IBM_QGSS23/labs/lab2_creating_entanglement_with_qiskit.ipynb

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    "## Lab 2 - Creating Entanglement with Qiskit:\n",
    "\n",
    "- This lab demonstrates interesting properties of *entangled* qubits. In particular, we will consider two experiments:\n",
    "    - **CHSH Inequality Violation** - This shows that quantum mechanics *cannot* be explained by a local hidden variable theory;\n",
    "    - **Teleportation** - Teleport an arbitrary quantum state using an entangled qubit pair as a resource.\n",
    "\n",
    "<br>\n",
    "\n",
    "- In particular, this lab demonstrates how to use new features from IBM Quantum:\n",
    "    - **Primitives** - Abstract measurement and error mitigation for scalable quantum computing;\n",
    "    - **Dynamic Circuits** - Mid-circuit measurement and feed-forward within the qubits' coherence time."
   ]
  },
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   "source": [
    "## Getting Started\n",
    "\n",
    "Start by importing some libraries we need, including the `Sampler` and `Estimator` primitives from IBM's Qiskit. While the primitives from `qiskit.providers` use a local statevector simulator by default, the syntax within this lab is easily generalizable to running experiments on real systems.\n",
    "\n",
    "To run on real hearware requires a IBM's Qiskit Runtime service instance. If you haven't done so already, follow the instructions in the Qiskit [Getting started guide](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/getting_started.html) to set one up. After setup, import the `Sampler` and `Estimator` primitives from `qiskit_ibm_runtime` instead. Additionally we will need `QiskitRuntimeService` and `Session`, which form the interface between IBM's Qiskit and IBM's Qiskit IBM Runtime. Then the below exercises can be run on real systems by instantiating the primitives in this way (as opposed to from `qiskit.primitives`):\n",
    "\n",
    "```\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Sampler, Estimator\n",
    "\n",
    "service = QiskitRuntimeService()\n",
    "backend = service.get_backend('...')\n",
    "session = Session(service=service, backend=backend)\n",
    "sampler = Sampler(session=session)\n",
    "estimator = Estimator(session=session)\n",
    "```\n",
    "\n",
    "Where additional options can be specified in the `Sampler` and `Estimator` with the `Options` class. See this [how-to](https://qiskit.org/ecosystem/ibm-runtime/how_to/run_session.html) for using Primitives with Runtime Sessions.\n"
   ]
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   "source": [
    "# required import of libraries and modules\n",
    "\n",
    "# import quantum circuit from IBM's Qiskit circuit module\n",
    "from qiskit.circuit import QuantumCircuit\n",
    "\n",
    "# import estimator and sample\n",
    "# from IBM's Qiskit primitives module\n",
    "from qiskit.primitives import Estimator, Sampler\n",
    "\n",
    "# import Sparse Pauli operator\n",
    "# from IBM's Qiskit quantum information module\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "# import histogram plotting\n",
    "# from IBM's Qiskit visualization module\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "# import numpy\n",
    "import numpy as np\n",
    "\n",
    "# import plotting from Matplotlib's pyplot module\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# OPTIONAL: use the dark background style\n",
    "# for the plotting from Matplotlib's pyplot module\n",
    "plt.style.use(\"dark_background\")"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHSH Inequality Violation\n",
    "\n",
    "### Warm Up\n",
    "\n",
    "Create circuits that put the qubit in the excited $|1\\rangle$ and superposition $|+\\rangle$ states, respectively, and measure them in different bases. This is done first with the `Sampler` primitive (which is most similar to the `backend.run()` used in the previous lab), and then with the `Estimator` primitive to show how measurement is abstracted in that we do not need to worry about rotating the qubit into the appropriate measurement basis. The primitives will be executed withing the `Session` context which allows efficiency to optimize workloads."
   ]
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       "<Figure size 185.453x117.056 with 1 Axes>"
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# create an excited state |1>\n",
    "\n",
    "# create a quantum circuit for one qubit\n",
    "# and to implement an excited state |1>\n",
    "qc_1 = QuantumCircuit(1)\n",
    "\n",
    "# apply a Pauli-X (bit flip / not) gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "qc_1.x(0)\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the excited state |1>\n",
    "qc_1.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
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       "<Figure size 185.453x117.056 with 1 Axes>"
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     "execution_count": 3,
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   ],
   "source": [
    "# create quantum superposition state |+>\n",
    "\n",
    "# create a quantum circuit for one qubit\n",
    "# and to implement a quantum superposition state |+>\n",
    "qc_plus = QuantumCircuit(1)\n",
    "\n",
    "# apply a Hadamard gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "qc_plus.h(0)\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the quantum superposition state |+>\n",
    "qc_plus.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampler Primitive\n",
    "\n",
    "First use the `Sampler` to measure qubits in the $Z$-basis (the physical basis in which qubits are measured). The `Sampler` will count the number of outcomes of the $|0\\rangle$ state and $|1\\rangle$ state, normalized by the number of shots (experiments performed). The `Sampler` also offers the ability to easily perform error mitigation (which is covered in Lab 5), which modifies this calculation, and hence the outcomes are refered to as *quasi-probabilities*.\n",
    "\n",
    "Measurments must be present in the circuit when using the `Sampler` primitive. Then the `Session` context is opened, the `Sampler` is instantiated, and `sampler.run()` is used to send the circuits to the backend, similar to the `backend.run()` syntax you may already be familiar with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# measure all the qubits of\n",
    "# the quantum circuit implementing\n",
    "# an excited state |1>\n",
    "qc_1.measure_all()\n",
    "\n",
    "# measure all the qubits of\n",
    "# the quantum circuit implementing\n",
    "# a quantum superposition state |+>\n",
    "qc_plus.measure_all()\n",
    "\n",
    "# create a Sampler object\n",
    "sampler = Sampler()\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# an excited state |1>, running the Sampler\n",
    "job_1 = sampler.run(qc_1)\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a quantum superposition state |+>, running the Sampler\n",
    "job_plus = sampler.run(qc_plus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{1: 1.0, 0: 1e-20}]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# retrieve the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing an excited state |1>\n",
    "quasi_dists_ket_1 = job_1.result().quasi_dists\n",
    "\n",
    "# fix the legend issue for\n",
    "# the quasi-distribution of the outcome 0\n",
    "quasi_dists_ket_1[0][0] = 1e-20\n",
    "\n",
    "# show the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing an excited state |1>\n",
    "quasi_dists_ket_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{0: 0.4999999999999999, 1: 0.4999999999999999}]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# retrieve the quasi-distribution of\n",
    "# the job for the quantum circuit implementing\n",
    "# a quantum superposition state |+>\n",
    "quasi_dists_ket_plus = job_plus.result().quasi_dists\n",
    "\n",
    "# show the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing a quantum superposition state |+>\n",
    "quasi_dists_ket_plus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the legend for the two quantum states\n",
    "# created before, namely the excited state |1> and\n",
    "# the quantum superposition state |+>\n",
    "legend = [\"Excited State\", \"Plus State\"]\n",
    "\n",
    "# plot the histogram for the quasi-distributions\n",
    "# for the two quantum states created before,\n",
    "# namely the excited state |1> and\n",
    "# the quantum superposition state |+>\n",
    "plot_histogram( [ quasi_dists_ket_1[0], quasi_dists_ket_plus[0] ],\n",
    "                  legend=legend, title=\"Measurement Results\\n\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result for the excited state is always $|1\\rangle$ wheres it is roughly half $|0\\rangle$ and half $|1\\rangle$ for the plus superposition state. This is because the $|0\\rangle$ and $|1\\rangle$ states are *eigenstates* of the $Z$ operator (with $+1$ and $-1$ eigenvalues, respectively).\n",
    "\n",
    "Let's switch and measure in the $X$ basis. Using the `Sampler` we must rotate the qubit from the $X$-basis to the $Z$-basis for measurement (because that is the only basis we can actually perform measurement in)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# remove all the qubits' measurements of\n",
    "# the quantum circuit implementing\n",
    "# an excited state |1>\n",
    "qc_1.remove_final_measurements()\n",
    "\n",
    "# remove all the qubits' measurements of\n",
    "# the quantum circuit implementing\n",
    "# a quantum superposition state |+>\n",
    "qc_plus.remove_final_measurements()\n",
    "\n",
    "\n",
    "# prepare the 1st qubit of the quantum circuit\n",
    "# implementing an excited state |1>,\n",
    "# for the X-Basis measurement,\n",
    "# applying a Hadamard gate\n",
    "qc_1.h(0)\n",
    "\n",
    "# prepare the 1st qubit of the quantum circuit\n",
    "# implementing a quantum superposition state |+>,\n",
    "# for the X-Basis measurement,\n",
    "# applying a Hadamard gate\n",
    "qc_plus.h(0)\n",
    "\n",
    "\n",
    "# measure all the qubits of\n",
    "# the quantum circuit implementing\n",
    "# an excited state |1>\n",
    "qc_1.measure_all()\n",
    "\n",
    "# measure all the qubits of\n",
    "# the quantum circuit implementing\n",
    "# a quantum superposition state |+>\n",
    "qc_plus.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# create a Sampler object\n",
    "sampler = Sampler()\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# an excited state |1>, running the Sampler\n",
    "job_1 = sampler.run(qc_1)\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a quantum superposition state |+>, running the Sampler\n",
    "job_plus = sampler.run(qc_plus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{0: 0.4999999999999999, 1: 0.4999999999999999}]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# retrieve the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing an excited state |1>,\n",
    "# measured in the X-Basis\n",
    "quasi_dists_ket_1 = job_1.result().quasi_dists\n",
    "\n",
    "# show the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing an excited state |1>,\n",
    "# measured in the X-Basis\n",
    "quasi_dists_ket_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{0: 0.9999999999999996, 1: 1e-20}]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# retrieve the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing a quantum superposition state |+>,\n",
    "# measured in the X-Basis\n",
    "quasi_dists_ket_plus = job_plus.result().quasi_dists\n",
    "\n",
    "# fix the legend issue for\n",
    "# the quasi-distribution of the outcome 1\n",
    "quasi_dists_ket_plus[0][1] = 1e-20\n",
    "\n",
    "# show the quasi-distribution of\n",
    "# the job for the quantum circuit\n",
    "# implementing a quantum superposition state |+>,\n",
    "# measured in the X-Basis\n",
    "quasi_dists_ket_plus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot the histogram for the quasi-distributions\n",
    "# for the two quantum states created before,\n",
    "# namely the excited state |1> and\n",
    "# the quantum superposition state |+>,\n",
    "# measured in the X-Basis\n",
    "plot_histogram( [ quasi_dists_ket_1[0], quasi_dists_ket_plus[0] ],\n",
    "                  legend=legend, title=\"Measurement Results\\n\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we see the opposite: the plus superposition always give the 1 result, hence an eigenstate of the $X$ operator, whereas the excited $|1\\rangle$ yields a roughtly fifty-fifty split. The $|+\\rangle$ and $|-\\rangle$ states are eigenstates of the $X$ operator, with eigenvalues $+1$ and $-1$, respectively. This is good to remember when considering how the `Estimator` works in the next subsection. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimator Primitive\n",
    "\n",
    "The IBM's Qiskit Runtime Primitives allow us to abstract measurement into the `Estimator` primitive, where it is specified as an *observable*. In particular, we can construct the same circuits, the excited $|1\\rangle$ and superposition $|+\\rangle$ as before. However, in the case of the `Estimator`, we *do not* add measurements to the circuit. Instead, specify a list of observables which take the form of Pauli strings. In our case for a measurement of a single qubit, we specify `'Z'` for the $Z$-basis and `'X'` for the $X$-basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# create a quantum circuit for one qubit\n",
    "# and to implement an excited state |1>\n",
    "qc2_1 = QuantumCircuit(1)\n",
    "\n",
    "# apply a Pauli-X (bit flip / not) gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "qc2_1.x(0)\n",
    "\n",
    "\n",
    "# create a quantum circuit for one qubit\n",
    "# and to implement a quantum superposition state |+>\n",
    "qc2_plus = QuantumCircuit(1)\n",
    "\n",
    "# apply a Hadamard gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "qc2_plus.h(0)\n",
    "\n",
    "\n",
    "# create a list for the observables for\n",
    "# the Sparse Pauli-Z and Pauli-X operators\n",
    "obsvs = list( SparsePauliOp( [ \"Z\", \"X\" ] ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# crate an Estimator object\n",
    "estimator = Estimator()\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# an excited state |1>, running the Estimator\n",
    "job2_1 = estimator.run( [ qc2_1 ] * len(obsvs), observables=obsvs )\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a quantum superposition state |+>, running the Estimator\n",
    "job2_plus = estimator.run( [ qc2_plus ] * len(obsvs), observables=obsvs )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-1.,  0.]), metadata=[{}, {}])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the results of the job ran by\n",
    "# the Estimator created before,\n",
    "# that was ran on the excited state |1>\n",
    "job2_1.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    |   <Z>   |   <X> \n",
      "----|-------------------------------\n",
      "|1> | -1.0    | 0.0\n",
      "|+> |  0.0    | 0.9999999999999998\n"
     ]
    }
   ],
   "source": [
    "# print a table with results (and eigenvalues) for\n",
    "# the quantum states created before and measured in the bases set before\n",
    "print(f'    |   <Z>   |   <X> ')\n",
    "print(f'----|-------------------------------')\n",
    "print(f'|1> | {job2_1.result().values[0]}    | {job2_1.result().values[1]}')\n",
    "print(f'|+> |  {job2_plus.result().values[0]}    | {job2_plus.result().values[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as before, we see the $|1\\rangle$ state expectation in the $Z$-basis is $-1$ (corresponding to its eigenvalue) and around zero in the $X$-basis (average over $+1$ and $-1$ eigenvalues), and vice-versa for the $|+\\rangle$ state (although its eigenvalue of the $X$ operators is $+1$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHSH Inequality\n",
    "\n",
    "Imagine Alice and Bob are given each one part of a bipartite entangled system. Each of them then performs two measurements on their part in two different bases. Let's call Alice's bases A and a and Bob's B and b. What is the expectation value of the quantity \n",
    "\n",
    "$$\n",
    "\\langle CHSH \\rangle = \\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle ?\n",
    "$$\n",
    "\n",
    "Now, Alice and Bob have one qubit each, so any measurement they perform on their system (qubit) can only yield one of two possible outcomes: +1 or -1. Note that whereas we typically refer to the two qubit states as $|0\\rangle$ and $|1\\rangle$, these are eigenstates, and a projective measurement will yield their eigenvalues, +1 and -1, respectively.\n",
    "\n",
    "Therefore, if any measurement of A, a, B, and b can only yield $\\pm 1$, the quantities $(B-b)$ and $(B+b)$ can only be 0 or $\\pm 2$. And thus, the quantity $A(B-b) + a(B+b)$ can only be either +2 or -2, which means that there should be a bound for the expectation value of the quantity we have called\n",
    "\n",
    "$$\n",
    "|\\langle CHSH \\rangle| = |\\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle| \\le 2.\n",
    "$$\n",
    "\n",
    "Now, the above discussion is oversimplified, because we could consider that the outcome on any set of measurements from Alice and Bob could depend on a set of local hidden variables, but it can be shown with some math that, even when that is the case, the expectation value of the quantity $CHSH$ should be bounded by 2 if local realism held.\n",
    "\n",
    "But what happens when we do these experiments with an entangled system? Let's try it!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step is to build the observable\n",
    "$$\n",
    "CHSH = A(B-b) + a(B+b) = AB - Ab + aB +ab\n",
    "$$\n",
    "where $A, a$ are each one of $\\{IX, IZ\\}$ for qubit 0 and $B, b$ are each one of $\\{XI, ZI\\}$ for qubit 1 (corresponding to little-endian notation). Paulis on different qubits can be composed by specifying order with a Pauli string, for example instantiating a `SparsePauliOp` with the `'ZX'` argument implies a measurement of $\\langle X \\rangle$ on `q0` and $\\langle Z \\rangle$ on `q1` . This *tensor* product (combining operations on *different* qubits) can be explicitly stated using the `.tensor()` method. Additionally, combining operations on the *same* qubit(s) uses the *compositional* product with the `.compose()` method. For example, all these statements create the same Pauli operator:\n",
    "\n",
    "```\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "ZX = SparsePauliOp('ZX')\n",
    "ZX = SparsePauliOp(['ZX'], coeffs=[1.]) # extendable to a sum of Paulis\n",
    "ZX = SparsePauliOp('Z').tensor(SparsePauliOp('X')) # extendable to a tensor product of Paulis\n",
    "ZX = SparsePauliOp('XZ').compose(SparsePauliOp('YY')) # extendable to a compositional product of Paulis\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 1 - Create an operator for CHSH witness. </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the Sparse Pauli operator from\n",
    "# the IBM's Qiskit quantum information module\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "\n",
    "# For Alice: A = Z ; a = X\n",
    "# For Bob: B = Z ; b = X\n",
    "\n",
    "# create the Sparse Pauli operator ZZ, for <AB>\n",
    "ZZ = SparsePauliOp.from_list( [ ( \"ZZ\", 1 ) ] )\n",
    "\n",
    "# create the Sparse Pauli operator ZX, for <Ab>\n",
    "ZX = SparsePauliOp.from_list( [ ( \"ZX\", 1 ) ] )\n",
    "\n",
    "# create the Sparse Pauli operator XZ, for <aB>\n",
    "XZ = SparsePauliOp.from_list( [ ( \"XZ\", 1 ) ] )\n",
    "\n",
    "# create the Sparse Pauli operator XX, for <ab>\n",
    "XX = SparsePauliOp.from_list( [ ( \"XX\", 1 ) ] )\n",
    "\n",
    "\n",
    "# create the list of required\n",
    "# operators ZZ, ZX, XZ, and XX\n",
    "ops = [ ZZ, ZX, XZ, XX ]\n",
    "\n",
    "\n",
    "# there are two possible CHSH witnesses\n",
    "\n",
    "# create operator for CHSH witness <CHSH_1>\n",
    "#     <CHSH_1> = <ZZ> - <ZX> + <XZ> + <XX> (=)\n",
    "# (=) <CHSH_1> = <AB> - <Ab> + <aB> + <ab>\n",
    "#obsv = ops[0] - ops[1] + ops[2] + ops[3]\n",
    "\n",
    "# create operator for CHSH witness <CHSH_2>\n",
    "#     <CHSH_2> = <ZZ> + <ZX> - <XZ> + <XX> (=)\n",
    "# (=) <CHSH_2> = <AB> + <Ab> - <aB> + <ab>\n",
    "obsv = ( ops[0] + ops[1] - ops[2] + ops[3] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the grader for the exercise 1 of the lab 2\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex1\n",
    "\n",
    "# grade the exercise 1 of the lab 2\n",
    "grade_lab2_ex1( obsv )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Entangled Qubit Pair\n",
    "\n",
    "Next we want to test the $CHSH$ observable on an entangled pair, for example the maximally-entangled Bell state\n",
    "$$\n",
    "|\\Phi\\rangle = \\frac{1}{\\sqrt{2}} \\left(|00\\rangle + |11\\rangle \\right)\n",
    "$$\n",
    "which is created with a Hadamard gate followed by a CNOT with the target on the same qubit as the Hadamard. Due to the simplifaction of measuring in just the $X$- and $Z$-bases as discussed above, we will *rotate* the Bell state around the Bloch sphere which is equivalant to changing the measurement basis as demonstrated in the Warmup section. This can be done by applying an $R_y(\\theta)$ gate where $\\theta$ is a `Parameter` to be specified at the `Estimator` API call. This produces the state\n",
    "$$\n",
    "|\\psi\\rangle = \\frac{1}{\\sqrt{2}} \\left(\\cos(\\theta/2) |00\\rangle + \\sin(\\theta/2)|11\\rangle \\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import the parameter from\n",
    "# the IBM's Qiskit circuit module\n",
    "from qiskit.circuit import Parameter\n",
    "\n",
    "# create a parameter for the theta angle\n",
    "theta = Parameter(\"θ\")\n",
    "\n",
    "\n",
    "# create a quantum circuit for two qubits\n",
    "# and to implement a parametrized quantum entangled pair\n",
    "qc = QuantumCircuit(2)\n",
    "\n",
    "\n",
    "# apply a Hadamard gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "qc.h(0)\n",
    "\n",
    "# apply a CX/CNOT gate to\n",
    "# the quantum circuit,\n",
    "# with control on 1st qubit\n",
    "# and target on 2nd qubit\n",
    "qc.cx(0, 1)\n",
    "\n",
    "# apply a RY (Rotation-Y) gate to\n",
    "# the quantum circuit, on the 1st qubit,\n",
    "# with the theta angle defined before\n",
    "qc.ry(theta, 0)\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# a parametrized quantum entangled pair\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we need to specify a `Sequence` of `Parameter`s that show a clear violation of the CHSH Inequality, namely \n",
    "$$\n",
    "|\\langle CHSH \\rangle| > 2.\n",
    "$$\n",
    "Let's make sure we have at least three points in violation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 2 - Create a Parameterization (i.e., a list or an array) of the angle in the above circuit (in radians).<br>\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Hint: Note the `type` for the `parameter_values` argument is `Sequence[Sequence[float]]`).</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# create a parameterization of theta angles that\n",
    "# will violate the CHSH inequality\n",
    "\n",
    "# number of theta angles to violate the CHSH inequality\n",
    "number_of_phases = 20\n",
    "\n",
    "\n",
    "# for the 1st CHSH witness\n",
    "#     <CHSH_1> = <ZZ> - <ZX> + <XZ> + <XX> (=)\n",
    "# (=) <CHSH_1> = <AB> - <Ab> + <aB> + <ab>\n",
    "#phases_chsh_1_1 = np.linspace(0.5 * np.pi, np.pi, number_of_phases)\n",
    "#phases_chsh_1_2 = np.linspace(1.5 * np.pi, 2 * np.pi, number_of_phases)\n",
    "\n",
    "\n",
    "# create the two lists of theta angles that\n",
    "# violate the CHSH inequality\n",
    "#angles_chsh_1_1 = [[ph] for ph in phases_chsh_1_1]\n",
    "#angles_chsh_1_2 = [[ph] for ph in phases_chsh_1_2]\n",
    "\n",
    "\n",
    "# merge the two lists of theta angles that\n",
    "# violate the CHSH inequality, for the final result\n",
    "#angles = angles_chsh_1_1 + angles_chsh_1_2\n",
    "\n",
    "\n",
    "\n",
    "# for the 2nd CHSH witness\n",
    "#     <CHSH_2> = <ZZ> + <ZX> - <XZ> + <XX> (=)\n",
    "# (=) <CHSH_2> = <AB> + <Ab> - <aB> + <ab>\n",
    "phases_chsh_2_1 = np.linspace( 0, ( 0.5 * np.pi ), number_of_phases )\n",
    "phases_chsh_2_2 = np.linspace( ( 1 * np.pi ) , ( 1.5 * np.pi ), number_of_phases )\n",
    "\n",
    "\n",
    "# create the two lists of theta angles that\n",
    "# violate the CHSH inequality\n",
    "angles_chsh_2_1 = [ [ph] for ph in phases_chsh_2_1 ]\n",
    "angles_chsh_2_2 = [ [ph] for ph in phases_chsh_2_2 ]\n",
    "\n",
    "\n",
    "# merge the two lists of theta angles that\n",
    "# violate the CHSH inequality, for the final result\n",
    "angles = angles_chsh_2_1 + angles_chsh_2_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your angles and observable by running with the `Estimator` before submitting to the grader."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3f2453e230>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# crate an Estimator object\n",
    "estimator = Estimator()\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a parametrized quantum entangled pair,\n",
    "# varying the elements in the list of\n",
    "# theta angles defined before\n",
    "job = estimator.run( [qc] * len(angles),\n",
    "                     observables=[obsv] * len(angles),\n",
    "                     parameter_values=angles )\n",
    "\n",
    "\n",
    "# retrieve the expectation values\n",
    "# from the results of the job ran by\n",
    "# the Estimator created before,\n",
    "# that was ran on the parametrized\n",
    "# quantum entangled pair\n",
    "exps = job.result().values\n",
    "\n",
    "\n",
    "# plot the angles theta parametrized from the list built before\n",
    "plt.plot( angles, exps, marker='x', ls='-', color=\"green\" )\n",
    "\n",
    "# plot the two classical bounds that violates the CHSH inequality\n",
    "plt.plot( angles, [2]*len(angles), ls=\"--\", color=\"red\", label=\"Classical Bound\" )\n",
    "plt.plot( angles, [-2]*len(angles), ls=\"--\", color=\"red\" )\n",
    "\n",
    "\n",
    "# add the X-axis label to the plot built before\n",
    "plt.xlabel(\"angle (rad)\")\n",
    "\n",
    "# add the Y-axis label to the plot built before\n",
    "plt.ylabel(\"CHSH Witness\")\n",
    "\n",
    "\n",
    "# add the title to the plot built before\n",
    "plt.title(\"CHSH Witnesses\\n\")\n",
    "\n",
    "\n",
    "# add the legend to the plot built before\n",
    "plt.legend(loc=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did you see at least 3 points outside the red dashed lines? If so, you are ready to send to the grader!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the grader for the exercise 2 of the lab 2\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex2\n",
    "\n",
    "# grade the exercise 2 of the lab 2\n",
    "grade_lab2_ex2( obsv, angles )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Teleportation\n",
    "\n",
    "Quantum information cannot be copied due to the *No Cloning Theorem*, however it can be \"teleported\" in the sense that a qubit can be entangled with a quantum resource, and via a protocol of measurements and *classical communication* of their results, the original quantum state can be reconstructed on a different qubit. This process destroys the information in the original qubit via measurement.\n",
    "\n",
    "In this exercise, we will construct a particular qubit state and then transfer that state to another qubit using the teleportation protocol. Here we will be looking at specific classical and quantum registers, so we need to import those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the classical and quantum registers\n",
    "# from the IBM's Qiksit circuit module\n",
    "from qiskit.circuit import ClassicalRegister, QuantumRegister"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create the circuit\n",
    "\n",
    "Define an angle $\\theta$ to rotate our qubit by. This will allow us to easily make comparisons for the original state and the teleported quantum state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 185.453x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a parameter for the theta angle\n",
    "theta = Parameter(\"θ\")\n",
    "\n",
    "\n",
    "# create a quantum register for one qubit\n",
    "# and to implement a parametrized quantum operation\n",
    "qr = QuantumRegister(1, \"q\")\n",
    "\n",
    "# create a quantum circuit with\n",
    "# the quantum register created before\n",
    "qc = QuantumCircuit(qr)\n",
    "\n",
    "\n",
    "# apply a RY (Rotation-Y) gate to\n",
    "# the quantum circuit, on the 1st qubit,\n",
    "# with the theta angle defined before\n",
    "qc.ry(theta, 0)\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# a parametrized quantum operation\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice possesses the quantum information $|\\psi\\rangle$ in the state of $q$ and wishes to transfer it to Bob. The resource they share is a special entangled state called a Bell state:\n",
    "\n",
    "$$\n",
    "|\\Phi^+\\rangle = \\frac{1}{2} \\left( |00\\rangle + |11\\rangle \\right)\n",
    "$$\n",
    "\n",
    "Here, the first of the pair going to Alice and the second to Bob. Hence, Alice has a 2-qubit register ($q$ and $Bell_0$) and Bob has a single-qubit register ($Bell_1$). We will construct the circuit by copying the original `qc` and adding the appropriate registers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 239.337x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a copy of the quantum circuit defined before\n",
    "# to initialize the quantum circuit implementing\n",
    "# a parametrized quantum teleportation\n",
    "tele_qc = qc.copy()\n",
    "\n",
    "\n",
    "# create a quantum register with two qubits\n",
    "# for the Bell State to be shared on\n",
    "# the parametrized quantum teleportation\n",
    "bell = QuantumRegister(2, \"Bell\")\n",
    "\n",
    "# create a classical register with two qubits\n",
    "# for Alice's part on the parametrized\n",
    "# quantum teleportation\n",
    "alice = ClassicalRegister(2, \"Alice\")\n",
    "\n",
    "# create a classical register with one qubit\n",
    "# for Bob's part on the parametrized\n",
    "# quantum teleportation\n",
    "bob = ClassicalRegister(1, \"Bob\")\n",
    "\n",
    "\n",
    "# add all the quantum and classical registers\n",
    "# created before to the quantum circuit implementing\n",
    "# a parametrized quantum teleportation\n",
    "tele_qc.add_register(bell, alice, bob)\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the 1st step of a parametrized\n",
    "# quantum teleportation\n",
    "tele_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create the Bell pair with $Bell_0$ going to Alice and $Bell_1$ going to Bob. This is done by using a Hadamard gate to put $Bell_0$ in the $|+\\rangle$ state and then performing a CNOT with the same qubit as the control. After they receive their respective qubit, they part ways."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 573.781x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add a barrier to the quantum circuit implementing\n",
    "# a parametrized quantum teleportation\n",
    "tele_qc.barrier()\n",
    "\n",
    "\n",
    "# create Bell state with the other two qubits,\n",
    "# in the quantum register defined before\n",
    "# for that purpose\n",
    "\n",
    "# apply a Hadamard gate to\n",
    "# the quantum circuit, on the 2nd qubit\n",
    "tele_qc.h(1)\n",
    "\n",
    "# apply a CX/CNOT gate to\n",
    "# the quantum circuit,\n",
    "# with control on 2nd qubit\n",
    "# and target on 3rd qubit\n",
    "tele_qc.cx(1, 2)\n",
    "\n",
    "\n",
    "# add a barrier to the quantum circuit implementing\n",
    "# a parametrized quantum teleportation\n",
    "tele_qc.barrier()\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the 2nd step of a parametrized\n",
    "# quantum teleportation\n",
    "tele_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, Alice performs a CNOT controlled by $q$ on $Bell_0$, which maps information about the state onto it. She then applies a Hadamard gate on $q$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 824.615x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# operations for Alice perform on her qubits\n",
    "# during the parametrized quantum teleportation\n",
    "\n",
    "# apply a CX/CNOT gate to\n",
    "# the quantum circuit,\n",
    "# with control on 1sr qubit\n",
    "# and target on 2nd qubit\n",
    "tele_qc.cx(0, 1)\n",
    "\n",
    "# apply a Hadamard gate to\n",
    "# the quantum circuit, on the 1st qubit\n",
    "tele_qc.h(0)\n",
    "\n",
    "\n",
    "# add a barrier to the quantum circuit implementing\n",
    "# a parametrized quantum teleportation\n",
    "tele_qc.barrier()\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the 3rd step of a parametrized\n",
    "# quantum teleportation\n",
    "tele_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now Alice measures her qubits and saves the results to her register."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UkpLi8jlRPQgPNYTVwsOeQ9v0/OLblJt/Uo3DW2jKde8qvI53PVkUgHerE1RymZIkuXn3baBWy8/P14gRI875ADrULsx5qCGsFh5mf3iT7rvqdb354A5d3OUavb78H2aXBAAAqhnBwXoYeagh1q5da3YJVSYl7UcFB9ZRm+iukqTLetyo15Y/oMKiAvn7mfBwBpM0btxYU6ZMUePGjc0uBTAFPQBvRw/AiggPqHLpmXu1N/0n3fFcV+ey/IJcHc1OU1SE99zYPDIyUjfddJPZZQCmoQfg7egBWBGXLcEj2jXvrdcmb3V+hQR5363WsrKy9PnnnztvNwd4G3oA3o4egBURHlDloiJa6bcTf9zT+lRetvIKTimyXrSJVVW/1NRU3X///UpNTTW7FMAU9AC8HT0AKyI8oMq1ie4qPx9/bd61WpL06bcv6+Iu13rVfAcAAAArYs4DPOKR6xdq9n8n6IWld6lpgzZ6+Pr3zC4JAAAA54nwAI9oGdVJL0/aZHYZAAAAqEJctgR4SFBQkNq3b6+goCCzSwFMQQ/A29EDsCJGHgAPad26tZYuXWp2GYBp6AF4O3oAVsTIAwAAAABDCA+AhyQnJ6tz585KTk42uxTAFPQAvB09ACsiPAAe4nA4VFhYKIfDYXYpgCnoAXg7egBWxJwHyMdfGjTR7Cpc4+NvdgUAYB0BvtLMa82uwjUBvmZXYC0hISHKycmpsuPNfu0DZZ/KVb3QED14x9hyr6tCSEhIlRwHriE8QDab5Mvz2wDAa9lsUiDvCLyazWZTaGholR0vIDBIAYXFCggMUmhoaLnXqL24bAkAAACAIXzOAHhI69attWzZMjVr1szsUgBT0APwdvQArIjwAHhIUFCQ4uLizC4DMA09AG9HD8CKuGwJ8JC0tDQ99thjSktLM7sUwBT0ALwdPQArIjwAHnLixAktWbJEJ06cMLsUwBT0ALwdPQArIjwAAAAAMITwAAAAAMAQwgMAAAAAQwgPgIf4+PioZ8+e8vGhzeCd6AF4O3oAVsS/ZsBD7Ha7fvjhB9ntdrNLAUxBD8Db0QOwIsIDAAAAAEMIDwAAAAAMITwAAAAAMITwAHhIWFiYRo4cqbCwMLNLAUxBD8Db0QOwIj+zCwCsKiYmRrNmzTK7DMA09AC8HT0AK2LkAfCQ/Px87d+/X/n5+WaXApiCHoC3owdgRYQHwENSUlI0ZMgQpaSkmF0KYAp6AN6OHoAVcdkSADkcUkGx2VUYF+Ar2WxmVwEAsAqHw6Hc3Fyzy3BJSEiIbCb8MiQ8AFBBsTTlQ7OrMG7mtVIgP70AAFUkNzdXderUMbsMl+Tk5Cg0NLTaz8tlSwAAAAAMITwAAAAAMISBf8BDEhIStGPHDrPLAExDD8Db0QOwIkYeAAAAABhCeAA8ZO/evRo7dqz27t1rdimAKegBeDt6AFbEZUuAh+Tm5mrbtm217tZvQFXxth4oKpb2H5MOZkoHj0mZOVJOXsm6U/nSiq1STITUsqFUL9jUUlFNvK0H4B0IDwAAnIcTudK3u6UNKVJ2XsXbFNml1Uklf/exSR1jpAHxUlxjnlkCoHYhPAAA4IaiYmnVT9IXyZLdYXw/u0PafrDkq0WkdH0fqXGY5+oEgKrEnAcAAFx0MFOa81nJaIIrweHP9h+VZq+U1iaXPOkdAGo6Rh4AD4mOjtbMmTMVHR1tdimAKazaA7+kS298VfJk9qpQZJeW/Sgdzpau7SX58LGeZVi1B+DdCA+Ah4SHh+uKK64wuwzANFbsgd2HpflfSYVVFBzO9P0eySbp2t7Mg7AKK/YAqo+Pj4/sdrvZZZRDeKhiDodDYWFhOnnypI4cOaLIyMizLod1ZWZm6rPPPtPQoUMVERFhdjlAtbNaD2TlSm9+7ZngUGrDHikqXLq4nefOgepjtR6AMWFhYerevbu6du2q8PBw+fr6Ki8vTykpKdq0aZP27NkjxzmuUwwMDNSSJUuUmJioGTNmVFPlxlg6PKxZs0aXXXZZueU2m01hYWFKSEjQzTffrAkTJshWRR/z7NmzRydPnlR0dHSZgFDZclhXenq6pk+frq5du/JLA17JSj3gcEgffi+dLnBtv8lDSm7Lmn1aeu5zY/ss3yp1iJYa1nW5TNQwVuoBnF1YWJjGjx+v2267TZ06dTrrtidOnNCSJUv08ssva8uWLeXWlwaH4cOHa/jw4SosLNScOXM8VbrLLH1l5Y8//ihJatiwofr37+/86tixowoKCpSYmKhbbrlFjz32WJWdc9u2bZKkrl27GloOwJrsDim3oOTNJhNha78t+6TkQ67vVy9YCg9x7bkOhcXSBxv4dwPUBsHBwZo9e7bS0tL0wgsvnDM4SCWXs91yyy3avHmzvvvuO/Xo0cO57szgIEk5OTn6/vvvPVa/Oyw98rB161ZJ0s0336xnn322zLqsrCxdf/31WrlypZ5//nk98cQTCgwMrLJzdunSxdBywEpSk7/UkmcGacB1s3XB8H9UuM2/x9kU23W4Rv1jeTVXVz3Sjkvf7JI275MKikqWhQRIvVtL/eL4NLk2cjikNcnVe849v5U8cC6WgWqgxhowYIDeeusttWnTpszyTZs2acOGDdq8ebPS0tJUXFysunXrqlOnTurRo4cGDhyosLCS+zP36dNHGzZs0KxZszRjxgwtWrSoTHAYNmyY1q9fX+3f29lYOjyUjjxU9IY9LCxMkydP1sqVK3X69GkdOXJEMTEx531ORh4A71Rsl5ZsKnlY2J/lFkjrdpR8DessXdaRCbG1yd4jUvqJ6j/vN7sID0BNddddd+k///mPfH6/Pdrp06f1xhtv6JVXXlFycsWfNnzyySeSpJCQEF1//fWaNGmSOnbsKF9fXz3yyCO68847Vb9+fUk1NzhIFr5s6fTp09q1a5ekyj/tL31cfGBgoKKiosqtLygo0Lx58zR48GA1aNBAgYGBatOmjR5++GHl5ORUeExGHlAqNDRU/fv3V2hoqNmlwMMcjpLLTCoKDn+2crv02XbP11QTWKUHvttjznm37nd9jgVqFqv0AMq699579fLLLzuDQ2Jiorp27ap777230uBwptzcXM2fP1/dunXTo48+qoKCkkavDcFBsnB42L59u4qLixUUFKS2bdtWuM2CBQskSVdffbV8fX3LrEtJSVH37t11++2366uvvlJkZKRatWql/fv3a+bMmbr44oud4aPU8ePHdfDgQYWGhpYZwqpsOawtNjZW8+fPV2xsrNmlwMO27Jd+2Gt8+//9XPJpttVZpQf2/mbOeYvsJQ+jQ+1llR7AH0aPHq0XXnjB+frZZ5/VRRdd5PzA2hVFRUWaO3duuTkNu3bt0jfffHPetXqKZcND6Sf9pcNBpbKysrRx40Zdc801Wrx4sdq1a6dZs2aV2TczM1NDhw5VUlKSbr31VqWlpemXX37Rjh07lJycrPbt22vLli16/vnnKzxnp06dnGn0bMthbcXFxcrJyVFxsQfv61hDFRXk6vTJoxV+WdE3rv/OcGuf2sYKPZCbLx2teKC5WqQSHmo1K/QA/hAZGanXXnvN+fqf//ynHnnkEbefxVA6OfrCCy+UJOdxunfvrnvvvff8C/YQy76TLZ3vsGnTJtlsNudXeHi4evfurTVr1uiZZ57Rhg0b1LRp0zL7Tpo0SSkpKZo0aZLmzZunRo0aOdfFxcXpxRdflCR9/PHHZfZjvgPOtHPnTvXs2VM7d+40u5Rqt2HJk3r9roYVfllN+gn3RhG2HpBy8qq8nBrFCj2QdsLc8xMeajcr9AD+8OKLLzrfE3700Ud68skn3T5WRXdVmjRpknP9jBkzauzVKpadMF36aX/btm3LPFfh+PHj+vXXX3X8+HEtWLBAo0aNcs54l6SkpCS9//77atKkSaUP5SgNAWlpaRWe05X5Dnv37tWkSZO0bt06+fn5aeTIkXr++efVoEEDV75dpx49eigjI8OtfXFuN910k+Ft09PTJUkrV650hlkj3n77bRerOn++/sG6crqBC/YN6jjodsX1HlPhuo+eLf/sFVfFx8WpuPD0eR+nKsR0HqE+N7zq8n7FdqnfoJHKPGj830ZNYNUeqEzTDn9RvxvfqHBd6TMczqZe0B9/Truy8u0qew7Eyv+t09SxfzNYLaqDt/WAu66ccJ9C69RTeka6YmJiyr2uac41etClSxeNHTtWknTs2DHdddddbp+rouBQOschPj5e9957r0JCQvToo49qwoQJlR4nLi7O7StamjRpok2bNrm1ryXDg91u108//SRJeuutt9S3b98y6zMzMzV+/HitWLFCV111lZKSkpz/8RctWiS73a7i4uIKHzAnyTmx5c8ToEpDwp9HGCpbfvLkSQ0aNEgRERFatGiRTp8+rYceekgjRoxQYmKiW/8gMjIyyoUaVJ0/z3M5m7y8POefruxnxv8/v8CQKj1eeJM4Ne84uEqPeaZD6YdUlG/8v6kn1Y095fa+x45n6VAt61er9kBlgptmVbqu9BkORvj4GN/2TAUFRTXqvwe8rwfcZf/9Ui17cbHS0tLKva5tzgwLTz75pA4fPuzWcc4WHCTpkUce0bhx41S/fn2NHTtWDzzwgDIzKx6CLA2n1c2S4eGXX35Rbm6ubDZbhQ/riIiI0Ny5c7VixQrt3LlTSUlJzu3Wrl0rSTpy5IiOHDn7tQhnToAqLCzUjh075OPjo86dO59zuSS9/vrrSktL09dff63mzZtLkmJiYtSvXz8tW7ZMo0ePdvl7b9Kkicv7wLiQEOO//YOCgpx/urJfdHS0y3WdL19/F55gVQM0jWpaY0YeQt14PIzD4ZDNZlO9EF/ZTPj/fT6s2gOVCatXed3ZBv4J1gsqCQ52u5R9lsvUKjuWn6+jRv33gPf1gLt8fp9v6uPrq+jo6HKvaxq73V7pm/G6detq3Lhxkko++H3nnXfcOse5goMknTp1Sm+99ZYmT56soKAgTZgwQXPnzq3weFFRUec18uAuS4aH0qHBli1bqk6dOhVuc+Yb/8OHDzvDQ2pqqiRp3759atGiheFzJicnq6CgQPHx8WV+QFS2XJKWL1+uAQMGOIODJPXt21etWrXSp59+6lZ4cHcICsa4ct1qUlKS3nzzTQ0bNkwJCQmG95s+fbo7pZ2X/CJpyofVflq37dq9W4E15KdXQZE07aOSZzkYZbPZ1LielLx5Xa173oNVe6Ayh7OlGZ9WvK6iy4z+bNqVJSMO2Xkl/05cdf1fL9d/n051fUd4jLf1gLueeWmhsnNOKapJlFJTU8u9rmlOnTpV6XvGM2+3+/7771d6u/6zMRIcSr3++uuaPHmyJOnyyy+vNDzs3r3blNsAW3LCtJFnKpw5ZNa4cWPn30+dKrkEoXSo0Sh3JksnJydX+MMkISHB0H2CUbPFx8crMTFR8fHxZpcCDwrwK3l6tKsGxFv/QXFW6IGGdWVqUG0WYd65cf6s0AOQLrjgAuffv/rqK5f3dyU4SCVX0JReFnXmuWsKS4aH0pGHP18mdKZ58+ZJKhka7Nixo3N56SjAmjVrXDqnO5Oljx8/rvDw8HLLIyIiKr2+DbWHv7+/IiIi5O/vb3Yp8LCL20l1g4xv36ie1LOV5+qpKazQAz42KcbEN/Ax7t07AzWEFXoAJbdOLbV582aX9nU1OPz5PA0aNKhxzwmxZHg42xv27OxsTZ061flsh9mzZ8t2xsd/V199taSSCSuLFy8ut39KSoqeeuopffnll2WWc5tW/NmBAwd0991368CBA2aXAg8LD5FuH2Rs/kODOtIdg6QgL3gvYZUe6Nr83Nt4QlS41KiuOedG1bBKD3i7M2/pv3u38TsTuhscpJLRh1JRUVEuVOt5NeSq4aqTmpqqo0dLHkT11FNPlblOLCMjQ/v371dRUZGCgoI0d+5cXXfddWX2nzx5slatWqX169drzJgxioiIUGxsrOx2uw4ePKhjx45Jkn799dcy+5WGhD8HlsqWSyWPIT9x4kS55ZmZmYqIYKy6tjt58qTWrVune+65x+xSqk1Mh4Ga9J7jrNuca31t1SxCuv8v0mfbS57hUPynu/4F+Ek9WkpDO7s2SlGbWaUHerSUPt1aMr+lOg2Is/6lbVZnlR7wdq+//rpWrVolf39/ORzGf4c99NBDbgUHSVq9erVyc3N1+vTpGjdHxHLhoXTUQfrjjbsk+fj4qF69euratasuvfRS3XHHHWrZsmW5/YODg/XFF1/olVde0aJFi5ScnKyffvpJkZGRio2N1bhx4zRixIgy+6ampurYsWOKjIwscweBypaXat++fYVzG5KTk3XRRRe5+58AgEki60p/6y+NvkDaul9avrVkMnqwv/Tkld4x2mBFwQElAeLbqnsUyjkF+UsXlP8VBcAEb731llv7zZo1S/369dOAAQNcCg6S9Nlnn+mzzz5z67yeZrnwMGLECJdSYUX8/f01ceJETZw40dD2MTExFZ6zsuWlRowYoalTpyo1NdX5wJTvv/9ee/bs0ezZs90rHoDp6gZJF7aV1iSVhIcAP4JDbTe0s7TtgHQqv3rON7Ib/2aA2i4/P1+jR49W+/bty3y4XdtZcs5DbXH77bcrKipKo0aN0vLly7V48WJdd9116tWrl0aNGmV2eQCA39UNkq7qUT3nim8i9WtTPecC4Fn5+fmWCg4S4cFU9erV09q1axUVFaWxY8fq1ltvVb9+/bR8+XK3H/qBmqNx48aaMmVKmVsBA97Eaj3QrYXUy8W7ZGWflk7kGnugnFTyULnr+jDXwSqs1gOAZMHLlmqb1q1ba/ny5WaXAQ+IjIzUTTfdZHYZgGms1gM2m3RtbymvUNp+0Ng+Rh4kVyo0ULrzEql+9T/zCR5itR4AJEYeAI/JysrS559/rqysLLNLAUxhxR7w9ZFuHCD1cePBgGfToI5072VS0/pVe1yYy4o9ABAeAA9JTU3V/fffX+NusQZUF6v2gK+PNLaPdPNFVXPb3QHx0kPDpCZh538s1CxW7QF4Ny5bAgDADZ2bSa0bSat/lr7/VTpd4Nr+7aKkwQlSGy6HB1CLEB4AAHBTaGDJcz2GdZG27Jd+OiilZkpZFUyQ9veVoutLrRpJfdtIDXl6NIBaiPAAAMB5CvArmQdROhci+7R0LEcqLC65zCk0sCQs+HKxMIBajvAAeEhQUJDat2+voKAquCgaqIW8uQfqBZd8wbt5cw/AuggPgIe0bt1aS5cuNbsMwDT0ALwdPQArYgAVAAAAgCGEB8BDkpOT1blzZyUnJ5tdCmAKegDejh6AFREeAA9xOBwqLCyUw+EwuxTAFPQAvB09ACtizgMABfhKM681uwrjAnzNrgAAYCUhISHKycmpsuPNfu0DZZ/KVb3QED14x9hyr6tCSEhIlRzHVYQHALLZpEB+GgAAvJTNZlNoaGiVHS8gMEgBhcUKCAxSaGhoude1GZctAQAAADCEzxoBD2ndurWWLVumZs2amV0KYAp6AN6OHoAVER4ADwkKClJcXJzZZQCmoQfg7egBWBGXLQEekpaWpscee0xpaWlmlwKYgh6At6MHYEWEB8BDTpw4oSVLlujEiRNmlwKYgh6At6MHYEWEBwAAAACGEB4AAAAAGEJ4AAAAAGAI4QHwEB8fH/Xs2VM+PrQZvBM9AG9HD8CK+NcMeIjdbtcPP/wgu91udimAKegBeDt6AFZEeAAAAABgCOEBAAAAgCGEBwAAAACGEB4ADwkLC9PIkSMVFhZmdimAKegBeDt6AFbkZ3YBgFXFxMRo1qxZZpcBmIYegLejB2BFjDwAHpKfn6/9+/crPz/f7FIAU9AD8Hb0AKyI8AB4SEpKioYMGaKUlBSzSwFMQQ/A29EDsCLCAwAAAABDCA8AAAAADCE8AAAAADCE8AAAAADAEG7VCnhIQkKCduzYYXYZgGnoAXg7egBWxMgDAAAAAEMID4CH7N27V2PHjtXevXvNLgUwBT0Ab0cPwIq4bAnwkNzcXG3btk25ublml4JqVFgsHTouHc6W8otKlhUUSamZUlS45OtFH9nQA/B29ACsiPAAAOfpVL608Vdp817p0AnJ7ii7/nShNOczyc9HahYh9WotdY+VAvkJDACoZfjVBQBuysmTVmyTNu0tGXE4lyK7tPdoydcnW6R+cdJfOhEiAAC1B7+yAMAN2w9K/91YEiDckVcorU2Wth+QrusjtW5ctfUBAOAJXnT1LVC9oqOjNXPmTEVHR5tdCqqQ3SEt2SS9+bX7weFMR3OkF9eUBAmroQfg7egBWBEjD4CHhIeH64orrjC7DFQhh0P67/fShj1Vf+xlP0oFxdKQTlV/bLPQA/B29ACsiJEHD3A4HKpXr55sNpuOHj16zuWwpszMTC1cuFCZmZlml4Iq8tl2zwSHUp9vl75L8dzxqxs9AG9HD8CKLB8e1qxZI5vNVu7Lx8dH9evX14ABA/Tmm2/K4XCc+2AG7dmzRydPnlR0dLQiIyPPuRzWlJ6erunTpys9Pd3sUlAF9h2VVie5ts/kIdK0K0v+NOqjzdKxHNfOU1PRA/B29ACsyPKXLf3444+SpIYNGyo+Pt65PDs7W3v27FFiYqISExO1Z88ePf3001Vyzm3btkmSunbtamg5gJqtoEh6/7uSy5ZcUS9YCg9x/VyLNkh3Xyr52FzbFwAAT7P8yMPWrVslSTfffLO++eYb59f27dt16NAhDRs2TJL0/PPPKz8/v0rP2aVLF0PLAdRs3++RfsuuvvOlHJaS06rvfAAAGGX58FA68lDRG/awsDBNnjxZknT69GkdOXKkSs7JyANgHQ6H9M2u6j+vGecEAOBcLB0eTp8+rV27Sn4DV/Zpf+kj4wMDAxUVFVVufUFBgebNm6fBgwerQYMGCgwMVJs2bfTwww8rJ6fiC5MZeYAkhYaGqn///goNDTW7FJyHlN+kw9U46lBqZ7p05GT1n7cq0QPwdvQArMjScx62b9+u4uJiBQUFqW3bthVus2DBAknS1VdfLV9f3zLrUlJSNHr0aCUlJcnPz0+tWrVSo0aNlJKSopkzZ2r16tVav369QkL+uKj5+PHjOnjwoEJDQ9WmTZtzLod1xcbGav78+WaXgfNk5uVDOw5JDSv+0VUr0APwdvQArMjSIw+ln/R37NixTDDIysrSxo0bdc0112jx4sVq166dZs2aVWbfzMxMDR06VElJSbr11luVlpamX375RTt27FBycrLat2+vLVu26Pnnn6/wnJ06dZKPj885l8O6iouLlZOTo+LiYrNLwXk4aOIdFs08d1WgB+Dt6AFYkaXfxZbOd9i0aVOZ27SGh4erd+/eWrNmjZ555hlt2LBBTZs2LbPvpEmTlJKSokmTJmnevHlq1KiRc11cXJxefPFFSdLHH39cZj/mO6DUzp071bNnT+3cudPsUuAmu0NKNfENfOox885dFegBeDt6AFZk6cuWSj/tb9u2bZnnKhw/fly//vqrjh8/rgULFmjUqFEKCwtzrk9KStL777+vJk2aaMaMGRUeuzQEpKWVvabB1fkOqampevbZZ7Vx40Zt27ZNBQUFVfrMCQDuyyss+TLL8Vzzzg0AQEUsGx7sdrt++uknSdJbb72lvn37llmfmZmp8ePHa8WKFbrqqquUlJTkvJxo0aJFstvtKi4u1mWXXVbh8QsKCiSp3CSo0pDw5xGGypanpKRoyZIl6tmzpwICApSYmOjqt1pGjx49lJGRcV7HQOVuuukmw9uWPhRo5cqVzlEwI95++20Xq4KnBNaJ1MjHt1a6fvKQkmc5VKZe0B9/Truy8u2yT0vPfV5++ancPMXE1Kw5UvQAvB09YMyVE+5TaJ16Ss9IV0xMTLnXVlfTv/8mTZpo06ZNbu1r2fDwyy+/KDc3VzabTZ06dSq3PiIiQnPnztWKFSu0c+dOJSUlObdbu3atJOnIkSPnvH1rbGys8++FhYXasWOHfHx81Llz53Mul6SLLrrI+cNl2rRp5x0eMjIyyo2GoOqU3p3LiLy8POefruzH/7+aIzD07P/fjD4EzsfH9YfFSVJRUUGN+/dAD8Db0QPG2H+f52EvLlZaWlq511Zn5e/fsuGhNOG3bNlSderUqXCbM9/4Hz582BkeUlNTJUn79u1TixYtDJ8zOTlZBQUFio+PL3MHpsqWS6ryydNNmjSp0uOhrD///zuboKAg55+u7BcdHe1yXfAMm4+viovy5esXWOH67NNn379eUElwsNul7LzKt6vsOIW5mTXu3wM9AG9HDxjj8/uNanx8fRUdHV3utdXV9O//fN4vWjY8GHmmwpnJr3Hjxs6/nzp1StIfnxgYVRMmS7s7BAVjXJn0VlhYqFtuuUV169aVv7+/4f2mT5/uTmnwkOc+lw5UMnG5okuNzjTtypIRh+w8adpHrp+7f7dYzf/9w4yagh6At6MHjHnmpYXKzjmlqCZRSk1NLffa6qz8/Vv2bkulIw9/vkzoTPPmzZNUkvA7duzoXN68eXNJ0po1a1w6Jw+Hw5n8/f0VERHh0i8M1DwxEeadu5mJ564K9AC8HT0AK7JseDjbG/bs7GxNnTrV+WyH2bNny2azOddfffXVkqRHHnlEixcvLrd/SkqKnnrqKX355ZdllteEkQfUHAcOHNDdd9+tAwcOmF0KzkNc43Nv4yltTDx3VaAH4O3oAViRJS9bSk1N1dGjRyVJTz31lObOnetcl5GRof3796uoqEhBQUGaO3eurrvuujL7T548WatWrdL69es1ZswYRUREKDY2Vna7XQcPHtSxYyXXMPz6669l9isNCX8OLJUth7WdPHlS69at0z333GN2KTgPnWKkOkFSjmtXMZ636PpSiwbVe86qRg/A29EDsCJLhofSUQfpjzfuUsnk5Hr16qlr16669NJLdccdd6hly5bl9g8ODtYXX3yhV155RYsWLVJycrJ++uknRUZGKjY2VuPGjdOIESPK7Juamqpjx44pMjKyzESYypYDqB38fKW+raXVSdV73gHx0hkDogAA1AiWDA8jRow47wet+fv7a+LEiZo4caKh7WNiYio8Z2XLAdQeF7WVEndLuQXVc77IOtIFsdVzLgAAXGHJ8FDblM6rSE5OLvM6NjZWPXr0MK0uACXqBkt/7SG9963nz2WTdF1fKYCfzgCAGohfTzXAmDFjKnx94403WuIpk96qcePGmjJlSpnbAKP2uiBW2n6w5Muo0uc3nOt5EGe6qJ3UupFLpdVY9AC8HT0AKyI81ABc1mRNkZGRuummm8wuA1XEZpNu6CtlnZb2HzW2z7meA/FnnWKkK7q5XltNRQ/A29EDsCLL3qoVMFtWVpY+//xzZWVlmV0Kqkigv3TnIKlVw6o/dtfm0o0DJF8L/VSmB+Dt6AFYkYV+TQE1S2pqqu6///5a/yRJlBUcIN11qXRJh6q5G5KfT8low/j+JXd2shJ6AN6OHoAVcdkSALjI37fkDX/nZtKH30vpJ9w7TquG0rW9pcZhVVoeAAAeQ3gAADfFRkoPDZNSfpMSd5VMprafYwqTv2/J5Ov+cVKzWv4QOACA9yE8AMB5sNmkuMYlX/lF0qHj0oFj0uFsqaCo5Nargf5SVLjULEJqGm69y5MAAN6D8AB4SFBQkNq3b6+goCCzS0E1CfSTWjYs+QI9ANADsCLCA+AhrVu31tKlS80uAzANPQBvRw/AirjbEgAAAABDCA+AhyQnJ6tz585KTk42uxTAFPQAvB09ACsiPAAe4nA4VFhYyBPE4bXoAXg7egBWRHgAAAAAYAjhAQAAAIAhhAcAAAAAhnCrVsBDWrdurWXLlqlZs2ZmlwKYgh6At6MHYEWEB8BDgoKCFBcXZ3YZgGnoAXg7egBWxGVLgIekpaXpscceU1pamtmlAKagB+Dt6AFYEeEB8JATJ05oyZIlOnHihNmlAKagB+Dt6AFYEeEBAAAAgCGEBwAAAACGEB4AAAAAGEJ4ADwkMjJSt912myIjI80uBTAFPQBvRw/AirhVK+CCdu3aubTtxRdf7MFqgOpHD8Db0QPwdow8AAAAADCE8AAAAADAEMIDAAAAAEMIDwAAAAAMITwAAAAAMITwAAAAAMAQwgMAAAAAQwgPAAAAAAwhPAAAAAAwhPAAAAAAwBDCAwAAAABDCA8AAAAADCE8eJnZs2erb9++ql+/vsLDwzVgwAB9/vnnZpcFAABwVitXrlTXrl0VGBio2NhYPffcc2aXVK2+/vprjRo1Si1atJDNZtP06dNNqYPw4GXWrl2rm2++WevWrdPGjRvVr18/jRgxQomJiWaXBgAAUKFNmzZp1KhRGjp0qLZu3app06Zp6tSpevXVV80urdrk5OSoQ4cOmjVrlpo0aWJaHX6mnRmm+Oyzz8q8njVrlj7//HMtXbpU/fv3N6kqAACAyj333HPq2bOnZsyYIUlq3769kpKS9Oyzz+rOO+80ubrqMWzYMA0bNkySNGXKFNPqYOTBy9ntdmVnZys0NNTsUgAAACqUmJioIUOGlFk2ZMgQ7d+/X6mpqSZV5Z0YefByzzzzjE6cOKHbb7/d7FIAAEAtk5pxRF9/v63c8tN5ec4/3/9kTbnXpQL8/TXqsv7y9z/7W9L09PRyl+qUvk5PT1dMTMx5fR/uKrbbtWx1ok7n5ZdZbvT7l6Q+3RPUqllU9RRcBQgPXuzll1/WM888o2XLlpnWdAAAoPZq2jhSp/MKtHtfxZ/+FxYVa/vOXyt9PfryAecMDjWZr4+PWjaL0gefrq1w/bm+/+ZNG6lFdGOP11mVuGzJS82ZM0cPPvigli1bpsGDB5tdDgAAqIV8bDZdPexiBQcFurxvfMtm6t21vaFto6KilJGRUWbZ4cOHnevM1LVDG3Vp39rl/fz9/XTNiEHy9aldb8drV7WoEk888YSeeuoprVy5kuAAAADOS1jdUI2+fIBL+4QEBerqYRfLZrMZ2r5///5atWpVmWWff/65WrRoUSOunhh1WX/VqxPi0j4jLumjyPphHqrIcwgPv3v77bdls9l00003lVm+b98+2Ww2xcbGmlJXVbvvvvs0e/Zsvfvuu2rbtq0yMjKUkZGhrKwss0sDAAC1VJf2rV369P3Kv1zo0pvt+++/Xxs3btSjjz6qnTt36p133tGLL76ohx9+2J1yq1xIcJDGDBtoePu2rZqpVxdjoy6lcnJytHXrVm3dulUFBQXKyMjQ1q1blZKS4mK158fy4WHo0KGy2Wyy2Wzatq38hB5v8+9//1t5eXm68sorFRUV5fyaNGmS2aUBAIBabNTlA1Svzrnv3tgtoY06tWvl0rF79uypjz/+WMuXL1eXLl30xBNP6Omnn65Rt2mNaxmjvt0TzrldSHCgrhpqfNSl1KZNm9StWzd169ZN6enpeumll9StWzfdeuut7pbslto7Q8WA9PR0rV692vl6wYIFmjt3rkvH8Pf3V9u2bRUdHV3V5ZnC4XCYXQIAALCgkKBAjRl+sd74cGWl24TVDdUVg917rtTw4cM1fPhwd8urFkMH9lbKvlQdyaz8ig5XR11KDRw4sEa8j7P0yMN7772n4uJihYeHS5IWLlyooqIil44RHR2tnTt36osvvvBAhTXbrl8P6rMvv1dO7mmzSwEAALVAXGyM+l3QsdL1Y4YPdGtydW0R8PskaJ9KRhW6d4xTp7aujbrUNJYOD++8844kafr06WrYsKEOHz5cbrINKuZwOPS/9Zv01ffbtH7jdrPLAQAAtcTQi3upYUR4ueUDenRSmxbWuJLjbJpFNdIl/buXWx5er47boy41iWXDw+bNm5WUlKTAwEBdf/31uvbaayX9ESiMOteE6eLiYr377ru6/PLL1bBhQwUGBqp58+YaMmSI5s+fr+Li4nL77N27V3fffbfatGmj4OBghYWF6aKLLtK7775bI4ajJOmXXw8qNeOI/P39dGHPzmaXAwAAagl/fz9dO2KQfHz++PS9UYP6+svFPU2sqnoN6ttNzaIaOl/bVDLqEhQYYF5RVcSy4aE0JAwbNkz169fXuHHjJEnLli3TiRMnquQc2dnZuuyyyzR+/HitXr1aAQEB6tKli+x2u/73v//ptttu08mTJ8vs88knnyghIUGvvPKK0tPTFRcXp/r16+ubb77R+PHjNX78eNMDhMPh0JpvNkuS+nbroDqhwabWAwAAapeYqIa6tN8FkkoepHbtyEHy97P0VNsyfH18dM2IQfL385Uk9e/ZSa2bNzW5qqphyfBQWFioRYsWSZIzNPTu3VtxcXHKz8/Xhx9+WCXnueWWW7Ru3TrFxMRo7dq1SktL08aNG5Wamqr09HQ9/fTT8vf3d26fnJyssWPHqrCwUHPmzNHx48e1fft27du3T1u2bFF8fLzee+89zZs3r0rqc9eZow4X9epiai0AAKB2Gti3q5pFNdLgARcounGk2eVUu4YR4Ro2qI8aR9bXXy6yzqiLzWH2x9we8Mknn2j06NEKDw9XRkaGAgNLJuY89dRTmjZtmvr27atvv/22zD5vv/22JkyYoBtvvFFvv/22c/m+ffvUsmVLtWjRQvv27XMu37x5s3r06CE/Pz/9+OOP6tix8slBpa655hr9v//3/zR9+nQ9+uij5dZv2bJFPXr0UOvWrbV79263vvcX31mqkznuT3B2OBw6dTpPdrtdAf7+lhheAwAA5nA47L/fktS125JaScl/g5r1eX3dOsG698a/urWvJcePSi9ZGjNmjDM4SCWjENOmTdN3332nXbt2KT4+3u1zfPzxx5JKbhtmJDgUFBTo008/lc1m0+23317hNt27d1eLFi2UkpKitLQ0t24PezLntLJzTrm8X0UKCgtVUFhYJccCAABA7We58HDs2DGtWLFC0h+XLJVq3bq1+vTpow0bNmjBggWaPn262+dJTk6WJPXt29fQ9rt371ZeXp78/Px05ZVXVrrdsWPHJMnt8FC3jvvzExh1AAAAsL7zeb9oufCwaNEiFRQUqEWLFrrwwgvLrf/b3/6mDRs26N1339X//d//ufx0v1LZ2dmSpLCwMEPbl07SLioqUmJi4jm3z83Ndasud4egJGnnngN6e/Hn8vf300N3jGWiNAAAAMqwXHgovWRp//798vGp/PqyAwcOaN26dbrkkkvcOk+9evUkSVlZlT9B8Ex16tSRJEVERDhHFzzB3TkPpaMOkmSTTS+8vbSqSwMAAEANwJyH3+3YsUObNm2SJDVu3LjS7XJycnTq1CktWLDA7fCQkJCgpUuX6rvvvjO0fVxcnAICApSZman09HRFRUW5dd5zqYo5D8x1AAAAQEUsFR5KRx26dOmirVu3VrrdRx99pL/+9a9asmSJXnrpJYWGhrp8riuvvFL/93//p5UrVyo5OVkdOnQ46/YhISEaOnSoPvnkE82dO1dz5sxx+ZxGuHMNG3MdAAAAvAdzHiTZ7Xa99957kqTx48efddvhw4erQYMGOnbsmJYsWXLO7SvSrVs3XXPNNfrvf/+roUOHasGCBbr44oud6w8fPqw333xTEydOdIaT6dOna/Xq1XruuecUGBioKVOmOC9/kkrmUaxYsUI//PCDnnvuOZdrktyb88BcBwAAABhRs246ex7WrFmjtLQ0+fr66oYbbjjrtgEBAbr22msl/TFa4Y558+Zp4MCBOnDggAYOHKiYmBj16tVLzZo1U1RUlKZOnarCMy7/6dixoxYvXqy6devqmWeeUWRkpDp37qw+ffqoTZs2ql+/vq6//vpyz6DwJJ4mDQAAAKMsEx5KQ8Dll19+1vkOpUpHG9atW6cDBw64dc569eppzZo1euONNzRw4EDl5uZq27Zt8vHx0V/+8he98cYbqlu3bpl9hg4dqh07dmjKlClq37699u7dq82bNysnJ0eDBg3Sc889V2VPwDZi195UniYNAAAAQyz5hGkYV1RcrC0/71ZefoEu6tXZ7HIAAABQgxEeAAAAABhimcuWAAAAAHgW4QEAAACAIYQHAAAAAIYQHgAAAAAYQngAAAAAYAjhAQAAAIAhhAcAAAAAhhAeAAAAABhCeAAAAABgCOEBAAAAgCGEBwAAAACGEB4AAAAAGEJ4AAAAAGAI4QEAAACAIYQHAAAAAIYQHgAAAAAYQngAAAAAYAjhAQAAAIAhhAcAAAAAhhAeAAAAABhCeAAAAABgCOEBAAAAgCGEBwAAAACGEB4AAAAAGEJ4AAAAAGAI4QEAAACAIYQHAAAAAIYQHgAAAAAYQngAAAAAYAjhAQAAAIAhhAcAAAAAhhAeAAAAABhCeAAAAABgCOEBAAAAgCGEBwAAAACGEB4AAAAAGEJ4AAAAAGAI4cELff311xo1apRatGghm82m6dOnm10SAAAAagHCgxfKyclRhw4dNGvWLDVp0sTscgAAAFBL2BwOh8PsImCe2NhY3XrrrXrsscfMLgUAAAA1HCMPAAAAAAwhPAAAAAAwhPAAAAAAwBDCAwAAAABDCA8AAAAADCE8VKNp06bJZrNp2rRpptaRk5OjrVu3auvWrSooKFBGRoa2bt2qlJQUU+sCAABAzebV4WHgwIGy2WzlvoKDgxUXF6fbbrtNO3bsMLvMKrdp0yZ169ZN3bp1U3p6ul566SV169ZNt956q9mlAQAAoAbzM7uAmqBZs2Zq3ry58/Vvv/2mffv2af78+VqwYIE+/vhjDR061MQKq9bAgQNl5PEeWdk5yssvUOOGEdVQFQAAAGo6rx55KHXzzTfrm2++cX7t2rVLe/fu1cCBA1VQUKBbb71VxcXFZpdZ7b74dov+9eZifblhq9mlAAAAoAYgPFQiOjpaL730kiTp0KFDSkpKMrmi6pWZdVKbfvpFDkmxMU3MLgcAAAA1AOHhLFq0aOH8e2FhYbn1mzdv1tixY9W0aVMFBASoUaNGGjVqlNatW3fOYx87dkz33HOPmjdvrsDAQLVs2VIPPvigsrOzq/R7cNeX3/0ou92huNhowgMAAAAkER7OauPGjZIkf39/tW7dusy6t956S71799aHH36ovLw8denSRT4+Plq2bJkuueQSzZgxo9LjZmZmqlevXnr11VcVFham+Ph47d+/X3PmzFG/fv107Ngxj35f51I66iBJl/a/wNRaAAAAUHMwYboCR48eVWJiou6//35J0t///neFh4c71//888+68847VVxcrKlTp2ratGny9/eX3W7Xyy+/rIkTJ2rq1Knq2bOnBg8eXO74r776qtq0aaMdO3YoPj5ekrRz505dccUVSkpK0sSJE7Vw4UK3an/xnaU6mXParX1Lnc7Ll93ukK+vj97/5IvzOhYAAABqlrp1gnXvjX91a1+bw8htdyxq4MCB+uqrrypdHxUVpSeeeEJ33HGHbDabc/mNN96oBQsWaNCgQVq7dm25/UrXDxw4sMwlTNOmTdNTTz0lSfrhhx/Uo0ePMvslJiZqwIAB8vHx0Z49exQbG+vy9/TMSwuVnXPK5f0AAADgHerVCdXUe25wa19GHlT+Vq0nT57U3r17yzwDoXfv3s71q1atkiTdd999FR5v8uTJWrBggdavX6/c3FyFhISUWd+nT59ywUGS+vfvr+7du2vLli1atWqV7rjjDpe/l7p1gl3e50yn8/JVWFQkX18fhQaf37EAAABQ85zP+0XCg0pu1frnpz4XFhbqxRdf1AMPPKBBgwbphx9+UEJCgrKysnT48GFJUseOHSs8XocOHeTj46Pi4mKlpKSoc+fO5dZXpkOHDtqyZYt++eUXt74Xd4egpJK5DnNe/0CSdNvYEUyUBgAAQBmEh0r4+/tr8uTJSkxM1NKlS/Xkk09q8eLFOnnypHObxo0bV7pv/fr1dezYsTLbl2rUqFGl5y09ZkX7GXE+cx6Y6wAAAGB95zPngfBwDv369dPSpUu1YcMGSVLdunWd6w4fPqxWrVqV26ewsFDHjx8vt32p3377rdLzlY5qVLSfESdzTp/3nIfiYjvzJgAAAFAO4eEcSueTl94+NSwsTI0bN9bhw4f1888/VxgekpOTZbfb5evrqzZt2lS4vjKl69q2betWve5ew8ZcBwAAAO/AnAcP+uabbySpzHMehgwZonfeeUf/+te/dMUVV5Tb51//+pck6aKLLio3WVqSNmzYoM2bN+uCC8o+Q+Hbb7/Vli1bZLPZdPnll7tVrztDUMx1AAAAgBE8JK4ShYWFmj17tj755BNJ0vjx453r/vGPf8jf31/r1q3TY4895nz6tMPh0Msvv6wFCxZIkqZOnVrhsf39/XXjjTcqJSXFuWzXrl2aMGGCJOnaa69Vy5YtPfJ9VYSnSQMAAMAIRh4kvfnmm1qzZo3zdemtWksnLY8ePdr5wDip5C5Lr732mm677TY9/fTTeuWVV9S6dWsdPHhQGRkZkqSnn366wgfESdKdd96pFStWqG3btkpISJAkJSUlyW63q3379nrxxRc99a2Ww9OkAQAAYBThQdLBgwd18OBB52s/Pz9FRkZqwIABuvHGG3XttdeW22fChAnq3LmzZs+era+++kpbt25VWFiYRo4cqfvuu0+XXHJJpeeLiIjQxo0b9fjjj+vTTz/Vb7/9ppiYGI0ZM0aPP/64wsLCPPJ9VqSgoFAxTRopMMCPUQcAAACclVc/YRolHA6H8gsKFRQYYHYpAAAAqMEIDwAAAAAMYcI0AAAAAEMIDwAAAAAMITwAAAAAMITwAAAAAMAQwgMAAAAAQwgPAAAAAAwhPAAAAAAwhPAAAAAAwBDCAwAAAABDCA8AAAAADCE8AAAAADCE8AAAAADAEMIDAAAAAEMIDwAAAAAMITwAAAAAMITwAAAAAMAQwgMAAAAAQwgPAAAAAAwhPAAAAAAwhPAAAAAAwBDCAwAAAABDCA8AAAAADCE8AAAAADCE8AAAAADAEMIDAAAAAEMIDwAAAAAMITwAAAAAMITwAAAAAMAQwgMAAAAAQwgPAAAAAAwhPAAAAAAwhPAAAAAAwBDCAwAAAABDCA8AAAAADCE8AAAAADCE8AAAAADAEMIDAAAAAEMIDwAAAAAMITwAAAAAMOT/A3ho5odEfV6qAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 991.837x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# measurements performed by Alice on\n",
    "# the qubit q and on her part of the Bell State,\n",
    "# performing the entanglement swapping\n",
    "tele_qc.measure( [ qr[0], bell[0] ], alice )\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the 4th step of a parametrized\n",
    "# quantum teleportation\n",
    "tele_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bob's qubit now has the information $|\\psi\\rangle$ from Alice's qubit $q$ encoded in $Bell_1$, but he does not know what basis to measure in to extract it. Accordingly, Alice must share the information in her register over a *classical* communication channel (this is why teleportation does not violate special relativity, no matter how far Alice and Bob are apart). She instructs Bob to perform an X gate on his qubit if her measurement of $Bell_0$ yields a 1 outcome, followed by a Z gate if her measurement of $q$ yields a 1.\n",
    "\n",
    "The applications of these gates can be conditioned on the measurement outcomes in two ways:\n",
    "- The `.c_if()` [instruction](https://qiskit.org/documentation/stubs/qiskit.circuit.Instruction.c_if.html), which applies the gate it modifies if the value of the `ClassicalRegister` index is equal to the value specified. Note that this works **only** on simulators;\n",
    "- The `.if_test()` [context](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.if_test.html) which operates similarly, but generalizes the syntax to allow for nested conditionals. This works on both simulators and actual hardware."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 3 - Add approriate conditional gates to transform Bob's qubit into the $Z$-basis. </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1159.06x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a copy of the quantum circuit defined before\n",
    "# to initialize the quantum circuit implementing\n",
    "# a parametrized quantum teleportation,\n",
    "# and to be graded with dynamic operations \n",
    "graded_qc = tele_qc.copy()\n",
    "\n",
    "\n",
    "##############################\n",
    "\n",
    "# add gates to graded_qc here\n",
    "\n",
    "# Bob, who already has the qubit teleported,\n",
    "# applies the following gates depending on\n",
    "# the state of the classical bits:\n",
    "# 00 -> Do nothing\n",
    "# 01 -> Apply X gate\n",
    "# 10 -> Apply Z gate\n",
    "# 11 -> Apply ZX gate\n",
    "\n",
    "# apply the Pauli-X (bit flip / not) gate on\n",
    "# the 2nd qubit of the Bell state if\n",
    "# the Alice's 2nd classical bit is 1\n",
    "graded_qc.x( bell[1] ).c_if( alice[1], 1 )\n",
    "\n",
    "# apply the Pauli-Z (phase flip) gate on\n",
    "# the 2nd qubit of the Bell state if\n",
    "# the Alice's 1st classical bit is 1\n",
    "graded_qc.z( bell[1] ).c_if( alice[0], 1 )\n",
    "\n",
    "##############################\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the parametrized quantum teleportation, to be graded\n",
    "graded_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, Bob can measure his qubit, which would yield results with the same probabilities as had Alice measured it originally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1326.28x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add a barrier to the quantum circuit implementing\n",
    "# a parametrized quantum teleportation, to be graded\n",
    "graded_qc.barrier()\n",
    "\n",
    "\n",
    "# measure the 2nd qubit of the Bell state to\n",
    "# the Bob's classical register\n",
    "graded_qc.measure( bell[1], bob )\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# a parametrized quantum teleportation, to be graded\n",
    "graded_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the grader for the exercise 3 of the lab 2\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex3\n",
    "\n",
    "# grade the exercise 3 of the lab 2\n",
    "grade_lab2_ex3( graded_qc, theta, 5 * ( np.pi / 7 ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The statevector simulator cannot work with dynamic circuits because measurement is not a unitary operation. Therefore we import the `Sampler` primitive from `qiskit_aer` to use the `AerSimulator`. We choose our angle to be $5\\pi/7$, which will yield a 1 result about 80\\% of the time and 0 result about 20\\% of the time. Then we run both circuits: the original one Alice had and the teleported one Bob receives. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Dists.: {'0': 0.2001953125, '1': 0.7998046875}\n",
      "Teleported Dists.: {'001': 0.0361328125, '011': 0.0498046875, '111': 0.201171875, '000': 0.0400390625, '010': 0.046875, '110': 0.2177734375, '100': 0.2060546875, '101': 0.2021484375}\n"
     ]
    }
   ],
   "source": [
    "# impor the Sampler from the IBM's Qiskit\n",
    "# Aer primitives module\n",
    "from qiskit_aer.primitives import Sampler\n",
    "\n",
    "\n",
    "# define the pretended theta angle\n",
    "angle = 5 * ( np.pi / 7 ) \n",
    "\n",
    "\n",
    "# create a Sampler object\n",
    "sampler = Sampler()\n",
    "\n",
    "\n",
    "# measure all the qubits on the quantum circuit\n",
    "# implementing a parametrized quantum teleportation\n",
    "qc.measure_all()\n",
    "\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a parametrized quantum teleportation,\n",
    "# with a static quantum circuit and\n",
    "# with the theta angle defined before\n",
    "job_static = sampler.run( qc.bind_parameters({theta: angle}) )\n",
    "\n",
    "# create a job for the quantum circuit implementing\n",
    "# a parametrized quantum teleportation,\n",
    "# with a dynamic quantum circuit and\n",
    "# with the theta angle defined before\n",
    "job_dynamic = sampler.run( graded_qc.bind_parameters({theta: angle}) )\n",
    "\n",
    "\n",
    "# print the measurement distributions of the qubits from\n",
    "# the parametrized quantum teleportation, with a static quantum circuit\n",
    "print( f\"Original Dists.: {job_static.result().quasi_dists[0].binary_probabilities()}\" )\n",
    "\n",
    "# print the measurement distributions of the qubits from\n",
    "# the parametrized quantum teleportation, with a dynamic quantum circuit\n",
    "print( f\"Teleported Dists.: {job_dynamic.result().quasi_dists[0].binary_probabilities()}\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wait, we see different results! While measuring Alice's original $q$ yields the expected ratio of outcomes, the teleported distributions have many more values. This is because the teleported circuit includes Alice's measurements of $q$ and $Bell_0$, whereas we only wish to see Bob's measurements of $Bell_1$ yield the same distribution. \n",
    "\n",
    "In order to rectify this, we must take the *marginal* counts, meaning we combine results in which Bob measures a 0 and all the results in which Bob measures a 1 over all the possible combinations. This is done with the `marginal_counts` [method](https://qiskit.org/documentation/stubs/qiskit.result.marginal_counts.html) from `qiskit.result`, which combines results over measurement indices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 4 - Marginalize the counts from measuring the teleported quantum state. <br>\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Hint: Remember that bit strings are reported in the little-endian convention).</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the counts marginalization from\n",
    "# the IBM's Qiskit result module\n",
    "from qiskit.result import marginal_counts\n",
    "\n",
    "# marginalize counts from the quasi-distributitions\n",
    "# obtained from the parametrized quantum teleportation\n",
    "tele_counts = marginal_counts( job_dynamic.result().quasi_dists[0]\n",
    "                               .binary_probabilities(), [2] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we marginalized correctly, we will see that the quasi-distributions from Alice's measurement and Bob's measurement are nearly identical, demonstrating that teleportation was successful!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the legend for the two quantum states\n",
    "# created before, namely the original quantum state to\n",
    "# be teleported and the quantum state which was indeed teleported\n",
    "legend = [ \"Original State\", \"Teleported State\" ]\n",
    "\n",
    "# plot the histogram for the quasi-distributions\n",
    "# for the two quantum states created before,\n",
    "# namely the original quantum state to be teleported\n",
    "# and the quantum state which was indeed teleported\n",
    "plot_histogram( [ job_static.result().quasi_dists[0]\n",
    "                  .binary_probabilities(), tele_counts ],\n",
    "                legend=legend, title=\"Measurement Results\\n\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the grader for the exercise 4 of the lab 2\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex4\n",
    "\n",
    "# grade the exercise 4 of the lab 2\n",
    "grade_lab2_ex4( tele_counts, job_dynamic.result() )"
   ]
  }
 ],
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