVCgw5e5RULbzib9MJsPkcSmSDfMAkDwoEZFhIe0uH9wvTtRhHmCgFxWdXo//+/cerPjHxzh/sVTocoiIiEThjuQB6HFzQJvnFQo5ptydAqVS2sNbbw7wReqIwSaXjRjSz+yhRmIjl8kwedxIqFxd2izz7+6DcWZcO+GoGOivo9frsWnTJtx5550IDAyESqVCWFgYUlNTsX79euhvMAbLlo6dyEV5ZTVcXV3MusiDiIjImSkUckw2EdzHDh+MoEA/gaqyr9sG9kVUr9a91ME3+WP07QMEqsi+uvt4YcKY5FbPyToI+mLDQH+NiooKjBkzBg8++CD27NkDV1dX9OvXDwaDAbt378bMmTNRWWn6JgW2ptPrse+HpotaRg7pDxcX3hOMiIios67vpY7oGYzbByUKWJF9yWUy3H/XyJa7nzYNxUlpdyiOFN3Spzf6xkS0PB55az9R30DrWgz013jkkUfw7bffIjQ0FPv27cPFixdx+PBhFBcXo6SkBK+88gpcXIR5F9fcO+/t5WHxzSKIiIic2W0D+iK6V4//3TxIAvOtm+PaXuqxwwc5zacTzZpvOubt6Y6Qm/1xR7J0Pp3gLDe/OXbsGAYOHAilUonjx4+jb9++Vtv3ug+/QGVVbRf2YERldS2MRiPcVK5wFehNBRERkdgZDAboDQa4KJ3zk26j0YiGRh1cXZSSuIGUJXQ6HWRyORRm3A3WHry93PHk9Pss2tY5/5pN+PLLLwEA48aNs2qYB4DKqlpUVFVbZV919Q2oq2+wyr6IiIicVS2ce8a4+gZmCSlhoP/NqVOnAABDh1r/Smdvr87fpKAt9s4TERERSV1X8iID/W8qKpruItetWzer79vSj08A4FBWDv69KxPeXh5Y+NgDvBiWiIiIiFphOvyNj48PAKC8vNzq+7Z8DH1T7zwANDbqsOq9zdYtjIiIiIgcAsfQW0GfPn3wxRdf4ODBg1bftzXG0HPsPBERERGZwkD/m4kTJ+Lll1/G9u3bcerUKSQkJFht35aNieLYeSIiIiJn0ZUx9Jy28hpTpkzBp59+irCwMHz00UcYMWJEy7LS0lK8//77mDNnDjw9PW1eC8fOExEREVFnMNBfo6KiAhMmTMB3330HAOjRowdCQkJQUlKCixcvwmg0oqysDN27d7dpHTq9Hqvf24yrFVUYf8dtSB5o3Wk0iYiIiEg6HGtGfYH5+Phg79692LBhA0aOHImamhr8/PPPkMvlGDt2LDZs2ABvb2+b13HsRB6uVlTxrrBEREREdEPsoXdAx7PzseO7wxgxpB9754mIiIioQwz0DqpRp4MMMiiVCqFLISIiIiIHxkBPRERERCRiHENPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGIM9EREREREIsZAT0REREQkYgz0REREREQixkBPRERERCRiDPRERERERCLGQE9EREREJGL/D90OJmsHmaYqAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"manual optimization\")\n",
    "ghz_backend2_error.draw(\"mpl\", idle_wires=False)\n",
    "        \n",
    "print(\"State Accuracy\")\n",
    "print(\"manual optimization:  \"+str(results_backend2_error[0][2]))\n",
    "print(\"transpiler optimization: \"+str(results_backend2_transpiler[3][2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As can be seen, the structure of the circuit remains the same even on level 3 of the transpiler optimized circuit, matching our circuit from chapter 2. However, they differ in the qubits that were selected for mapping the logical circuit onto the real physical hardware. Taking this into account, the transpiler apparently has a better intuition on how to balance the importances of different kinds of errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pass Manager\n",
    "In the first chapter it has been used a different method to transpile the circuit, it's called Pass Manager:\n",
    "a pass manager is an object that stores a list of transpiler passes and can execute them on a circuit. Create a pass manager by initializing a PassManager with a list of transpiler passes. To run the transpilation on a circuit, call the run method with a circuit as input.\n",
    "\n",
    "It is very useful in the context of running various circuits and taking the output of the previous one as input for the following one. It is also very useful to have a fine-grained control on the various stages of transpilation.\n",
    "\n",
    "This is not an objective of the notebook, so I'll leave to you to go into detail of this: https://docs.quantum.ibm.com/guides/transpile-with-pass-managers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 4. Best system ..? <a name=mem><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We improved the performance on the backend (Fake_Kyiv) that reported the worst results on the circuit proposed, with no optimization. Other systems performed very well though, so let's see how well the transpilation embedded in Qiskit works with those that already performed well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'fake_sherbrooke'"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend1.backend_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "optimization_level_0: 94.15%\n",
      "optimization_level_1: 97.225%\n",
      "optimization_level_2: 97.3625%\n",
      "optimization_level_3: 97.32499999999999%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_backend1_transpiler = []\n",
    "\n",
    "optimization_levels = [0,1,2,3]\n",
    "\n",
    "sampler=Sampler(mode=backend1)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "for optim_level in optimization_levels:\n",
    "\n",
    "    transpiled_circuit = transpile(ghz, backend=backend1, optimization_level=optim_level)\n",
    "\n",
    "    counts = sampler.run([transpiled_circuit]).result()[0].data.c.get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend1_transpiler.append((optim_level, counts, state_accuracy)) # store\n",
    "    \n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([\"optimization_level_\"+str(optim_level)+': '+str(state_accuracy) \n",
    "                 for optim_level, counts, state_accuracy in results_backend1_transpiler]))\n",
    "\n",
    "# plot results\n",
    "plot_distribution([counts for optim_level, counts, state_accuracy in results_backend1_transpiler],\n",
    "               legend=[\"optimization_level_\"+str(optim_level) for optim_level, counts, state_accuracy in results_backend1_transpiler],\n",
    "               title=backend1.backend_name,\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see backends that have high accuracy without transpliation optimization, not always have better accuracy after proceeding with the optimization: in the end Fake_Kyiv system have better accuracy on this circuit, > 98% indeed, with respect to Fake_Sherbrooke which reached 97% of accuracy, both after performing an optimized transpilation! (results can vary depending on runs)\n",
    "\n",
    "This emphasize the fundamental role that this transpilation optimization process cover in the era of NISQ (Noisy Intermediate-Scale Quantum) devices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "\n",
    "\n",
    "---\n",
    "\n",
    "Congratulations! In this tutorial, we found ways to greatly increase the probability with which we can win the Quantum GHZ game on a quantum computer. Please note that there is a large field of research revolving around optimising quantum hardware and software - and we only covered a few simple ones of them. Therefore feel free to dig deeper into the topic or run your own circuits on the [IBM Quantum Platform](quantum-computing.ibm.com).\n",
    "\n",
    "Thank you!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "*Lennart Schulze, IBM Germany, lennart.schulze@ibm.com*\n",
    "\n",
    "*Dr. Jan-Rainer Lahmann, IBM Germany, Jan.Lahmann@de.ibm.com*\n",
    "\n",
    "updated by *Davide Moretti, IBM Italy, davide.moretti1@ibm.com*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "---\n",
    "\n",
    "&nbsp; \n",
    "\n",
    "&nbsp; \n",
    "\n",
    "&nbsp; \n",
    "\n",
    "&nbsp; \n",
    "\n",
    "&nbsp; \n",
    "\n",
    "\n",
    "## *Appendix*<a name=appendix><a/>\n",
    "[[Top](#top)]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Running this notebook on real quantum computers<a name=appendix></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "You can run the entire on real quantum hardware provided and made accesible by IBM on the [IBM Quantum Platform](https://quantum-computing.ibm.com).\n",
    "You should take into consideration that this will take longer, as each job submitted for execution to either of the quantum computers is queued based on a fair share algorithm. Therefore, you will most likely need to wait until other jobs queued before yours are finished. You can see the status of your jobs under \"Pending Results\" on the [Results page](https://quantum.ibm.com/workloads).\n",
    "\n",
    "As the first chapter executes circuits on all suitable devices, it will take especially long. For this reason we'll provide guidance for that chapter seperately."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Connect IBM Quantum Platform Account**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We need to connect to the QiskitRuntimeService through our IBM Quantum Platform account in order to be able to execute the results on real hardware.\n",
    "\n",
    "If you haven't linked your IBM Quantum Platform Account yet, follow this [guide](https://docs.quantum.ibm.com/guides/setup-channel) and paste your credentials in the following cell. Remember to remove your credentials at the [end of the tutorial](#end)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# save IBM Quantum Experience account credentials\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\", token='put your API token here')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Using real Quantum Computers**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We simply need to change the \"backend\" variable. Just execute the following cell or use it to replace the corresponding cell above, then execute the cell in chapter 1 in which the circuits are executed and review the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Available backends:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<IBMBackend('ibm_brisbane')>,\n",
       " <IBMBackend('ibm_kyiv')>,\n",
       " <IBMBackend('ibm_sherbrooke')>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Available backends:\")\n",
    "service.backends()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "First, we need to change our backend variables for the real devices we would like to examine. You can pick the real devices corresponding to the mock ones we used above or choose your own based on the selection returned by the previous cell. (Again execute the cell here or replace the code in the corresponding cell above.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# higher accuracy\n",
    "backend1 = service.backend(\"ibm_sherbrooke\")\n",
    "\n",
    "# lower accuracy\n",
    "backend2 = service.backend(\"ibm_kyiv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take ibm_kyiv for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "97.625%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results from different optimization levels on backend 2\n",
    "\n",
    "sampler = Sampler(mode=backend2)\n",
    "sampler.options.default_shots=shots\n",
    "\n",
    "transpiled_circuit = transpile(ghz, backend=backend2, optimization_level=2)\n",
    "\n",
    "counts = sampler.run([transpiled_circuit]).result()[0].data.c.get_counts() # get results\n",
    "\n",
    "state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+ state_accuracy)\n",
    "\n",
    "# plot results\n",
    "plot_distribution(counts, bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is perfectly in accordance with the one simulated locally using the mock backend!\n",
    "This confirm the goodness of the Fake Backends configurations we used before running on real hardware, in this way developers can save precious computational time on real Quantum devices by running the algorithm before on the fake backends and knowing what results they can expect.\n",
    "Good job!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.2.2'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import qiskit.version\n",
    "qiskit.version.get_version_info()"
   ]
  }
 ],
 "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}