QISKIT lab2 Aheli.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",
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting Started\n",
    "\n",
    "Start by importing some libraries we need, including the `Sampler` and `Estimator` primitives from 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 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. TODO: include video links and such. 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 Qiskit and 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",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit.circuit import QuantumCircuit\n",
    "from qiskit.primitives import Estimator, Sampler\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('dark_background') # optional"
   ]
  },
  {
   "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, respectivly, 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
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      "text/plain": [
       "<Figure size 185.453x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create excited |1> state\n",
    "qc_1 = QuantumCircuit(1)\n",
    "qc_1.x(0)\n",
    "qc_1.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 185.453x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create superposition |+> state\n",
    "qc_plus = QuantumCircuit(1)\n",
    "qc_plus.h(0)\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": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "qc_1.measure_all()\n",
    "qc_plus.measure_all()\n",
    "\n",
    "sampler = Sampler()\n",
    "job_1 = sampler.run(qc_1)\n",
    "job_plus = sampler.run(qc_plus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{1: 1.0}]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job_1.result().quasi_dists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{0: 0.4999999999999999, 1: 0.4999999999999999}]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job_plus.result().quasi_dists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "legend = [\"Excited State\", \"Plus State\"] # TODO: Excited State does not appear\n",
    "plot_histogram([job_1.result().quasi_dists[0], job_plus.result().quasi_dists[0]], legend=legend)"
   ]
  },
  {
   "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": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "qc_1.remove_final_measurements()\n",
    "qc_plus.remove_final_measurements()\n",
    "\n",
    "# rotate into the X-basis\n",
    "qc_1.h(0)\n",
    "qc_plus.h(0)\n",
    "\n",
    "qc_1.measure_all()\n",
    "qc_plus.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sampler = Sampler()\n",
    "job_1 = sampler.run(qc_1)\n",
    "job_plus = sampler.run(qc_plus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram([job_1.result().quasi_dists[0], job_plus.result().quasi_dists[0]], legend=legend)"
   ]
  },
  {
   "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 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": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "qc2_1 = QuantumCircuit(1)\n",
    "qc2_1.x(0)\n",
    "\n",
    "qc2_plus = QuantumCircuit(1)\n",
    "qc2_plus.h(0)\n",
    "\n",
    "obsvs = list(SparsePauliOp(['Z', 'X']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "estimator = Estimator()\n",
    "job2_1 = estimator.run([qc2_1]*len(obsvs), observables=obsvs)\n",
    "job2_plus = estimator.run([qc2_plus]*len(obsvs), observables=obsvs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-1.,  0.]), metadata=[{}, {}])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job2_1.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    |   <Z>   |   <X> \n",
      "----|------------------\n",
      "|1> | -1.0    | 0.0\n",
      "|+> | 0.0 | 0.9999999999999998\n"
     ]
    }
   ],
   "source": [
    "# TODO: make this into module that outputs a nice table\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": {
    "tags": []
   },
   "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": [
    "Ex 1 - create an operator for CHSH witness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    " # create operator for chsh witness\n",
    "obsv =A = SparsePauliOp('IX')\n",
    "a = SparsePauliOp('IZ')\n",
    "B = SparsePauliOp('XI')\n",
    "b = SparsePauliOp('ZI')\n",
    "\n",
    "term1 = A @ B\n",
    "term2 = A @ b\n",
    "term3 = a @ B\n",
    "term4 = a @ b\n",
    "\n",
    "obsv = term1 - term2 + term3 + term4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex1\n",
    "\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": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import Parameter\n",
    "\n",
    "theta = Parameter('θ')\n",
    "\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0, 1)\n",
    "qc.ry(theta, 0)\n",
    "\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": [
    "Ex 2 - Create a Parameterization (i.e., list, array) of the angle in the above circuit (in radians)\n",
    "\n",
    "Hint: Note the `type` for the `parameter_values` argument is `Sequence[Sequence[float]]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# create a parameterization of angles that will violate the inequality\n",
    "\n",
    "angles = [[theta] for theta in np.linspace(0, 4*np.pi, 500)]"
   ]
  },
  {
   "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": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7c5b244eb0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "estimator = Estimator()\n",
    "job = estimator.run([qc]*len(angles), observables=[obsv]*len(angles), parameter_values=angles)\n",
    "exps = job.result().values\n",
    "\n",
    "plt.plot(angles, exps, marker='x', ls='-', color='green')\n",
    "plt.plot(angles, [2]*len(angles), ls='--', color='red', label='Classical Bound')\n",
    "plt.plot(angles, [-2]*len(angles), ls='--', color='red')\n",
    "plt.xlabel('angle (rad)')\n",
    "plt.ylabel('CHSH Witness')\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": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex2\n",
    "\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": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "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 state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 185.453x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = Parameter('θ')\n",
    "\n",
    "qr = QuantumRegister(1, 'q')\n",
    "qc = QuantumCircuit(qr)\n",
    "qc.ry(theta, 0)\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",
    "$$\n",
    "|\\Phi^+\\rangle = \\frac{1}{2} \\left( |00\\rangle + |11\\rangle \\right)\n",
    "$$\n",
    "with 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": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 239.337x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tele_qc = qc.copy()\n",
    "bell = QuantumRegister(2, 'Bell')\n",
    "alice = ClassicalRegister(2, 'Alice')\n",
    "bob = ClassicalRegister(1, 'Bob')\n",
    "tele_qc.add_register(bell, alice, bob)\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": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 573.781x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create Bell state with other two qubits\n",
    "tele_qc.barrier()\n",
    "tele_qc.h(1)\n",
    "tele_qc.cx(1, 2)\n",
    "tele_qc.barrier()\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": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 824.615x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# alice operates on her qubits\n",
    "tele_qc.cx(0, 1)\n",
    "tele_qc.h(0)\n",
    "tele_qc.barrier()\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": 27,
   "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\n",
      "text/plain": [
       "<Figure size 991.837x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tele_qc.measure([qr[0], bell[0]], alice)\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": [
    "Ex 3 - Add approriate conditional gates to transform Bob's qubit into the $Z$-basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1159.06x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graded_qc = tele_qc.copy()\n",
    "\n",
    "##############################\n",
    "# add gates to graded_qc here\n",
    "\n",
    "graded_qc.x(bell[1]).c_if(alice[1], 1)\n",
    "graded_qc.z(bell[1]).c_if(alice[0], 2)\n",
    "\n",
    "##############################\n",
    "\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": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1326.28x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graded_qc.barrier()\n",
    "graded_qc.measure(bell[1], bob)\n",
    "graded_qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex3\n",
    "\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": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Dists: {'0': 0.1728515625, '1': 0.8271484375}\n",
      "Teleported Dists: {'101': 0.1787109375, '001': 0.04296875, '010': 0.0556640625, '000': 0.0439453125, '110': 0.2158203125, '100': 0.2021484375, '011': 0.0439453125, '111': 0.216796875}\n"
     ]
    }
   ],
   "source": [
    "from qiskit_aer.primitives import Sampler\n",
    "\n",
    "angle = 5*np.pi/7\n",
    "\n",
    "sampler = Sampler()\n",
    "qc.measure_all()\n",
    "job_static = sampler.run(qc.bind_parameters({theta: angle}))\n",
    "job_dynamic = sampler.run(graded_qc.bind_parameters({theta: angle}))\n",
    "\n",
    "print(f\"Original Dists: {job_static.result().quasi_dists[0].binary_probabilities()}\")\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": [
    "Ex 4 - Marginalize the teleported counts\n",
    "\n",
    "Hint: Remember that bit strings are reported in the little-endian convention."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'101': 0.1787109375, '001': 0.04296875, '010': 0.0556640625, '000': 0.0439453125, '110': 0.2158203125, '100': 0.2021484375, '011': 0.0439453125, '111': 0.216796875}\n"
     ]
    }
   ],
   "source": [
    "from qiskit.result import marginal_counts\n",
    "\n",
    "# marginalize counts\n",
    "result_dynamic = job_dynamic.result().quasi_dists[0].binary_probabilities()\n",
    "print(result_dynamic)\n",
    "tele_counts = marginal_counts(result_dynamic, indices=[2]) # marginalize counts"
   ]
  },
  {
   "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": 33,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "legend = ['Original State', 'Teleported State']\n",
    "plot_histogram([job_static.result().quasi_dists[0].binary_probabilities(), tele_counts], legend=legend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "from qc_grader.challenges.qgss_2023 import grade_lab2_ex4\n",
    "\n",
    "grade_lab2_ex4(tele_counts, job_dynamic.result())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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