Challenge1_BasicQuantumCircuits.ipynb

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    "# Introduction to Qiskit\n",
    "Welcome to the Quantum Challenge! Here you will be using Qiskit, the open source quantum software development kit developed by IBM Quantum and community members around the globe. The following exercises will familiarize you with the basic elements of Qiskit and quantum circuits. \n",
    "\n",
    "To begin, let us define what a quantum circuit is:\n",
    "\n",
    "> **\"A quantum circuit is a computational routine consisting of coherent quantum operations on quantum data, such as qubits. It is an ordered sequence of quantum gates, measurements, and resets, which may be conditioned on real-time classical computation.\"** (https://qiskit.org/textbook/ch-algorithms/defining-quantum-circuits.html)\n",
    "\n",
    "While this might be clear to a quantum physicist, don't worry if it is not self-explanatory to you.  During this exercise you will learn what a qubit is, how to apply quantum gates to it, and how to measure its final state. You will then be able to create your own quantum circuits! By the end, you should be able to explain the fundamentals of quantum circuits to your colleagues.\n",
    "\n",
    "Before starting with the exercises, please run cell *Cell 1* below by clicking on it and pressing 'shift' + 'enter'. This is the general way to execute a code cell in the Jupyter notebook environment that you are using now. While it is running, you will see `In [*]:` in the top left of that cell. Once it finishes running, you will see a number instead of the star, which indicates how many cells you've run. You can find more information about Jupyter notebooks here: https://qiskit.org/textbook/ch-prerequisites/python-and-jupyter-notebooks.html.\n",
    "\n",
    "---\n",
    "For useful tips to complete this exercise as well as pointers for communicating with other participants and asking questions, please take a look at the following [repository](https://github.com/qiskit-community/may4_challenge_exercises). You will also find a copy of these exercises, so feel free to edit and experiment with these notebooks.\n",
    "\n",
    "---"
   ]
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   "source": [
    "# Cell 1\n",
    "import numpy as np\n",
    "\n",
    "from qiskit import Aer, QuantumCircuit, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "from IPython.display import display, Math, Latex\n",
    "\n",
    "from may4_challenge import plot_state_qsphere\n",
    "from may4_challenge.ex1 import minicomposer\n",
    "from may4_challenge.ex1 import check1, check2, check3, check4, check5, check6, check7, check8\n",
    "from may4_challenge.ex1 import return_state, vec_in_braket, statevec"
   ]
  },
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    "## Exercise I:  Basic Operations on Qubits and Measurements\n",
    "\n",
    "### Writing down single-qubit states\n",
    "Let us start by looking at a single qubit. The main difference between a classical bit, which can take the values 0 and 1 only, is that a quantum bit, or **qubit**, can be in the states $\\vert0\\rangle$, $\\vert1\\rangle$, as well as a linear combination of these two states. This feature is known as superposition, and allows us to write the most general state of a qubit as: \n",
    "\n",
    "$$\\vert\\psi\\rangle = \\sqrt{1-p}\\vert0\\rangle + e^{i \\phi} \\sqrt{p}  \\vert1\\rangle$$\n",
    "\n",
    "If we were to measure the state of this qubit, we would find the result $1$ with probability $p$, and the result $0$ with probability $1-p$. As you can see, the total probability is $1$, meaning that we will indeed measure either $0$ or $1$, and no other outcomes exists.\n",
    "\n",
    "In addition to $p$, you might have noticed another parameter above. The variable $\\phi$ indicates the relative quantum phase between the two states $\\vert0\\rangle$ and $\\vert1\\rangle$. As we will discover later, this relative phase is quite important. For now, it suffices to note that the quantum phase is what enables interference between quantum states, resulting in our ability to write quantum algorithms for solving specific tasks.\n",
    "\n",
    "If you are interested in learning more, we refer you to [the section in the Qiskit textbook on representations of single-qubit states](https://qiskit.org/textbook/ch-states/representing-qubit-states.html).\n",
    "\n",
    "### Visualizing quantum states\n",
    "We visualize quantum states throughout this exercise using what is known as a `qsphere`. Here is how the `qsphere` looks for the states $\\vert0\\rangle$ and $\\vert1\\rangle$, respectively. Note that the top-most part of the sphere represents the state $\\vert0\\rangle$, while the bottom represents $\\vert1\\rangle$.\n",
    "\n",
    "<img src=\"qsphere01.png\" alt=\"qsphere with states 0 and 1\" style=\"width: 400px;\"/>\n",
    "\n",
    "It should be no surprise that the superposition state with quantum phase $\\phi = 0$ and probability $p = 1/2$ (meaning an equal likelihood of measuring both 0 and 1) is shown on the `qsphere` with two points. However, note also that the size of the circles at the two points is smaller than when we had simply $\\vert0\\rangle$ and $\\vert1\\rangle$ above. This is because the size of the circles is proportional to the probability of measuring each one, which is now reduced by half.\n",
    "\n",
    "<img src=\"qsphereplus.png\" alt=\"qsphere with superposition 1\" style=\"width: 200px;\"/>\n",
    "\n",
    "In the case of superposition states, where the quantum phase is non-zero, the qsphere allows us to visualize that phase by changing the color of the respective blob. For example, the state with $\\phi = 90^\\circ$ (degrees) and probability $p = 1/2$ is shown in the `qsphere` below. \n",
    "\n",
    "<img src=\"qspherey.png\" alt=\"qsphere with superposition 2\" style=\"width: 200px;\"/>\n",
    "\n",
    "### Manipulating qubits\n",
    "Qubits are manipulated by applying quantum gates. Let's go through an overview of the different gates that we will consider in the following exercises.\n",
    "\n",
    "First, let's describe how we can change the value of $p$ for our general quantum state. To do this, we will use two gates:\n",
    "\n",
    "1. **$X$-gate**: This gate flips between the two states $\\vert0\\rangle$ and $\\vert1\\rangle$. This operation is the same as the classical NOT gate. As a result, the $X$-gate is sometimes referred to as a bit flip or NOT gate. Mathematically, the $X$ gate changes $p$ to $1-p$, so in particular from 0 to 1, and vice versa.\n",
    "\n",
    "2. **$H$-gate**: This gate allows us to go from the state $\\vert0\\rangle$  to the state $\\frac{1}{\\sqrt{2}}\\left(\\vert0\\rangle + \\vert1\\rangle\\right)$. This state is also known as the $\\vert+\\rangle$. Mathematically, this means going from $p=0, \\phi=0$ to  $p=1/2, \\phi=0$.  As the final state of the qubit is a superposition of $\\vert0\\rangle$ and $\\vert1\\rangle$, the Hadamard gate represents a true quantum operation.\n",
    "\n",
    "Notice that both gates changed the value of $p$, but not $\\phi$. Fortunately for us, it's quite easy to visualize the action of these gates by looking at the figure below.\n",
    "\n",
    "<img src=\"quantumgates.png\" alt=\"quantum gates\" style=\"width: 400px;\"/>\n",
    "\n",
    "Once we have the state $\\vert+\\rangle$, we can then change the quantum phase by applying several other gates. For example, an $S$ gate adds a phase of $90$ degrees to $\\phi$, while the $Z$ gate adds a phase of $180$ degrees to $\\phi$. To subtract a phase of $90$ degrees, we can apply the $S^\\dagger$ gate, which is read as S-dagger, and commonly written as `sdg`. Finally, there is a $Y$ gate which applies a sequence of $Z$ and $X$ gates.\n",
    "\n",
    "You can experiment with the gates $X$, $Y$, $Z$, $H$, $S$ and $S^\\dagger$ to become accustomed to the different operations and how they affect the state of a qubit. To do so, you can run *Cell 2* which starts our circuit widget. After running the cell, choose a gate to apply to a qubit, and then choose the qubit (in the first examples, the only qubit to choose is qubit 0).  Watch how the corresponding state changes with each gate, as well as the description of that state. It will also provide you with the code that creates the corresponding quantum circuit in Qiskit below the qsphere.\n",
    "\n",
    "If you want to learn more about describing quantum states, Pauli operators, and other single-qubit gates, see chapter 1 of our textbook: https://qiskit.org/textbook/ch-states/introduction.html."
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   "source": [
    "# Cell 2\n",
    "# press shift + return to run this code cell\n",
    "# then, click on the gate that you want to apply to your qubit\n",
    "# next, you have to choose the qubit that you want to apply it to (choose '0' here)\n",
    "# click on clear to restart\n",
    "minicomposer(1, dirac=True, qsphere=True)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Here are four small exercises to attain different states on the qsphere. You can either solve them with the widget above and copy paste the code it provides into the respective cells to create the quantum circuits, or you can directly insert a combination of the following code lines into the program to apply the different gates: \n",
    "\n",
    "    qc.x(0)    # bit flip\n",
    "    qc.y(0)    # bit and phase flip\n",
    "    qc.z(0)    # phase flip\n",
    "    qc.h(0)    # superpostion\n",
    "    qc.s(0)    # quantum phase rotation by pi/2 (90 degrees)\n",
    "    qc.sdg(0)  # quantum phase rotation by -pi/2 (90 degrees)\n",
    "    \n",
    "The '(0)' indicates that we apply this gate to qubit 'q0', which is the first (and in this case only) qubit.\n",
    "\n",
    "Try to attain the given state on the qsphere in each of the following exercises.\n",
    "### I.i) Let us start  by performing a bit flip. The goal is to reach the state $\\vert1\\rangle$ starting from state $\\vert0\\rangle$. <img src=\"state1.png\" width=\"300\"> \n",
    "\n",
    "\n",
    "If you have reached the desired state with the widget, copy and paste the code from *Cell 2* into *Cell 3* (where it says \"FILL YOUR CODE IN HERE\") and run it to check your solution."
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     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 1/8\n"
     ]
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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 3\n",
    "def create_circuit():\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.x(0)\n",
    "    return qc\n",
    "\n",
    "# check solution\n",
    "qc = create_circuit()\n",
    "state = statevec(qc)\n",
    "check1(state)\n",
    "plot_state_qsphere(state.data, show_state_labels=True, show_state_angles=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.ii) Next, let's create a superposition. The goal is to reach the state $|+\\rangle = \\frac{1}{\\sqrt{2}}\\left(|0\\rangle + |1\\rangle\\right)$. <img src=\"stateplus.png\" width=\"300\"> \n",
    "Fill in the code in the lines indicated in *Cell 4*. If you prefer the widget, you can still copy the code that the widget gives in *Cell 2* and paste it into *Cell 4*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 2/8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 4\n",
    "def create_circuit2():\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.h(0)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit2()\n",
    "state = statevec(qc)\n",
    "check2(state)\n",
    "plot_state_qsphere(state.data, show_state_labels=True, show_state_angles=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.iii) Let's combine those two. The goal is to reach the state $|-\\rangle = \\frac{1}{\\sqrt{2}}\\left(|0\\rangle - |1\\rangle\\right)$. <img src=\"stateminus.png\" width=\"300\"> \n",
    "Can you combine the above two tasks to come up with the solution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 3/8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 5\n",
    "def create_circuit3():\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.h(0)\n",
    "    qc.z(0)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit3()\n",
    "state = statevec(qc)\n",
    "check3(state)\n",
    "plot_state_qsphere(state.data, show_state_labels=True, show_state_angles=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.iv) Finally, we move on to the complex numbers. The goal is to reach the state $|\\circlearrowleft\\rangle = \\frac{1}{\\sqrt{2}}\\left(|0\\rangle - i|1\\rangle\\right)$. <img src=\"stateleft.png\" width=\"300\"> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 4/8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 6\n",
    "def create_circuit4():\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.h(0)\n",
    "    qc.sdg(0)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit4()\n",
    "state = statevec(qc)\n",
    "check4(state)\n",
    "plot_state_qsphere(state.data, show_state_labels=True, show_state_angles=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Exercise II: Quantum Circuits Using Multi-Qubit Gates\n",
    "\n",
    "Great job! Now that you've understood the single-qubit gates, let us look at gates operating on multiple qubits. The basic gates on two qubits are given by\n",
    "\n",
    "    qc.cx(c,t)       # controlled-X (= CNOT) gate with control qubit c and target qubit t\n",
    "    qc.cz(c,t)       # controlled-Z gate with control qubit c and target qubit t\n",
    "    qc.swap(a,b)     # SWAP gate that swaps the states of qubit a and qubit b\n",
    "\n",
    "If you'd like to read more about the different multi-qubit gates and their relations, visit chapter 2 of our textbook: https://qiskit.org/textbook/ch-gates/introduction.html.\n",
    "\n",
    "As before, you can use the two-qubit circuit widget below to see how the combined two qubit state evolves when applying different gates (run *Cell 7*) and get the corresponding code that you can copy and paste into the program. Note that for two qubits a general state is of the form $a|00\\rangle + b |01\\rangle + c |10\\rangle + d|11\\rangle$, where $a$, $b$, $c$, and $d$ are complex numbers whose absolute values squared give the probability to measure the respective state; e.g., $|a|^2$ would be the probability to end in state '0' on both qubits. This means we can now have up to four points on the qsphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d1a7e3dcb702431386d1c1053cb59ff9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Label(value='Select a gate to add to the circuit:')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e8fce37e86f84721b5c498790823f220",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HBox(children=(Button(description='I', style=ButtonStyle()), Button(description='X', style=Butt…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7d85f65be5084e11a02ef27cf1c8fb7f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HTML(value='<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\\n<!DOCTYPE svg PUBLIC \"-//W3…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "657cc7ee86824f9c88c4146242836b6b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HTML(value='')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cell 7\n",
    "# press shift + return to run this code cell\n",
    "# then, click on the gate that you want to apply followed by the qubit(s) that you want it to apply to\n",
    "# for controlled gates, the first qubit you choose is the control qubit and the second one the target qubit\n",
    "# click on clear to restart\n",
    "\n",
    "minicomposer(2, dirac = True, qsphere = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with the canonical two qubit gate, the controlled-NOT (also CNOT or CX) gate.  Here, as with all controlled two qubit gates, one qubit is labelled as the \"control\", while the other is called the \"target\". If the control qubit is in state $|0\\rangle$, it applies the identity $I$ gate to the target, i.e., no operation is performed. Instead, if the control qubit is in state $|1\\rangle$, an X-gate is performed on the target qubit. Therefore, with both qubits in one of the two classical states, $|0\\rangle$ or $|1\\rangle$, the CNOT gate is limited to classical operations.\n",
    "\n",
    "This situation changes dramatically when we first apply a Hadamard gate to the control qubit, bringing it into the superposition state $|+\\rangle$.  The action of a CNOT gate on this non-classical input can produce highly entangled states between control and target qubits. If the target qubit is initially in the $|0\\rangle$ state, the resulting state is denoted by $|\\Phi^+\\rangle$, and is one of the so-called Bell states. \n",
    "\n",
    "### II.i) Construct the Bell state $|\\Phi^+\\rangle = \\frac{1}{\\sqrt{2}}\\left(|00\\rangle + |11\\rangle\\right)$.  <img src=\"phi+.png\" width=\"300\"> \n",
    "For this state we would have probability $\\frac{1}{2}$ to measure \"00\" and probability $\\frac{1}{2}$ to measure \"11\". Thus, the outcomes of both qubits are perfectly correlated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (0.707+0i)|00\\rangle + (0.707+0i)|11\\rangle$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 5/8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 298.592x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 8\n",
    "def create_circuit():\n",
    "    qc = QuantumCircuit(2)\n",
    "    qc.h(0)\n",
    "    qc.cnot(0,1)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit()\n",
    "state = statevec(qc) # determine final state after running the circuit\n",
    "display(Math(vec_in_braket(state.data)))\n",
    "check5(state)\n",
    "qc.draw(output='mpl') # we draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, try to create the state of perfectly anti-correlated qubits. Note the minus sign here, which indicates the relative phase between the two states. \n",
    "### II.ii) Construct the Bell state $\\vert\\Psi^-\\rangle = \\frac{1}{\\sqrt{2}}\\left(\\vert01\\rangle - \\vert10\\rangle\\right)$. <img src=\"psi-.png\" width=\"300\"> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (-0.707+0i)|01\\rangle + (0.707+0i)|10\\rangle$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 6/8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 9\n",
    "def create_circuit6():\n",
    "    qc = QuantumCircuit(2,2) # this time, we not only want two qubits, but also \n",
    "                             # two classical bits for the measurement later\n",
    "    qc.x(0)\n",
    "    qc.x(1)\n",
    "    qc.h(0)\n",
    "    qc.cnot(0,1)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit6()\n",
    "state = statevec(qc) # determine final state after running the circuit\n",
    "display(Math(vec_in_braket(state.data)))\n",
    "check6(state)\n",
    "qc.measure(0, 0) # we perform a measurement on qubit q_0 and store the information on the classical bit c_0\n",
    "qc.measure(1, 1) # we perform a measurement on qubit q_1 and store the information on the classical bit c_1\n",
    "qc.draw(output='mpl') # we draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can tell from the circuit (and the code) we have added measurement operators to the circuit. Note that in order to store the measurement results, we also need two classical bits, which we have added when creating the quantum circuit: `qc = QuantumCircuit(num_qubits, num_classicalbits)`.\n",
    "\n",
    "In *Cell 10* we have defined a function `run_circuit()` that will run a circuit on the simulator. If the right state is prepared, we have probability $\\frac{1}{2}$ to measure each of the two outcomes, \"01\" and \"10\". However, performing the measurement with 1000 shots does not imply that we will measure exactly 500 times \"01\" and 500 times \"10\".  Just like flipping a coin multiple times, it is unlikely that one will get exactly a 50/50 split between the two possible output values.  Instead, there are fluctuations about this ideal distribution. You can call `run_circuit` multiple times to see the variance in the ouput.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'01': 490, '10': 510}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 10\n",
    "def run_circuit(qc):\n",
    "    backend = Aer.get_backend('qasm_simulator') # we choose the simulator as our backend\n",
    "    result = execute(qc, backend, shots = 1000).result() # we run the simulation\n",
    "    counts = result.get_counts() # we get the counts\n",
    "    return counts\n",
    "\n",
    "counts = run_circuit(qc)\n",
    "print(counts)\n",
    "plot_histogram(counts) # let us plot a histogram to see the possible outcomes and corresponding probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.iii) You are given the quantum circuit described in the function below. Swap the states of the first and the second qubit.  \n",
    "This should be your final state: <img src=\"stateIIiii.png\" width=\"300\"> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (0.866+0i)|01\\rangle + -0.5i|11\\rangle$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct 🎉! Well done!\n",
      "Your progress: 7/8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 11\n",
    "def create_circuit7():\n",
    "    qc = QuantumCircuit(2)\n",
    "    qc.rx(np.pi/3,0)\n",
    "    qc.x(1)\n",
    "    return qc\n",
    "\n",
    "qc = create_circuit7()\n",
    "qc.cnot(0,1)\n",
    "qc.cnot(1,0)\n",
    "qc.cnot(0,1)\n",
    "state = statevec(qc) # determine final state after running the circuit\n",
    "display(Math(vec_in_braket(state.data)))\n",
    "check7(state)\n",
    "plot_state_qsphere(state.data, show_state_labels=True, show_state_angles=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.iv) Write a program from scratch that creates the GHZ state (on three qubits), $\\vert \\text{GHZ}\\rangle = \\frac{1}{\\sqrt{2}} \\left(|000\\rangle + |111 \\rangle \\right)$, performs a measurement with 2000 shots, and returns the counts.  <img src=\"ghz.png\" width=\"300\"> \n",
    "If you want to track the state as it is evolving, you could use the circuit widget from above for three qubits, i.e., `minicomposer(3, dirac=True, qsphere=True)`. For how to get the counts of a measurement, look at the code in *Cell 9* and *Cell 10*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'000': 1008, '111': 992}\n",
      "Correct 🎉! Well done!\n",
      "Your progress: 8/8\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <p style=\"border: 2px solid black; padding: 2rem;\">\n",
       "        Congratulations 🎉! Submit the following text\n",
       "        <samp\n",
       "            style=\"font-family: monospace; background-color: #eee;\"\n",
       "        >[104, 52, 100, 97, 109, 65, 114, 100]</samp>\n",
       "        on the\n",
       "        <a href=\"https://quantum-computing.ibm.com/challenges/4anniversary/?exercise=1&amp;answer=%5B104%2C+52%2C+100%2C+97%2C+109%2C+65%2C+114%2C+100%5D\" target=\"_blank\">\n",
       "            IBM Quantum Challenge page\n",
       "        </a>\n",
       "        to see if you are correct.\n",
       "    </p>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc=QuantumCircuit(3,3)\n",
    "qc.h(0)\n",
    "qc.cnot(0,1)\n",
    "qc.toffoli(0,1,2)\n",
    "qc.measure(0,0)\n",
    "qc.measure(1,1)\n",
    "qc.measure(2,2)\n",
    "backend = Aer.get_backend('qasm_simulator') # we choose the simulator as our backend\n",
    "result = execute(qc, backend, shots = 2000).result() # we run the simulation\n",
    "counts = result.get_counts() # we get the counts\n",
    "qc.draw()\n",
    "print(counts)\n",
    "check8(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations for finishing this introduction to Qiskit! Once you've reached all 8 points, the solution string will be displayed. You need to copy and paste that string on the IBM Quantum Challenge page to complete the exercise and track your progress.\n",
    "\n",
    "Now that you have created and run your first quantum circuits, you are ready for the next exercise, where we will make use of the actual hardware and learn how to reduce the noise in the outputs."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}