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*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "name": "#%% md\n"
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   },
   "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 QASM 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."
   ]
  },
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   "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. Running Measurement Error Mitigation [[Go](#mem)]\n",
    "1. Combining the techniques [[Go](#all)]\n",
    "\n",
    "Appendix [[Go](#appendix)]\n",
    "* A: Solution for chapter 5. [[Go](#appendix-a)]\n",
    "* B: Running this notebook on real Quantum Computers [[Go](#appendix-b)]\n",
    "\n",
    "_____"
   ]
  },
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   "cell_type": "markdown",
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   },
   "source": [
    "## Setup\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   "source": [
    "First, let's do the necessary imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
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   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, execute, transpile, Aer, IBMQ # circuit creation and execution\n",
    "from qiskit.visualization import plot_histogram # visualize results\n",
    "from qiskit.utils.mitigation import complete_meas_cal,CompleteMeasFitter # measurement error mitigation\n",
    "\n",
    "import pandas as pd # handy tools for calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Next 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": 2,
   "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": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": 4,
   "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": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "state accuracy on the simulator: 100.0%\n"
     ]
    }
   ],
   "source": [
    "counts = execute(ghz, backend=Aer.get_backend('qasm_simulator'), shots=shots).result().get_counts() # execution on simulator\n",
    "state_accuracy = get_state_accuracy(counts)\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://qiskit.org/documentation/stubs/qiskit.quantum_info.hellinger_fidelity.html?highlight=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": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.providers.fake_provider import *\n",
    "# mock devices\n",
    "\n",
    "backends = [FakeYorktown(), FakeMelbourne(), FakeVigo(), FakeOurense(), FakeValencia(), FakeLondon(),\n",
    "                FakeBurlington(), FakeEssex()] # no mock santiago available"
   ]
  },
  {
   "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": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_backends = []\n",
    "\n",
    "for backend in backends:\n",
    "    counts = execute(ghz, backend=backend, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backends.append((backend.name(), counts, state_accuracy)) # store results\n",
    "    \n",
    "# plot results\n",
    "plot_histogram([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": 8,
   "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_ourense</td>\n",
       "      <td>91.9375%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fake_valencia</td>\n",
       "      <td>87.3625%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>fake_melbourne</td>\n",
       "      <td>86.175%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fake_burlington</td>\n",
       "      <td>85.4375%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fake_essex</td>\n",
       "      <td>84.8625%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fake_vigo</td>\n",
       "      <td>84.75%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fake_yorktown</td>\n",
       "      <td>78.5125%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fake_london</td>\n",
       "      <td>76.375%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           backend state_accuracy\n",
       "0     fake_ourense       91.9375%\n",
       "1    fake_valencia       87.3625%\n",
       "2   fake_melbourne        86.175%\n",
       "3  fake_burlington       85.4375%\n",
       "4       fake_essex       84.8625%\n",
       "5        fake_vigo         84.75%\n",
       "6    fake_yorktown       78.5125%\n",
       "7      fake_london        76.375%"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# setup ordered table\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 a high state accuracy to test the optimization techniques in the remaining chapters. In addition, we will pick one system with a lower accuracy to compare against later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# high accuracy\n",
    "backend1 = FakeVigo()\n",
    "\n",
    "# lower accuracy\n",
    "backend2 = FakeYorktown()"
   ]
  },
  {
   "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 our two picked devices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<FakeVigo('fake_vigo')>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "backend1"
   ]
  },
  {
   "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 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 956.385x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend1: 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_backend1 = QuantumCircuit(5,3, name=f\"GHZ yyx {backend1.name()} optimized\") # note that we use 5 qubits here to match the configuration of the device\n",
    "ghz_backend1.h(1) # we map qubit 0 to qubit 1 and qubit 1 to qubit 0 ..\n",
    "ghz_backend1.cx(1,0) # .. to ensure that all logical CNOT gates are performed on physical connections\n",
    "ghz_backend1.cx(1,2)\n",
    "ghz_backend1.barrier()\n",
    "ghz_backend1.sdg([1,0]) \n",
    "ghz_backend1.h(range(n))\n",
    "ghz_backend1.barrier()\n",
    "ghz_backend1.measure([1,0,2], range(n))\n",
    "ghz_backend1.draw(\"mpl\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's compare the two circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "GHZ yyx default: 85.3%\n",
      "GHZ yyx fake_vigo optimized: 87.1%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results between original and coupling map optimized circuit on backend1\n",
    "results_backend1_coupling = []\n",
    "\n",
    "circuits = [ghz, ghz_backend1]\n",
    "for circuit in circuits:\n",
    "    transpiled_circuit = transpile(circuit, backend=backend1, optimization_level=0)\n",
    "    counts = execute(circuit, backend=backend1, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend1_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_backend1_coupling]))\n",
    "\n",
    "plot_histogram([counts for circuit_name, counts, state_accuracy in results_backend1_coupling],\n",
    "               legend=[circuit_name for circuit_name, counts, state_accuracy in results_backend1_coupling],\n",
    "               title=backend1.name(),\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As you can see, the state accuracy improved by around 2% 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 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 956.385x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend1: 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_backend1_error = QuantumCircuit(5,3, name=f\"GHZ yyx {backend1.name()} error rate optimised\") # note that we use 5 qubits here to match the configuration of the device\n",
    "ghz_backend1_error.h(3) # qubit with best adjacent multi-qubit gates error rates (cnot)\n",
    "ghz_backend1_error.cx(3,1)\n",
    "ghz_backend1_error.cx(3,4) \n",
    "ghz_backend1_error.barrier()\n",
    "ghz_backend1_error.sdg([3,1]) # avoid 4 as it has a worse single qubit error rate\n",
    "ghz_backend1_error.h([3,1,4]) # best readout error rates\n",
    "ghz_backend1_error.barrier()\n",
    "ghz_backend1_error.measure([3,1,4], range(n)) # readout still in same order\n",
    "ghz_backend1_error.draw(\"mpl\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "GHZ yyx default: 85.3%\n",
      "GHZ yyx fake_vigo optimized: 87.1%\n",
      "GHZ yyx fake_vigo error rate optimised: 91.025%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results between original, coupling map, and error rates optimized circuit on backend1\n",
    "results_backend1_error = []\n",
    "\n",
    "circuits = [ghz_backend1_error]\n",
    "for circuit in circuits:\n",
    "    transpiled_circuit = transpile(circuit, backend=backend1, optimization_level=0)\n",
    "    counts = execute(circuit, backend=backend1, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "    state_accuracy = get_state_accuracy(counts) # calculate state accuracy\n",
    "    results_backend1_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_backend1_coupling+results_backend1_error]))\n",
    "\n",
    "plot_histogram([counts for circuit_name, counts, state_accuracy in results_backend1_coupling+results_backend1_error],\n",
    "               legend=[circuit_name for circuit_name, counts, state_accuracy in results_backend1_coupling+results_backend1_error],\n",
    "               title=backend1.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://qiskit.org/documentation/apidoc/transpiler_preset.html) 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 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "optimization_level_0: 83.975%\n",
      "optimization_level_1: 93.25%\n",
      "optimization_level_2: 93.25%\n",
      "optimization_level_3: 92.77499999999999%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare results from different optimization levels on backend 1\n",
    "results_backend1_transpiler = []\n",
    "\n",
    "optimization_levels = [0,1,2,3]\n",
    "#print(ghz)\n",
    "for optim_level in optimization_levels:\n",
    "    transpiled_circuit = transpile(ghz, backend=backend1, optimization_level=optim_level)\n",
    "    #print(transpiled_circuit)\n",
    "    counts = execute(ghz, backend=backend1, shots=shots, optimization_level=optim_level).result().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_histogram([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.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, and from 1 to 2, while level 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": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original circuit\n",
      "     ┌───┐           ░ ┌─────┐┌───┐ ░ ┌─┐      \n",
      "q_0: ┤ H ├──■────■───░─┤ Sdg ├┤ H ├─░─┤M├──────\n",
      "     └───┘┌─┴─┐  │   ░ ├─────┤├───┤ ░ └╥┘┌─┐   \n",
      "q_1: ─────┤ X ├──┼───░─┤ Sdg ├┤ H ├─░──╫─┤M├───\n",
      "          └───┘┌─┴─┐ ░ └┬───┬┘└───┘ ░  ║ └╥┘┌─┐\n",
      "q_2: ──────────┤ X ├─░──┤ H ├───────░──╫──╫─┤M├\n",
      "               └───┘ ░  └───┘       ░  ║  ║ └╥┘\n",
      "c: 3/══════════════════════════════════╩══╩══╩═\n",
      "                                       0  1  2 \n",
      "optimization level: 0\n",
      "global phase: π/2\n",
      "               ┌─────────┐┌────┐┌─────────┐                          ░ »\n",
      "      q_0 -> 0 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■───────────────────■───░─»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐     ┌───┐     ┌─┴─┐ ░ »\n",
      "      q_1 -> 1 ────────────────────────────┤ X ├──■──┤ X ├──■──┤ X ├─░─»\n",
      "                                           └───┘┌─┴─┐└─┬─┘┌─┴─┐└───┘ ░ »\n",
      "      q_2 -> 2 ─────────────────────────────────┤ X ├──■──┤ X ├──────░─»\n",
      "                                                └───┘     └───┘      ░ »\n",
      "ancilla_0 -> 3 ────────────────────────────────────────────────────────»\n",
      "                                                                       »\n",
      "ancilla_1 -> 4 ────────────────────────────────────────────────────────»\n",
      "                                                                       »\n",
      "          c: 3/════════════════════════════════════════════════════════»\n",
      "                                                                       »\n",
      "«               ┌──────────┐┌─────────┐   ┌────┐  ┌─────────┐ ░ ┌─┐      \n",
      "«      q_0 -> 0 ┤ Rz(-π/2) ├┤ Rz(π/2) ├───┤ √X ├──┤ Rz(π/2) ├─░─┤M├──────\n",
      "«               ├─────────┬┘└──┬────┬─┘┌──┴────┴─┐└─────────┘ ░ └╥┘   ┌─┐\n",
      "«      q_1 -> 1 ┤ Rz(π/2) ├────┤ √X ├──┤ Rz(π/2) ├────────────░──╫────┤M├\n",
      "«               ├─────────┴┐┌──┴────┴─┐└──┬────┬─┘┌─────────┐ ░  ║ ┌─┐└╥┘\n",
      "«      q_2 -> 2 ┤ Rz(-π/2) ├┤ Rz(π/2) ├───┤ √X ├──┤ Rz(π/2) ├─░──╫─┤M├─╫─\n",
      "«               └──────────┘└─────────┘   └────┘  └─────────┘ ░  ║ └╥┘ ║ \n",
      "«ancilla_0 -> 3 ──────────────────────────────────────────────░──╫──╫──╫─\n",
      "«                                                             ░  ║  ║  ║ \n",
      "«ancilla_1 -> 4 ──────────────────────────────────────────────░──╫──╫──╫─\n",
      "«                                                             ░  ║  ║  ║ \n",
      "«          c: 3/═════════════════════════════════════════════════╩══╩══╩═\n",
      "«                                                                0  1  2 \n",
      "optimization level: 1\n",
      "global phase: π/2\n",
      "                                                                              »\n",
      "ancilla_0 -> 0 ───────────────────────────────────────────────────────────────»\n",
      "               ┌─────────┐┌────┐┌─────────┐           ░    ┌────┐  ┌─────────┐»\n",
      "      q_0 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐  │   ░    ├────┤  ├─────────┤»\n",
      "      q_1 -> 2 ────────────────────────────┤ X ├──┼───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "                                           └───┘┌─┴─┐ ░ ┌──┴────┴─┐└──┬────┬─┘»\n",
      "      q_2 -> 3 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├───┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘   └────┘  »\n",
      "ancilla_1 -> 4 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "          c: 3/═══════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«                                      \n",
      "«ancilla_0 -> 0 ───────────────────────\n",
      "«                           ░ ┌─┐      \n",
      "«      q_0 -> 1 ────────────░─┤M├──────\n",
      "«                           ░ └╥┘┌─┐   \n",
      "«      q_1 -> 2 ────────────░──╫─┤M├───\n",
      "«               ┌─────────┐ ░  ║ └╥┘┌─┐\n",
      "«      q_2 -> 3 ┤ Rz(π/2) ├─░──╫──╫─┤M├\n",
      "«               └─────────┘ ░  ║  ║ └╥┘\n",
      "«ancilla_1 -> 4 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«          c: 3/═══════════════╩══╩══╩═\n",
      "«                              0  1  2 \n",
      "optimization level: 2\n",
      "global phase: π/2\n",
      "                                                                              »\n",
      "ancilla_0 -> 0 ───────────────────────────────────────────────────────────────»\n",
      "               ┌─────────┐┌────┐┌─────────┐           ░    ┌────┐  ┌─────────┐»\n",
      "      q_0 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐  │   ░    ├────┤  ├─────────┤»\n",
      "      q_1 -> 2 ────────────────────────────┤ X ├──┼───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "                                           └───┘┌─┴─┐ ░ ┌──┴────┴─┐└──┬────┬─┘»\n",
      "      q_2 -> 3 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├───┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘   └────┘  »\n",
      "ancilla_1 -> 4 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "          c: 3/═══════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«                                      \n",
      "«ancilla_0 -> 0 ───────────────────────\n",
      "«                           ░ ┌─┐      \n",
      "«      q_0 -> 1 ────────────░─┤M├──────\n",
      "«                           ░ └╥┘┌─┐   \n",
      "«      q_1 -> 2 ────────────░──╫─┤M├───\n",
      "«               ┌─────────┐ ░  ║ └╥┘┌─┐\n",
      "«      q_2 -> 3 ┤ Rz(π/2) ├─░──╫──╫─┤M├\n",
      "«               └─────────┘ ░  ║  ║ └╥┘\n",
      "«ancilla_1 -> 4 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«          c: 3/═══════════════╩══╩══╩═\n",
      "«                              0  1  2 \n",
      "optimization level: 3\n",
      "global phase: π/2\n",
      "                                                                              »\n",
      "ancilla_0 -> 0 ───────────────────────────────────────────────────────────────»\n",
      "               ┌─────────┐┌────┐┌─────────┐           ░    ┌────┐  ┌─────────┐»\n",
      "      q_0 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐  │   ░    ├────┤  ├─────────┤»\n",
      "      q_1 -> 2 ────────────────────────────┤ X ├──┼───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "                                           └───┘┌─┴─┐ ░ ┌──┴────┴─┐└──┬────┬─┘»\n",
      "      q_2 -> 3 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├───┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘   └────┘  »\n",
      "ancilla_1 -> 4 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "          c: 3/═══════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«                                      \n",
      "«ancilla_0 -> 0 ───────────────────────\n",
      "«                           ░ ┌─┐      \n",
      "«      q_0 -> 1 ────────────░─┤M├──────\n",
      "«                           ░ └╥┘┌─┐   \n",
      "«      q_1 -> 2 ────────────░──╫─┤M├───\n",
      "«               ┌─────────┐ ░  ║ └╥┘┌─┐\n",
      "«      q_2 -> 3 ┤ Rz(π/2) ├─░──╫──╫─┤M├\n",
      "«               └─────────┘ ░  ║  ║ └╥┘\n",
      "«ancilla_1 -> 4 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«          c: 3/═══════════════╩══╩══╩═\n",
      "«                              0  1  2 \n"
     ]
    }
   ],
   "source": [
    "# compare transpiled circuits for different optimization levels on backend 1\n",
    "\n",
    "optimization_levels = [0,1,2,3]\n",
    "print(\"original circuit\")\n",
    "print(ghz)\n",
    "for optim_level in optimization_levels:\n",
    "    print(f\"optimization level: {optim_level}\")\n",
    "    transpiled_circuit = transpile(ghz, backend=backend1, optimization_level=optim_level)\n",
    "    print(transpiled_circuit)\n"
   ]
  },
  {
   "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": 17,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "manual optimization\n",
      "                     ░              ░          \n",
      "q_0: ────────────────░──────────────░──────────\n",
      "          ┌───┐      ░ ┌─────┐┌───┐ ░    ┌─┐   \n",
      "q_1: ─────┤ X ├──────░─┤ Sdg ├┤ H ├─░────┤M├───\n",
      "          └─┬─┘      ░ └─────┘└───┘ ░    └╥┘   \n",
      "q_2: ───────┼────────░──────────────░─────╫────\n",
      "     ┌───┐  │        ░ ┌─────┐┌───┐ ░ ┌─┐ ║    \n",
      "q_3: ┤ H ├──■────■───░─┤ Sdg ├┤ H ├─░─┤M├─╫────\n",
      "     └───┘     ┌─┴─┐ ░ └┬───┬┘└───┘ ░ └╥┘ ║ ┌─┐\n",
      "q_4: ──────────┤ X ├─░──┤ H ├───────░──╫──╫─┤M├\n",
      "               └───┘ ░  └───┘       ░  ║  ║ └╥┘\n",
      "c: 3/══════════════════════════════════╩══╩══╩═\n",
      "                                       0  1  2 \n",
      "State Accuracy\n",
      "manual optimization:  91.025%\n",
      "transpiler optimization: 92.77499999999999%\n"
     ]
    }
   ],
   "source": [
    "print(\"manual optimization\")\n",
    "print(ghz_backend1_error)\n",
    "\n",
    "print(\"State Accuracy\")\n",
    "print(\"manual optimization:  \"+str(results_backend1_error[0][2]))\n",
    "print(\"transpiler optimization: \"+str(results_backend1_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": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 4. Measurement Error Mitigation<a name=mem><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "So far, we achieved some improvements of the state accuracy with manual optimization and to a small extent with transpiler optimization. While these are rather simple steps to take, there is an entire research field dealing with how to mitigate quantum computer hardware imperfection with software driven techniques, one of which we will examine now. \n",
    "\n",
    "\n",
    "As discussed earlier, there are various types of errors that can perpetrate noisy results when executing a quantum circuit. A significant one is that what happens when the quantum states are read from qubits forcing them to collapse into classical states, i.e. our experiment should return one of our four targeted classical states (001, 010, 100, or 111). However, we've seen that in our results a lot more states than these incorrectly appear. \n",
    "\n",
    "These returned result represent the real results plus the readout error. Hence, knowing the devices' readout error behavior, we can estimate the real results from our obtained results through matrix multiplication, which is called Measurement Error Mitigation. For this, each basis state (one of the 2^n combinations of 0 and 1 per each of the n qubits, e.g. 00, 01, 10, 11 for 2 qubits) is measured on the device so to derive its measurment errors, allowing to restore our real counts.\n",
    "\n",
    "For a detailed explenation of how Measurement Error Mitigation works have a look at the [Qiskit Textbook](https://qiskit.org/textbook/ch-quantum-hardware/measurement-error-mitigation.html) or the well explained Qiskit [youtube video](https://www.youtube.com/watch?v=yuDxHJOKsVA) on MEM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "noisy: 85.2%\n",
      "mitigated: 94.54053920295355%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# measurement error mitigation on backend 1\n",
    "\n",
    "results_backend1_mem = []\n",
    "\n",
    "# normal execution\n",
    "noisy_counts = execute(ghz, backend=backend1, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "noisy_state_accuracy = get_state_accuracy(noisy_counts) # calculate state accuracy from original results\n",
    "results_backend1_mem.append((\"noisy\", noisy_counts, noisy_state_accuracy))\n",
    "\n",
    "# measurement error mitigation\n",
    "qr = QuantumRegister(n)\n",
    "meas_calibs, state_labels = complete_meas_cal(qr=qr, circlabel='mcal') # setup calibration measures on basis states\n",
    "\n",
    "cal_results = execute(meas_calibs, backend=backend1, shots=shots).result() # execute calibration measures\n",
    "meas_fitter = CompleteMeasFitter(cal_results, state_labels, circlabel='mcal')\n",
    "meas_filter = meas_fitter.filter # get the filter object from calibration\n",
    "\n",
    "mitigated_counts = meas_filter.apply(noisy_counts) # apply filter to get mitigated results\n",
    "mitigated_state_accuracy = get_state_accuracy(mitigated_counts) # calculate state accuracy from mitigated results\n",
    "results_backend1_mem.append((\"mitigated\", mitigated_counts, mitigated_state_accuracy))\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(label)+': '+str(state_accuracy) for label, counts, state_accuracy in results_backend1_mem]))\n",
    "\n",
    "# plot results\n",
    "plot_histogram([counts for optim_level, counts, state_accuracy in results_backend1_mem],\n",
    "               legend=[label for label, counts, state_accuracy in results_backend1_mem],\n",
    "               title=backend1.name(),\n",
    "               bar_labels=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As can be seen, there is a visible improvement on the system with a high accuracy as result from the measurement error mitigated results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "While this is what we looked for, let's compare the results to the mitigated results from another, natively less accurate system in order to understand the capabilities of measurement error mitigation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<FakeYorktown('fake_yorktown')>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "noisy: 78.45%\n",
      "mitigated: 95.08666104317838%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# measurement error mitigation on backend 2\n",
    "\n",
    "results_backend2_mem = []\n",
    "\n",
    "# normal execution\n",
    "noisy_counts = execute(ghz, backend=backend2, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "noisy_state_accuracy = get_state_accuracy(noisy_counts) # calculate state accuracy from original results\n",
    "results_backend2_mem.append((\"noisy\", noisy_counts, noisy_state_accuracy))\n",
    "\n",
    "# measurement error mitigation\n",
    "qr = QuantumRegister(n)\n",
    "meas_calibs, state_labels = complete_meas_cal(qr=qr, circlabel='mcal') # setup calibration measures on basis states\n",
    "\n",
    "cal_results = execute(meas_calibs, backend=backend2, shots=shots).result() # execute calibration measures\n",
    "meas_fitter = CompleteMeasFitter(cal_results, state_labels, circlabel='mcal')\n",
    "meas_filter = meas_fitter.filter # get the filter object from calibration\n",
    "\n",
    "mitigated_counts = meas_filter.apply(noisy_counts) # apply filter to get mitigated results\n",
    "mitigated_state_accuracy = get_state_accuracy(mitigated_counts)\n",
    "results_backend2_mem.append((\"mitigated\", mitigated_counts, mitigated_state_accuracy))\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(label)+': '+str(state_accuracy) for label, counts, state_accuracy in results_backend2_mem]))\n",
    "\n",
    "# plot results\n",
    "plot_histogram([counts for optim_level, counts, state_accuracy in results_backend2_mem],\n",
    "               legend=[label for label, counts, state_accuracy in results_backend2_mem],\n",
    "               title=backend2.name(),\n",
    "               bar_labels=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As can be seen, this is a truly remarkable improvement, demonstrating the power of measurement error mitigation. This implies that a large part of the erroneous results on backend 2 is due to measurement errors. In addition, it is worth noting that the effect of the measurement error mitigation fluctuates over different applications on the same backend, which in turn depends on the device's quality in the first place. Try it by executing the above cell multiple times. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 5. Combining the optimization techniques<a name=all><a/>\n",
    "[[Top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We've now successfully gone through a variety of optimization techniques that differ in approach, complexity and results.\n",
    "However, the results for our system are still under 100%, which is what we aim for. Therefore, let's attempt to get the maximum fidelity through combining all of the measures discussed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "noisy: 85.52499999999999%\n",
      "manual: 90.95%\n",
      "transpiler: 93.125%\n",
      "transpiler - mitigated: 100.00000000010687%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend1\n",
    "\n",
    "results_backend1_all = []\n",
    "\n",
    "# basic circuit\n",
    "noisy_counts = execute(ghz, backend=backend1, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "noisy_state_accuracy = get_state_accuracy(noisy_counts) # calculate state accuracy from original results\n",
    "results_backend1_all.append((\"noisy\", noisy_counts, noisy_state_accuracy))\n",
    "\n",
    "# manually optimized circuit\n",
    "manual_counts = execute(ghz_backend1_error, backend=backend1, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "manual_state_accuracy = get_state_accuracy(manual_counts)\n",
    "results_backend1_all.append((\"manual\", manual_counts, manual_state_accuracy))\n",
    "\n",
    "\n",
    "# transpiler optimization (level 3 overrides manually optimized circuit)\n",
    "transpiler_counts = execute(ghz, backend=backend1, shots=shots, \n",
    "                                   optimization_level=3).result().get_counts() # get results\n",
    "transpiler_state_accuracy = get_state_accuracy(transpiler_counts)\n",
    "results_backend1_all.append((\"transpiler\", transpiler_counts, transpiler_state_accuracy))\n",
    "\n",
    "# transpiler optimization + measurement error mitigation\n",
    "qr = QuantumRegister(n)\n",
    "meas_calibs, state_labels = complete_meas_cal(qr=qr, circlabel='mcal') # setup calibration measures on basis states\n",
    "cal_results = execute(meas_calibs, backend=backend1, shots=shots).result() # execute calibration measures\n",
    "meas_fitter = CompleteMeasFitter(cal_results, state_labels, circlabel='mcal')\n",
    "meas_filter = meas_fitter.filter # get the filter object from calibration\n",
    "mitigated_counts = meas_filter.apply(transpiler_counts) # apply filter on previous results to get mitigated results\n",
    "mitigated_state_accuracy = get_state_accuracy(mitigated_counts)\n",
    "results_backend1_all.append((\"transpiler - mitigated\", mitigated_counts, mitigated_state_accuracy))\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(label)+': '+str(state_accuracy) for label, counts, state_accuracy in results_backend1_all]))\n",
    "\n",
    "# plot results\n",
    "plot_histogram([counts for label, counts, state_accuracy in results_backend1_all],\n",
    "               legend=[label for label, counts, state_accuracy in results_backend1_all],\n",
    "               title=backend1.name(),\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "If we wish to understand the effects better, we can inspect the transpiled circuit for each technique in order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***  fake_vigo  ***\n",
      "basic circuit\n",
      "global phase: π/2\n",
      "               ┌─────────┐┌────┐┌─────────┐                          ░ »\n",
      "      q_0 -> 0 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■───────────────────■───░─»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐     ┌───┐     ┌─┴─┐ ░ »\n",
      "      q_1 -> 1 ────────────────────────────┤ X ├──■──┤ X ├──■──┤ X ├─░─»\n",
      "                                           └───┘┌─┴─┐└─┬─┘┌─┴─┐└───┘ ░ »\n",
      "      q_2 -> 2 ─────────────────────────────────┤ X ├──■──┤ X ├──────░─»\n",
      "                                                └───┘     └───┘      ░ »\n",
      "ancilla_0 -> 3 ────────────────────────────────────────────────────────»\n",
      "                                                                       »\n",
      "ancilla_1 -> 4 ────────────────────────────────────────────────────────»\n",
      "                                                                       »\n",
      "          c: 3/════════════════════════════════════════════════════════»\n",
      "                                                                       »\n",
      "«               ┌──────────┐┌─────────┐   ┌────┐  ┌─────────┐ ░ ┌─┐      \n",
      "«      q_0 -> 0 ┤ Rz(-π/2) ├┤ Rz(π/2) ├───┤ √X ├──┤ Rz(π/2) ├─░─┤M├──────\n",
      "«               ├─────────┬┘└──┬────┬─┘┌──┴────┴─┐└─────────┘ ░ └╥┘   ┌─┐\n",
      "«      q_1 -> 1 ┤ Rz(π/2) ├────┤ √X ├──┤ Rz(π/2) ├────────────░──╫────┤M├\n",
      "«               ├─────────┴┐┌──┴────┴─┐└──┬────┬─┘┌─────────┐ ░  ║ ┌─┐└╥┘\n",
      "«      q_2 -> 2 ┤ Rz(-π/2) ├┤ Rz(π/2) ├───┤ √X ├──┤ Rz(π/2) ├─░──╫─┤M├─╫─\n",
      "«               └──────────┘└─────────┘   └────┘  └─────────┘ ░  ║ └╥┘ ║ \n",
      "«ancilla_0 -> 3 ──────────────────────────────────────────────░──╫──╫──╫─\n",
      "«                                                             ░  ║  ║  ║ \n",
      "«ancilla_1 -> 4 ──────────────────────────────────────────────░──╫──╫──╫─\n",
      "«                                                             ░  ║  ║  ║ \n",
      "«          c: 3/═════════════════════════════════════════════════╩══╩══╩═\n",
      "«                                                                0  1  2 \n",
      "manually optimized circuit (coupling map and error map)\n",
      "global phase: π/2\n",
      "                                                ░                        »\n",
      "q_0 -> 0 ───────────────────────────────────────░────────────────────────»\n",
      "                                     ┌───┐      ░ ┌──────────┐┌─────────┐»\n",
      "q_1 -> 1 ────────────────────────────┤ X ├──────░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "                                     └─┬─┘      ░ └──────────┘└─────────┘»\n",
      "q_2 -> 2 ──────────────────────────────┼────────░────────────────────────»\n",
      "         ┌─────────┐┌────┐┌─────────┐  │        ░ ┌──────────┐┌─────────┐»\n",
      "q_3 -> 3 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "         └─────────┘└────┘└─────────┘     ┌─┴─┐ ░ ├─────────┬┘└──┬────┬─┘»\n",
      "q_4 -> 4 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├────┤ √X ├──»\n",
      "                                          └───┘ ░ └─────────┘    └────┘  »\n",
      "    c: 3/════════════════════════════════════════════════════════════════»\n",
      "                                                                         »\n",
      "«                                ░          \n",
      "«q_0 -> 0 ───────────────────────░──────────\n",
      "«            ┌────┐  ┌─────────┐ ░    ┌─┐   \n",
      "«q_1 -> 1 ───┤ √X ├──┤ Rz(π/2) ├─░────┤M├───\n",
      "«            └────┘  └─────────┘ ░    └╥┘   \n",
      "«q_2 -> 2 ───────────────────────░─────╫────\n",
      "«            ┌────┐  ┌─────────┐ ░ ┌─┐ ║    \n",
      "«q_3 -> 3 ───┤ √X ├──┤ Rz(π/2) ├─░─┤M├─╫────\n",
      "«         ┌──┴────┴─┐└─────────┘ ░ └╥┘ ║ ┌─┐\n",
      "«q_4 -> 4 ┤ Rz(π/2) ├────────────░──╫──╫─┤M├\n",
      "«         └─────────┘            ░  ║  ║ └╥┘\n",
      "«    c: 3/══════════════════════════╩══╩══╩═\n",
      "«                                   0  1  2 \n",
      "transpiler optimized circuit\n",
      "global phase: π/2\n",
      "                                                                              »\n",
      "ancilla_0 -> 0 ───────────────────────────────────────────────────────────────»\n",
      "               ┌─────────┐┌────┐┌─────────┐           ░    ┌────┐  ┌─────────┐»\n",
      "      q_0 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐  │   ░    ├────┤  ├─────────┤»\n",
      "      q_1 -> 2 ────────────────────────────┤ X ├──┼───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "                                           └───┘┌─┴─┐ ░ ┌──┴────┴─┐└──┬────┬─┘»\n",
      "      q_2 -> 3 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├───┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘   └────┘  »\n",
      "ancilla_1 -> 4 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "          c: 3/═══════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«                                      \n",
      "«ancilla_0 -> 0 ───────────────────────\n",
      "«                           ░ ┌─┐      \n",
      "«      q_0 -> 1 ────────────░─┤M├──────\n",
      "«                           ░ └╥┘┌─┐   \n",
      "«      q_1 -> 2 ────────────░──╫─┤M├───\n",
      "«               ┌─────────┐ ░  ║ └╥┘┌─┐\n",
      "«      q_2 -> 3 ┤ Rz(π/2) ├─░──╫──╫─┤M├\n",
      "«               └─────────┘ ░  ║  ║ └╥┘\n",
      "«ancilla_1 -> 4 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«          c: 3/═══════════════╩══╩══╩═\n",
      "«                              0  1  2 \n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# inspect circuits on backend1\n",
    "print(\"*** \",backend1.name(),\" ***\")\n",
    "print(\"basic circuit\")\n",
    "print(transpile(ghz, backend=backend1, optimization_level=0))\n",
    "print(\"manually optimized circuit (coupling map and error map)\")\n",
    "print(transpile(ghz_backend1_error, backend=backend1, optimization_level=0))\n",
    "print(\"transpiler optimized circuit\")\n",
    "print(transpile(ghz, backend=backend1, optimization_level=3))\n",
    "# (measurement error mitigation doesn't transform the circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Great, we can see that the combination of methods really produces a tremendous value for the state accuracy of backend 1, close to the ideal value of 100%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Applying the combined techniques on another backend**\n",
    "\n",
    "Now it's your turn! Can you combine all the methods for backend 2? To get started, we provided a possible configuration of a manually optimized circuit for backend 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 956.385x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend 2: coupling map + error rate optimised circuit\n",
    "\n",
    "# map: qubit 0 -> qubit 1\n",
    "# qubit 1 -> qubit 2\n",
    "# qubit 2 -> qubit 0\n",
    "\n",
    "ghz_backend2_error = QuantumCircuit(5,3, name=f\"GHZ yyx {backend2.name()} error rate optimised\") # note that we use 5 qubits here to match the configuration of the device\n",
    "ghz_backend2_error.h(1) \n",
    "ghz_backend2_error.cx(1,2)\n",
    "ghz_backend2_error.cx(1,0) \n",
    "ghz_backend2_error.barrier()\n",
    "ghz_backend2_error.sdg([1,2]) # better single qubit error rate\n",
    "ghz_backend2_error.h([1,2,0])\n",
    "ghz_backend2_error.barrier()\n",
    "ghz_backend2_error.measure([1,2,0], range(n)) # readout still in same order\n",
    "ghz_backend2_error.draw(\"mpl\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now, your task is to fill in the following cell to execute each optimization step in order just as we did with backend 1.\n",
    "\n",
    "\n",
    "*(Hint: You can copy the code from the previous cell and change the variables for those relevant for backend 2. The solution can be found in the [appendix](#appendix-a) at the end of this notebook.)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "noisy: 85.52499999999999%\n",
      "manual: 90.95%\n",
      "transpiler: 93.125%\n",
      "transpiler - mitigated: 100.00000000010687%\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "max() arg is an empty sequence",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [24]\u001b[0m, in \u001b[0;36m<cell line: 32>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mState Accuracy \u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m+\u001b[39m\n\u001b[1;32m     29\u001b[0m       \u001b[38;5;124m\"\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mjoin([\u001b[38;5;28mstr\u001b[39m(label)\u001b[38;5;241m+\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m: \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;28mstr\u001b[39m(state_accuracy)  \u001b[38;5;28;01mfor\u001b[39;00m label, counts, state_accuracy \u001b[38;5;129;01min\u001b[39;00m results_backend2_all]))\n\u001b[1;32m     31\u001b[0m \u001b[38;5;66;03m# plot results\u001b[39;00m\n\u001b[0;32m---> 32\u001b[0m \u001b[43mplot_histogram\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mcounts\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mlabel\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcounts\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstate_accuracy\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mresults_backend2_all\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m     33\u001b[0m \u001b[43m               \u001b[49m\u001b[43mlegend\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m[\u001b[49m\u001b[43mlabel\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mlabel\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcounts\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstate_accuracy\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mresults_backend2_all\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m     34\u001b[0m \u001b[43m               \u001b[49m\u001b[43mtitle\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mbackend2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mname\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m     35\u001b[0m \u001b[43m               \u001b[49m\u001b[43mbar_labels\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/opt/anaconda3/envs/Fun-with-Quantum/lib/python3.9/site-packages/qiskit/utils/lazy_tester.py:165\u001b[0m, in \u001b[0;36mLazyDependencyManager.require_in_call.<locals>.out\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    162\u001b[0m \u001b[38;5;129m@functools\u001b[39m\u001b[38;5;241m.\u001b[39mwraps(function)\n\u001b[1;32m    163\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mout\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m    164\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrequire_now(feature)\n\u001b[0;32m--> 165\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunction\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/opt/anaconda3/envs/Fun-with-Quantum/lib/python3.9/site-packages/qiskit/visualization/counts_visualization.py:219\u001b[0m, in \u001b[0;36mplot_histogram\u001b[0;34m(data, figsize, color, number_to_keep, sort, target_string, legend, bar_labels, title, ax, filename)\u001b[0m\n\u001b[1;32m    217\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_ylabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mProbabilities\u001b[39m\u001b[38;5;124m\"\u001b[39m, fontsize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m14\u001b[39m)\n\u001b[1;32m    218\u001b[0m all_vals \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mconcatenate(all_pvalues)\u001b[38;5;241m.\u001b[39mravel()\n\u001b[0;32m--> 219\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_ylim([\u001b[38;5;241m0.0\u001b[39m, \u001b[38;5;28mmin\u001b[39m([\u001b[38;5;241m1.2\u001b[39m, \u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1.2\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mval\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mval\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mall_vals\u001b[49m\u001b[43m)\u001b[49m])])\n\u001b[1;32m    220\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdesc\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;129;01min\u001b[39;00m sort:\n\u001b[1;32m    221\u001b[0m     ax\u001b[38;5;241m.\u001b[39minvert_xaxis()\n",
      "\u001b[0;31mValueError\u001b[0m: max() arg is an empty sequence"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### YOUR WORK ###\n",
    "\n",
    "# backend 2\n",
    "\n",
    "results_backend2_all = []\n",
    "noisy_counts = {}\n",
    "manual_counts = {}\n",
    "transpiler_counts = {}\n",
    "mitigated_counts = {}\n",
    "\n",
    "# basic circuit\n",
    "## YOUR CODE HERE ##\n",
    "results_backend2_all.append((\"noisy\", noisy_counts, noisy_state_accuracy))\n",
    "\n",
    "# manually optimized circuit\n",
    "## YOUR CODE HERE ##\n",
    "results_backend2_all.append((\"manual\", manual_counts, manual_state_accuracy))\n",
    "\n",
    "# transpiler optimization (level 3 overrides manually optimized circuit)\n",
    "## YOUR CODE HERE ##\n",
    "results_backend2_all.append((\"transpiler\", transpiler_counts, transpiler_state_accuracy))\n",
    "\n",
    "# transpiler optimization + measurement error mitigation\n",
    "## YOUR CODE HERE ##\n",
    "results_backend2_all.append((\"transpiler - mitigated\", mitigated_counts, mitigated_state_accuracy))\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(label)+': '+str(state_accuracy)  for label, counts, state_accuracy in results_backend2_all]))\n",
    "\n",
    "# plot results\n",
    "plot_histogram([counts for label, counts, state_accuracy in results_backend2_all],\n",
    "               legend=[label for label, counts, state_accuracy in results_backend2_all],\n",
    "               title=backend2.name(),\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "If you get a state accuracy of around 95% you did a good job!\n",
    "\n",
    "Finally, we can inspect the transpiled circuits to understand the results better:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***  fake_yorktown  ***\n",
      "basic circuit\n",
      "global phase: π/2\n",
      "               ┌─────────┐┌────┐┌─────────┐           ░ ┌──────────┐┌─────────┐»\n",
      "      q_0 -> 0 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘┌─┴─┐  │   ░ ├──────────┤├─────────┤»\n",
      "      q_1 -> 1 ────────────────────────────┤ X ├──┼───░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "                                           └───┘┌─┴─┐ ░ ├─────────┬┘└──┬────┬─┘»\n",
      "      q_2 -> 2 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├────┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘    └────┘  »\n",
      "ancilla_0 -> 3 ────────────────────────────────────────────────────────────────»\n",
      "                                                                               »\n",
      "ancilla_1 -> 4 ────────────────────────────────────────────────────────────────»\n",
      "                                                                               »\n",
      "          c: 3/════════════════════════════════════════════════════════════════»\n",
      "                                                                               »\n",
      "«                  ┌────┐  ┌─────────┐ ░ ┌─┐      \n",
      "«      q_0 -> 0 ───┤ √X ├──┤ Rz(π/2) ├─░─┤M├──────\n",
      "«                  ├────┤  ├─────────┤ ░ └╥┘┌─┐   \n",
      "«      q_1 -> 1 ───┤ √X ├──┤ Rz(π/2) ├─░──╫─┤M├───\n",
      "«               ┌──┴────┴─┐└─────────┘ ░  ║ └╥┘┌─┐\n",
      "«      q_2 -> 2 ┤ Rz(π/2) ├────────────░──╫──╫─┤M├\n",
      "«               └─────────┘            ░  ║  ║ └╥┘\n",
      "«ancilla_0 -> 3 ──────────────────────────╫──╫──╫─\n",
      "«                                         ║  ║  ║ \n",
      "«ancilla_1 -> 4 ──────────────────────────╫──╫──╫─\n",
      "«                                         ║  ║  ║ \n",
      "«          c: 3/══════════════════════════╩══╩══╩═\n",
      "«                                         0  1  2 \n",
      "manually optimized circuit (coupling map and error map)\n",
      "global phase: π/2\n",
      "                                          ┌───┐ ░ ┌─────────┐    ┌────┐  »\n",
      "q_0 -> 0 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├────┤ √X ├──»\n",
      "         ┌─────────┐┌────┐┌─────────┐     └─┬─┘ ░ ├─────────┴┐┌──┴────┴─┐»\n",
      "q_1 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "         └─────────┘└────┘└─────────┘┌─┴─┐      ░ ├──────────┤├─────────┤»\n",
      "q_2 -> 2 ────────────────────────────┤ X ├──────░─┤ Rz(-π/2) ├┤ Rz(π/2) ├»\n",
      "                                     └───┘      ░ └──────────┘└─────────┘»\n",
      "q_3 -> 3 ───────────────────────────────────────░────────────────────────»\n",
      "                                                ░                        »\n",
      "q_4 -> 4 ───────────────────────────────────────░────────────────────────»\n",
      "                                                ░                        »\n",
      "    c: 3/════════════════════════════════════════════════════════════════»\n",
      "                                                                         »\n",
      "«         ┌─────────┐            ░       ┌─┐\n",
      "«q_0 -> 0 ┤ Rz(π/2) ├────────────░───────┤M├\n",
      "«         └──┬────┬─┘┌─────────┐ ░ ┌─┐   └╥┘\n",
      "«q_1 -> 1 ───┤ √X ├──┤ Rz(π/2) ├─░─┤M├────╫─\n",
      "«            ├────┤  ├─────────┤ ░ └╥┘┌─┐ ║ \n",
      "«q_2 -> 2 ───┤ √X ├──┤ Rz(π/2) ├─░──╫─┤M├─╫─\n",
      "«            └────┘  └─────────┘ ░  ║ └╥┘ ║ \n",
      "«q_3 -> 3 ───────────────────────░──╫──╫──╫─\n",
      "«                                ░  ║  ║  ║ \n",
      "«q_4 -> 4 ───────────────────────░──╫──╫──╫─\n",
      "«                                ░  ║  ║  ║ \n",
      "«    c: 3/══════════════════════════╩══╩══╩═\n",
      "«                                   0  1  2 \n",
      "transpiler optimized circuit\n",
      "global phase: π/2\n",
      "                                           ┌───┐      ░    ┌────┐  ┌─────────┐»\n",
      "      q_1 -> 0 ────────────────────────────┤ X ├──────░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               ┌─────────┐┌────┐┌─────────┐└─┬─┘      ░    ├────┤  ├─────────┤»\n",
      "      q_0 -> 1 ┤ Rz(π/2) ├┤ √X ├┤ Rz(π/2) ├──■────■───░────┤ √X ├──┤ Rz(π/2) ├»\n",
      "               └─────────┘└────┘└─────────┘     ┌─┴─┐ ░ ┌──┴────┴─┐└──┬────┬─┘»\n",
      "      q_2 -> 2 ─────────────────────────────────┤ X ├─░─┤ Rz(π/2) ├───┤ √X ├──»\n",
      "                                                └───┘ ░ └─────────┘   └────┘  »\n",
      "ancilla_0 -> 3 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "ancilla_1 -> 4 ───────────────────────────────────────────────────────────────»\n",
      "                                                                              »\n",
      "          c: 3/═══════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«                           ░    ┌─┐   \n",
      "«      q_1 -> 0 ────────────░────┤M├───\n",
      "«                           ░ ┌─┐└╥┘   \n",
      "«      q_0 -> 1 ────────────░─┤M├─╫────\n",
      "«               ┌─────────┐ ░ └╥┘ ║ ┌─┐\n",
      "«      q_2 -> 2 ┤ Rz(π/2) ├─░──╫──╫─┤M├\n",
      "«               └─────────┘ ░  ║  ║ └╥┘\n",
      "«ancilla_0 -> 3 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«ancilla_1 -> 4 ───────────────╫──╫──╫─\n",
      "«                              ║  ║  ║ \n",
      "«          c: 3/═══════════════╩══╩══╩═\n",
      "«                              0  1  2 \n"
     ]
    }
   ],
   "source": [
    "# inspect circuits on backend2\n",
    "\n",
    "print(\"*** \",backend2.name(),\" ***\")\n",
    "print(\"basic circuit\")\n",
    "print(transpile(ghz, backend=backend2, optimization_level=0))\n",
    "print(\"manually optimized circuit (coupling map and error map)\")\n",
    "print(transpile(ghz_backend2_error, backend=backend2, optimization_level=0))\n",
    "print(\"transpiler optimized circuit\")\n",
    "print(transpile(ghz, backend=backend2, optimization_level=3))\n",
    "# (measurement error mitigation doesn't transform the circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "\n",
    "\n",
    "---\n",
    "\n",
    "Congratulations! In this tutorial, we found ways to greatly increase the probabbility 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 [IBM Quantum Experience](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*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "<a name=end></a>**Important:** If running this notebook on a shared system (e.g. mybinder.org), remember to log off from your IBM Q account in case you used it for execution on real devices by running the following cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "IBMQ.disable_account()\n",
    "IBMQ.delete_account()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "---\n",
    "## .\n",
    "## .\n",
    "## .\n",
    "## .\n",
    "\n",
    "\n",
    "## *Appendix*<a name=appendix><a/>\n",
    "[[Top](#top)]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### A: Solutions (Chapter 5)<a name=appendix-a><a/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State Accuracy \n",
      "noisy: 79.03750000000001%\n",
      "manual: 78.9125%\n",
      "transpiler: 79.03750000000001%\n",
      "transpiler - mitigated: 96.09300239715827%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### SOLUTION TO CHAPTER 5 #####\n",
    " \n",
    "results_backend2_all = []\n",
    "\n",
    "# basic circuit\n",
    "noisy_counts = execute(ghz, backend=backend2, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "noisy_state_accuracy = get_state_accuracy(noisy_counts) # calculate state accuracy from original results\n",
    "results_backend2_all.append((\"noisy\", noisy_counts, noisy_state_accuracy))\n",
    "\n",
    "# manually optimized circuit (coupling map and error map)\n",
    "manual_counts = execute(ghz_backend2_error, backend=backend2, shots=shots, optimization_level=0).result().get_counts() # get results\n",
    "manual_state_accuracy =  get_state_accuracy(manual_counts)\n",
    "results_backend2_all.append((\"manual\", manual_counts, manual_state_accuracy))\n",
    "\n",
    "# transpiler optimization (level 3 overrides manual optimization circuit)\n",
    "transpiler_counts = execute(ghz, backend=backend2, shots=shots, \n",
    "                                   optimization_level=3).result().get_counts() # get results\n",
    "transpiler_state_accuracy =  get_state_accuracy(transpiler_counts)\n",
    "results_backend2_all.append((\"transpiler\", transpiler_counts, transpiler_state_accuracy))\n",
    "\n",
    "# transpiler optimization + measurement error mitigation\n",
    "qr = QuantumRegister(n)\n",
    "meas_calibs, state_labels = complete_meas_cal(qr=qr, circlabel='mcal') # setup calibration measures on basis states\n",
    "cal_results = execute(meas_calibs, backend=backend2, shots=shots).result() # execute calibration measures\n",
    "meas_fitter = CompleteMeasFitter(cal_results, state_labels, circlabel='mcal')\n",
    "meas_filter = meas_fitter.filter # get the filter object from calibration\n",
    "mitigated_counts = meas_filter.apply(transpiler_counts) # apply filter on previous results to get mitigated results\n",
    "mitigated_state_accuracy =  get_state_accuracy(mitigated_counts)\n",
    "results_backend2_all.append((\"transpiler - mitigated\", mitigated_counts, mitigated_state_accuracy))\n",
    "\n",
    "# compare state accuracies\n",
    "print(\"State Accuracy \\n\"+\n",
    "      \"\\n\".join([str(label)+': '+str(state_accuracy) for label, counts, state_accuracy in results_backend2_all]))\n",
    "\n",
    "# plot results\n",
    "plot_histogram([counts for label, counts, state_accuracy in results_backend2_all],\n",
    "               legend=[label for label, counts, state_accuracy in results_backend2_all],\n",
    "               title=backend2.name(),\n",
    "               bar_labels=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### B: Running this notebook on real quantum computers<a name=appendix-b></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 Experience](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-computing.ibm.com/results).\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 Experience Account**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We need to connect to our IBM Quantum Experience account in order to be able to execute the results on real hardware.\n",
    "\n",
    "If you haven't linked your IBM Quantum Experience Account yet, follow this [guide](https://qiskit.org/documentation/install.html#install-access-ibm-q-devices-label) 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": 28,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# save IBM Quantum Experience account credentials\n",
    "IBMQ.save_account('PUT_YOUR_IBMQ_TOKEN_HERE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Having stored your account credentials, run the following to activate your account. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# load IBM Quantum Experience account \n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider('ibm-q') # get provider"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Using real Quantum Computers in chapter 1**"
   ]
  },
  {
   "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": 30,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IBM Q backends: ['ibmq_lima', 'ibmq_belem', 'ibmq_quito', 'ibmq_manila', 'ibm_nairobi', 'ibm_oslo']\n"
     ]
    }
   ],
   "source": [
    "backends = provider.backends(filters=lambda x:  # get available quantum computer from IBM Q provider where\n",
    "                            x.configuration().n_qubits >= n and  # number of qubits high enough\n",
    "                            not x.configuration().simulator and  # only real devices (no simulator)\n",
    "                            x.status().operational==True) # only devices that work\n",
    "print(f\"IBM Q backends: {[str(backend.name()) for backend in backends]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Using real Quantum Computers in chapters 2-5**"
   ]
  },
  {
   "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": 32,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# higher accuracy\n",
    "backend1 = provider.get_backend(\"ibmq_manila\")\n",
    "\n",
    "# lower accuracy\n",
    "backend2 = provider.get_backend(\"ibmq_belem\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Almost done! However, as the name indicates, chapter 2 uses circuits that are manually optimized to specifically fit the default devices used so far. In order to get reasonable results in its sections, you now need to review the coupling and error map of the devices you picked by executing the first two cells in chapter 2. \n",
    "\n",
    "Based on this, your job is to create a new circuit for each (or decide to leave the default one if it is already fitting) that fits its coupling map, i.e. so that all qubits that interact with a cnot gate in the circuit are physically connected as indicated in the coupling map. Then, adapt the circuit again so to pick qubits with the lowest error rates. This doesn't need to be accurate, as it is hard to weigh the effects of the different kinds of errors present. A good indicator if you did a good job is that the state accuracy of the result is not significantly lower than that of the default circuit or that of the coupling map sensitive circuit without error optimization, respectively. Once you're done, execute the remaining cells in chapters 2-5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 162.08x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend1: coupling map optimised circuit\n",
    "\n",
    "ghz_backend1 = QuantumCircuit(5,3, name=f\"GHZ yyx {backend1.name()} optimised\") \n",
    "### YOUR CODE HERE ###\n",
    "\n",
    "\n",
    "ghz_backend1.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 162.08x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend2: coupling map optimised circuit\n",
    "\n",
    "ghz_backend2 = QuantumCircuit(5,3, name=f\"GHZ yyx {backend2.name()} optimised\") \n",
    "### YOUR CODE HERE ###\n",
    "\n",
    "\n",
    "ghz_backend2.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 162.08x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend1: coupling map + error rate optimised circuit\n",
    "\n",
    "ghz_backend1_error = QuantumCircuit(5,3, name=f\"GHZ yyx {backend1.name()} error rate optimised\") \n",
    "### YOUR CODE HERE ###\n",
    "\n",
    "ghz_backend1_error.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 162.08x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backend2: coupling map + error rate optimised circuit\n",
    "\n",
    "ghz_backend2_error = QuantumCircuit(5,3, name=f\"GHZ yyx {backend2.name()} error rate optimised\") \n",
    "### YOUR CODE HERE ###\n",
    "\n",
    "ghz_backend2_error.draw(\"mpl\")"
   ]
  }
 ],
 "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}