exercises/week-1/ex_1a_en.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prologue - Your first day at the lab\n",
    "\n",
    "*You just started your graduate studies with Dr. Ryoko as your advisor.<br/>\n",
    "On your first day, you arrive at the lab only to find no one there.*\n",
    "\n",
    "\n",
    "*You decide to look around while waiting for your advisor to arrive. <br/>\n",
    "Suddenly, one of the monitors nearby lights up and startles you.*<br/> \n",
    "\n",
    "*There in the monitor, looking straight at you was Dr. Ryoko,* <br/> \n",
    "*wearing her signature traditional Japanese outfit.*\n",
    "\n",
    "\n",
    "*Dr. Ryoko greets you and tells you that she is visiting another lab.* <br/> \n",
    "*She tells you that she is in the middle of an important experiment,*<br/> \n",
    "*and won't be back for another few weeks.*<br/> \n",
    "\n",
    "*She asks you to work on these exercises until she returns...*\n",
    "\n",
    "[<< Click here to communicate with Dr. Ryoko through the web cam >>](https://youtu.be/eLw7fWb2xv4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week1-A: Adder in Quantum Circuits\n",
    "\n",
    "Hi! Welcome to our lab. This week, we will start by learning how to perform simple additions using quantum circuits.<br/>\n",
    "\n",
    "Just like in classical computation, where you can combine different logical gates (e.g., AND, OR, XOR, etc.) to create binary adders, you can make adders with quantum circuits as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before starting the exercises, run the first cell below by clicking on it and then pressing 'shift' + 'enter'. This is the general way to execute a code cell in a 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda3/envs/qiskit023_2/lib/python3.7/site-packages/qiskit/providers/ibmq/ibmqfactory.py:192: UserWarning: Timestamps in IBMQ backend properties, jobs, and job results are all now in local time instead of UTC.\n",
      "  warnings.warn('Timestamps in IBMQ backend properties, jobs, and job results '\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing standard Qiskit libraries and configuring account\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit import IBMQ, Aer, execute\n",
    "from qiskit.visualization import plot_bloch_multivector\n",
    "\n",
    "# If you run this code outside IBM Quantum Experience,\n",
    "# run the following commands to store your API token locally.\n",
    "# Please refer https://qiskit.org/documentation/install.html#access-ibm-quantum-systems\n",
    "# IBMQ.save_account('MY_API_TOKEN')\n",
    "\n",
    "# Loading your IBM Q account(s)\n",
    "IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What are quantum circuits?\n",
    "Quantum circuits are models for quantum computation in which a computation is a sequence of quantum gates. Let's take a look at some of the popular quantum gates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### X Gate\n",
    "An X gate equates to a rotation around the X-axis of the Bloch sphere by $\\pi$ radians.\n",
    "It maps $|0\\rangle$ to $|1\\rangle$ and $|1\\rangle$ to $|0\\rangle$. It is the quantum equivalent of the NOT gate for classical computers and is sometimes called a bit-flip. If you are not familiar with linear algebra, you can learn it here: https://qiskit.org/textbook/ch-appendix/linear_algebra.html.\n",
    "\n",
    "$X = \\begin{pmatrix}\n",
    "0 & 1 \\\\\n",
    "1 & 0 \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.507x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an X-gate on a |0> qubit\n",
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.x(q[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: There is a new syntax that omits `Quantum Register` , but in this challenge, we will use the above syntax because it is easier to understand the algorithms of complex quantum circuits. (You can see the new notation [here](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.html?highlight=quantumcircuit#qiskit.circuit.QuantumCircuit).）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(qc, backend).result().get_statevector(qc, decimals=3)\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### H Gate\n",
    "A Hadamard gate represents a rotation of $\\pi$ about the axis that is in the middle of the $X$-axis and $Z$-axis.\n",
    "It maps the basis state $|0\\rangle$ to $\\frac{|0\\rangle + |1\\rangle}{\\sqrt{2}}$, which means that a measurement will have equal probabilities of being `1` or `0`, creating a 'superposition' of states. This state is also written as $|+\\rangle$.\n",
    "\n",
    "$H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}\n",
    "1 & 1 \\\\\n",
    "1 & -1 \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.797x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an H-gate on a |0> qubit\n",
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.h(q[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(qc, backend).result().get_statevector(qc, decimals=3)\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Z Gate\n",
    "The Z gate represents a rotation around the Z-axis of the Bloch sphere by $\\pi$ radians. It is sometimes called a 'phase shift gate'.\n",
    "\n",
    "$Z = \\begin{pmatrix}\n",
    "1 & 0 \\\\\n",
    "0 & -1 \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.997x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an Z-gate on |+>\n",
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.h(q[0])\n",
    "qc.z(q[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(qc, backend).result().get_statevector(qc, decimals=3)\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CX Gate (CNOT Gate)\n",
    "The controlled NOT (or CNOT or CX) gate acts on two qubits. It performs the NOT operation (equivalent to applying an X gate) on the second qubit only when the first qubit is $|1\\rangle$ and otherwise leaves it unchanged. Note: Qiskit numbers the bits in a string from right to left.\n",
    "\n",
    "$CX = \\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 159.923x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an CX-gate on |00>\n",
    "q = QuantumRegister(2)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.cx(q[0],q[1])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CZ Gate\n",
    "The CZ gate acts on two qubits, called a 'control bit' and a 'target bit'. It flips the sign (equivalent to applying the phase shift Z gate) of the target qubit if and only if the control qubit is $|1\\rangle$.\n",
    "\n",
    "$CZ = \\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & -1\\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 159.778x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an CZ-gate on |00>\n",
    "q = QuantumRegister(2)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.cz(q[0],q[1])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: A CZ gate can also be constructed from a CX gate and an H gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 280.323x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's make CZ-gate with CX-gate and H-gate\n",
    "q = QuantumRegister(2)\n",
    "qc = QuantumCircuit(q)\n",
    "\n",
    "qc.h(q[1])\n",
    "qc.cx(q[0],q[1])\n",
    "qc.h(q[1])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CCX Gate\n",
    "The CCX gate is also called a Toffoli gate.\n",
    "The CCX gate is a three-bit gate, with two controls and one target as their input and output. If the first two bits are in the state $|1\\rangle$, it applies a Pauli-X (or NOT) on the third bit. Otherwise, it does nothing. Note: Qiskit numbers the bits in a string from right to left.\n",
    "\n",
    "$CCX = \\begin{pmatrix}\n",
    "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 172.904x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an CCX-gate on |000>\n",
    "q = QuantumRegister(3)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.ccx(q[0],q[1],q[2])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To learn about other quantum gates, refer to [Single Qubit Gates](https://qiskit.org/textbook/ch-states/single-qubit-gates.html) in the Qiskit Textbook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating logical gates with quantum gates\n",
    "Now let's start creating a classic logic gate using quantum gates.\n",
    "Each gate and their truth tables will be shown. Here we denote quantum registers as 'q' and classical registers as 'c' where we encode the output of the measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NOT Gate\n",
    "As was mentioned before, an X gate can be considered a NOT gate. The truth table for a NOT gate looks like this:\n",
    "\n",
    "\n",
    "|input|output|\n",
    "|--|--|\n",
    "|0|1|\n",
    "|1|0|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 219.978x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a Quantum Circuit with 1 quantum register and 1 classical register\n",
    "q = QuantumRegister(1)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "qc.x(q[0])\n",
    "qc.measure(q[0], c[0])    # Map the quantum measurement to the classical bits\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AND Gate\n",
    "The truth table for an AND Gate looks like this:\n",
    "\n",
    "|A (input)|B (input)|output|\n",
    "|--|--|--|\n",
    "|0|0|0|\n",
    "|0|1|0|\n",
    "|1|0|0|\n",
    "|1|1|1|\n",
    "\n",
    "With a CCX gate, the result of an AND gate for two control bits will be output to its target bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 233.395x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.measure(q[2], c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NAND Gate\n",
    "A NAND gate can be made by applying a NOT gate after applying an AND gate.\n",
    "\n",
    "|A(input)|B(input)|output|\n",
    "|--|--|--|\n",
    "|0|0|1|\n",
    "|0|1|1|\n",
    "|1|0|1|\n",
    "|1|1|0|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 293.595x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.x(q[2])\n",
    "qc.measure(q[2], c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OR Gate\n",
    "\n",
    "|A(input)|B(input)|output|\n",
    "|--|--|--|\n",
    "|0|0|0|\n",
    "|0|1|1|\n",
    "|1|0|1|\n",
    "|1|1|1|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 353.795x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "\n",
    "qc.cx(q[1], q[2])\n",
    "qc.cx(q[0], q[2])\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.measure(q[2], c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### XOR Gate\n",
    "|A(input)|B(input)|output|\n",
    "|--|--|--|\n",
    "|0|0|0|\n",
    "|0|1|1|\n",
    "|1|0|1|\n",
    "|1|1|0|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOwAAADWCAYAAADSMm7fAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAAYPUlEQVR4nO3df1TUdb7H8eeMoIAaIJi/UBRQUgLEyXXC4ke5Kbfa9ZiSuNdraSs3K9NyzUOnXLUlMm7aOa633X5czt4t9Uhulgt2yYTVcjHStNHYAQ1xkih/FKAIysz9Y47oyG/8zo8Pvh/nzHH4fr/z+b4H5zWfz/cz3+Grs9lsNoQQStC7uwAhROdJYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIUoHViLxcLixYuJj4/Hz88PnU6HyWRqsV1hYSE6na7V28WLF91QuRDd4+XuAm5EeXk5W7ZswWAwkJiYyM6dO9vdPjs7m8mTJzss69OnjzNLFIDNBjqdu6voGZQObEJCAtXV1QDk5OR0GNjIyEiMRqMrSrvp/VgDRf+CL7+F+ktwiy8Yw+HuMdDf193Vqctjh8RWq5Xs7GxGjx6Nj48PsbGxFBUVERkZycKFCwHQ6z22/Jua+XtYmwefme1hBaiph/8z2Zf/UOPe+lTmsa/4BQsWsGbNGtLT08nPzyc1NZW0tDSOHz+OwWDoVpvz58/Hy8uLwMBAZsyYQWlpqcZViwsN8HYRXG4CWyvr6y7CW0VgbW2l6JBHDok3bdpETk4OhYWFJCYmApCcnMyBAwfYtm0bEyZM6FJ7/v7+LF26lKSkJAICAjCZTGRmZmI0GikpKSEiIsIZT+OmtP84NFxue70New9b9j1EDnFZWT2GRwY2MzOTadOmNYf1ioiICLy9vYmJielSe3FxccTFxTX/nJCQwNSpU4mOjiYzM5N33nmneV1FRQXz5s2jqqqKPn36sHHjRu6+++4O96GTWRUApi/fyfDbp6DX92pzG5vVym+XrWPPe8tcWJnnstk6P9zwuCGxxWLBZDIxa9asFusqKyuJiorSZGY3PDwco9FIcXGxw/L09HQefvhhzGYzf/rTn5g9ezaNjY03vL+bhd6rNzpd+y8rG1b0Xr1dVFHP4pGBBRg8eLDD8vr6eoqKiro8HG6PzWZz6BlPnz7N3r17WbBgAQDx8fEMHTqU3bt3d6otudlIm56MvoPRhl7vxR+ef8rttXrKrSs8LrDBwcEAmM1mh+Vr166lqqqq2xNO1ysrK6O4uJhJkyY1L6usrGTQoEEOPfioUaM4ceKEJvu8GcRHtD7ZdC3vXmAY5ZJyehyPO4YNCwsjJiaGzMxMBgwYwLBhw8jNzSUvLw+gRWBzc3MBKCkpAaCgoIDS0lL69u1LSkoKAHPmzGHkyJEYDAYCAwMxmUxkZWXh6+tLRkaGC59dzzc0EJLHwu5v2t7moYng4+26mnoSna2rfbILmM1m0tPT2b9/P0FBQcybN4/+/fuTkZFBbW0tvr5XP3lva7InNDSUiooKALKysti8eTMVFRWcP3+egQMHMmXKFFauXEl4eHjzY06fPk1oaChnz55t7mUnTpzISy+9xNSpU533hHsYmw0KS+GTI3C+4eryoH7wwHiIC3VbacrzyMC2Zu7cuRw6dIjDhw87dT/33Xcf06dPZ9GiRXz++efMnDmTiooKeveWSZKuutwEyzbb7z/1Sxg1EPQymX5DPG5I3JaSkhKXnFb4xhtv8Mgjj7B+/Xp69+7Npk2bJKzd5HXNJzvht7qvjp5EicDW1dVhNptZtGiR0/cVFhbGP/7xD6fvR4juUCKw/fr1o6mpyd1lCOF2HvexjhCibRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRQigRVCIRJYIRSidGAtFguLFy8mPj4ePz8/dDodJpOpxXaFhYXodLpWbxcvXnRD5UJ0jxLXh21LeXk5W7ZswWAwkJiYyM6dO9vdPjs7m8mTJzss69OnjzNL1ESTFY58BydOg04HYQPhtqGg17m7MuFqSgc2ISGB6upqAHJycjoMbGRkJEaj0RWlaaa8Gv7yGdTUOy4f0BceuRtGBLmnLuEeHjsktlqtZGdnM3r0aHx8fIiNjaWoqIjIyEgWLlwIgF7vseVr4uQZeONTqK1vue7cefjjJ1Bd4/q6hPt47Ct+wYIFrFmzhvT0dPLz80lNTSUtLY3jx49jMBi61eb8+fPx8vIiMDCQGTNmUFpaqnHV2so/bB8O21pZZwMaL8MnLQ/ZRQ/mkUPiTZs2kZOTQ2FhIYmJiQAkJydz4MABtm3bxoQJE7rUnr+/P0uXLiUpKYmAgABMJhOZmZkYjUZKSkqIiIhwxtO4IT/Xw9FT7W9jAw6cgJkToY+3S8oSbuaRPWxmZibTpk1rDusVEREReHt7ExMT06X24uLieO211/jVr35FQkICixYtoqioiMbGRjIzMx22ffHFFxkzZgx6vZ7c3NxO76OtWeju3sZE3dGp/TZZ4dZhYZrvX6ubs34/PenWFR4XWIvFgslkYtasWS3WVVZWEhUVpcnMbnh4OEajkeLiYofl06ZNY+fOnSQkJNzwPm5E44WfO79tvRzI3iw8bkhssVgAGDx4sMPy+vp6ioqKSElJ0WxfNputxTtcfHx8t9vSks0Ga/Pg+59aP4YF+0c8EbdCfe1pTfetpSXv2v/V+vdzs/K4HjY4OBgAs9nssHzt2rVUVVV1e8LpemVlZRQXFzNp0iRN2tOaTgf33d52WMEe6nujXFaS8AAe18OGhYURExNDZmYmAwYMYNiwYeTm5pKXlwfQIrBXjjNLSkoAKCgooLS0lL59+zb3xnPmzGHkyJEYDAYCAwMxmUxkZWXh6+tLRkaGC59d18SF2j+++fBgy3U6YNYv4LYhLi9LuJHO5oFjFbPZTHp6Ovv37ycoKIh58+bRv39/MjIyqK2txdfXt3nbtg7aQ0NDqaioACArK4vNmzdTUVHB+fPnGThwIFOmTGHlypWEh4e3+vikpCSefPJJZs6cqfnz66rvf4bPymDPv+w/J4+FyaMhuL976+qMK0Pi9b9xbx09hcf1sABjxoxh9+7dDsvmzp3LuHHjHMIKnTs2WrFiBStWrNC0Rlca7A8P3XE1sL/u2qdaogfxuGPYtpSUlGh2/NqeF154gZCQEPbt20d6ejohISEcO3bM6fsVojOUCGxdXR1ms7nLJ0x0x5o1a7BYLDQ0NHDmzBksFkubw2YhXM0jh8TX69evH01NTe4uQwi3U6KHFULYSWCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgEVgiFSGCFUIgSf4RNiO5YsmQJX331lVv2PX78eNavX695uxJY0WN99dVXFBUVubsMTcmQWAiFSGCFUIgEVgFWq/2CWFf8WANWj7uEWUvnG67eP3EaGi65r5aeQo5hPVSTFY58B5+XwfEfofHy1XV/+Ah8vCFiEMRHwG1DQd/6Rfxc7nSt/Up7hyrh7Pmry9d9bL9E5iB/MIwEYwT093FXleqSwHqgitPw3j74oabtbS5eApPFfgsJhDl3wtBA19V4vYbLsOMr2Puvti9CbcM+Uvj7Ifj4a/i3WEi6DfQyzus0+VV5mE+Pwusftx/W61nOwX/lw75y59XVnh9r4dU8++UwOztSv2y1X6h6wydwoaHj7YWdBNaDfHLE/iLuzuFpkw22FNuH0K50pg42FNiHwt1x/Ef470/tIwZV+fv7u2xfSgfWYrGwePFi4uPj8fPzQ6fTYTKZWmxXWFiITqdr9Xbx4kU3VN5SWbV9SNme9b/p+ErmuV+A5axmZbXLaoW/7IWf69vepjM1nzwL20q0ra2rvL29mT59OtnZ2ezatYtDhw5x8OBBPvzwQ1588UWMRmOrj3vllVfYv38/Q4cOdUmdSh/DlpeXs2XLFgwGA4mJiezcubPd7bOzs5k8ebLDsj59+jizxE5pvAyb/6lNW1ab/fj32RTo5eS346J/wYkz2rS1/zjEhcJY17zum3l7e7Ns2TKeeuophgwZ0mL9+PHjefDBB1m1ahUHDx5k9erVfPDBB4A9rMuXL+fSpUvExMRw6tQpp9erdGATEhKorq4GICcnp8PARkZGtvlO6U4HT9iHllo59RN8cwpuD9GuzetdboJdR7Vt85Mjrg1sVFQU7777LrGxsQCYTCa2bt1KSUkJFouFXr16MWbMGO68807mzJlDXFwcf/vb39i8eTPV1dU8/fTTXLp0iVmzZnX42tOKxw6JrVYr2dnZjB49Gh8fH2JjYykqKiIyMpKFCxcCoO8h04ufOeG4c69Z+zavdfgk1Gl8NHHsB6j6Sds22zJx4kT27t1LbGwsx44d47777iM6OprVq1eTl5fH4cOHOXjwIFu2bGHJkiWEhITw1FNPUVdXx+zZsx3Cun37dtcUjQcHdsGCBaxZs4b09HTy8/NJTU0lLS2N48ePYzAYutXm/Pnz8fLyIjAwkBkzZlBaWqpx1V1X3wiVGg0rr1X+g/2zXGcpq3ZOu+bvndPutUJCQti5cycBAQG8//77xMTEUFBQ0O5jGhsb2bBhA++9917zMrPZzEcffeTsch145JB406ZN5OTkUFhYSGJiIgDJyckcOHCAbdu2MWHChC615+/vz9KlS0lKSiIgIACTyURmZiZGo5GSkhIiIiKc8TQ6xVkTRJeboPpn5302e9JJdTur3Wu9+eabDBgwgPz8fGbPns3ly5c7fhD2Y9aFCxdy6dIlampqiIqKYsmSJbz22mtOrvgqnc1m87iT3KKjowkJCSE/P99h+XPPPce6deuora1tMVmUk5PDo48+ytdff83tt9/e4T6OHTtGdHQ0s2fP5p133gHg3LlzzJ07F7PZjK+vL4MGDWLjxo2dCrRO171TjSIn/4Zpj//VYVlHs6ptWfKu488frE3hxGHnHFv99o/f4+c/yGFZd+q+vuaTR3ax7eUpN1BZ++6//3527NjB2bNnGTduXPMcSEeunWCaNWsWjY2N5OXlceHCBUJCQjh37ly3a+pKBD1uSGyxWDCZTMyaNavFusrKSqKiojSZ2Q0PD8doNFJcXNy8TKfTsWTJEsxmM4cOHeKBBx7g0UcfveF9tUeH884p7O6bSCdbV6xduyeeeAKAl19+udth3b59O/n5+Xz88cf4+fnxyCOPOLFiRx43JLZYLAAMHjzYYXl9fT1FRUWkpKRoti+bzebwog4ICGDKlKvv7vHx8axdu7bTbXXHN6fgT7sdl13f61xxpQdra/31inblMSKoW2V1KGuH4xcSoPW6ulrzgyn38H6mNoO+pKQkh+/DBgYGkpKSQkNDQ/OoqiOthfWKN954g6lTp5KWlsa6descHpeYmEhhYaEmz+NaHtfDBgcHA/YD+mutXbuWqqqqbk84Xa+srIzi4mImTZrU5jbr169n+vTpmuyvLSEDnNOuXgdDApzTNjiv7uFOahdonvs4cOAAZ892fLDcXlgBdu3aBUBMTAze3t7aF9wKj+thw8LCiImJITMzkwEDBjBs2DByc3PJy8sDaBHY3NxcAEpK7KfKFBQUUFpaSt++fZt74zlz5jBy5EgMBgOBgYGYTCaysrLw9fUlIyOj1TpWrVpFeXk5n376qbOeKmD/xsqtt3Tt3OHOGBEE3r20bfNa4bdCybfatxt2q/ZtXhEVFQXAoUOHOty2o7AC1NbWUl5eTkREBBEREXzzzTea13w9jwusXq9n69atpKen8/jjjxMUFMS8efN44oknyMjIICYmxmH76491n3nmGQBCQ0OpqKgA7O+AmzdvZuPGjZw/f56BAwcyZcoUVq5cSXh4eIsaXnrpJXbs2EFBQQF+fn7OeaLXuDMCth/Qts340dq2d724UPjgS/u3dLQyJABGBmvX3vW++OILVq9ezT//2f5pZQ888ECHYb3i9ddfJygo6IYmnbrC4wILMGbMGHbvdjywmzt3LuPGjcPX19dheWeOHVesWMGKFSs6te9Vq1aRl5dHQUEBAQEBna75RkwKgwITXGjUpr0APxg/Qpu22uLjbX9T2K1hp5I8Fpw5T7Zv3z727dvX4XY7duzg1Vdf5bPPPuvwpIgNGzZoVV6neGRgW1NSUuL00wqPHDnC73//e8LDw0lKSmpe7uy/vOfXBx6aCP/7mTbtPTwJervgf3ZaDHx9Ek5rcFpl5BCYOOrG29HK8uXL3V1Cq5QIbF1dHWazmUWLFjl1P1FRUd2e7b1RE0Kh7Hv457G2t+nMTOs941x3Pm4fL/iPu+zfaW1sY2jcmZoD/CDN6NzetadQIrD9+vWjqanJ3WU4lU4Hqb+w328vtO1Jug0eHK9ZSZ0yIgj+Mxn+XNi977QG9YPH77GHVnTM4z7WuZnp9fbh7L/Hg2/vzj+uvw/MT4DpBvf0UmG3wnP324e1XWEMh2UpENzfOXX1REr0sDcTnQ7uGAW3DbH3tJ+XOf4xs2sN7A+Tx8AvwsCvCwF3hsC+9p62tMr+TaGjp6C1owuvXvYZ5rvH4LSTOnoyCayH6ucDU6Lg3nHw0wX7SfG19fZA3+JrP8HA38OGkTqd/fh57FD7xz2nzkF1jf2LCL29YGgADPa3h1Z0jwTWw+l09t4rsK+7K+maPl4waqD9JrQjx7BCKEQCK4RCZEgseqzx48d3+THHK6sACBsxxOG+K/bdGR75BXYh3GXFK38GIOu5hQ73PYUMiYVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIVQiARWCIVIYIXQUGFhIVFRUURERPDYY49p/ud5JbBCaMRqtfLYY4+xdetWysvLqamp4a9//WvHD+wCCawQGvniiy8YOnQo48aNA2DBggW8//77mu5DAiuERiwWC8OHD2/+ecSIEZw8eVLTfcjfdBI3NZvNRm5+Eaeqzzgsf/1/3m/1vjFuHJPGj22zLWeTHlbc1HQ6HQkTY/jxzE9U/XA1tNffr/rhDE1NVibc3vaFd4cPH+7Qo1ZWVhISEqJpvRJYcdMbNHAAUxMntruNXq/j4QeT8fZqe1B6xx13YLFYOHr0KABvv/02M2bM0LRWCWwr7r33XnQ6HcuWLXN3KcJFJt8RTdiItq/T+cu77mDYoPYvD9+rVy/eeustZs6cSXh4OP369WPu3Lma1inHsNd5++23+eYbDS8rLpSg1+lIvT+JdW9vpaHR8bqZI4YOImFSbKfaueeee5p7WGeQHvYa1dXV/O53v2P9+vXuLkW4QcAt/fj1Lyc7LOvt7UXqA0n00ntGVDyjChf4+uuveeihhwgODsbHx4fRo0fz/PPPO2zz5JNPYjQaSU1NdVOVwt3iokYTHTmq+ef777mT4EB/N1bk6KYYEn/55ZckJCQwfPhwXn31VUJDQ/n222/5/PPPm7fZvn07eXl5HDlyxI2VCnfT6XRMn3o3FZbvGTZ4IL+Ivc3dJTm4KS7VkZSUxNGjRykrK8Pfv+W7ZU1NDWPHjuXpp59m+fLlgP0/7tlnnyU7O7tT+7hyWQchuqorlwLp8UPiCxcusGfPHtLS0loNK8Dy5csJDg7mmWeecXF1QnRNjx8Snzt3DqvV2uYH2Pv37+fNN9/k73//O3V1dQ7rGhoa+Omnn+jfvz+9erV/2XBPumCS6Ll6fGADAwPR6/V89913ra4/evQoVquVlJSUFus2bNjAhg0b2LNnD3fddVe7+5EhseiurrzZ9/jA+vn5kZCQwKZNm1i9ejW33HKLw/pp06axe/fuFo9LTk4mNTWVxx9/nOjoaFeVK0S7bopJpyuzxKGhoSxfvpzQ0FAqKyvZs2cPb731VquP6eqkkxCu0ON7WACDwcC+fft44YUXWLp0KRcvXmT48OHMnj3b3aUJ0SU3RQ8rRE/R4z/WEaInkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAKkcAKoRAJrBAK+X9MOqoFteVNnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 293.595x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "qc.cx(q[1], q[2])\n",
    "qc.cx(q[0], q[2])\n",
    "qc.measure(q[2], c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NOR Gate\n",
    "\n",
    "|A(input)|B(input)|output|\n",
    "|--|--|--|\n",
    "|0|0|1|\n",
    "|0|1|0|\n",
    "|1|0|0|\n",
    "|1|1|0|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 413.849x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3)\n",
    "c = ClassicalRegister(1)\n",
    "qc = QuantumCircuit(q,c)\n",
    "\n",
    "qc.cx(q[1], q[2])\n",
    "qc.cx(q[0], q[2])\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.x(q[2])\n",
    "qc.measure(q[2], c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adder\n",
    "An adder is a digital logic circuit that performs addition of numbers. \n",
    "\n",
    "In this example, we are going to take a look at the simplest adders, namely half adder and full adder."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Half Adder\n",
    "The half adder is used to add together the two least significant digits in a binary sum.\n",
    "It has two single binary inputs, called A and B, and two outputs C (carry out) and S (sum).\n",
    "The output C will be used as an input to the Full Adder, which will be explained later, for obtaining the value in the higher digit.\n",
    "\n",
    "Half adders can be described with the truth table shown below.\n",
    "\n",
    "|A (input)|B (input)|S (sum)|C (carry out)|\n",
    "|-----------|------------|------------|------------|\n",
    "|0|0|0|0|\n",
    "|0|1|1|0|\n",
    "|1|0|1|0|\n",
    "|1|1|0|1|\n",
    "\n",
    "From the truth table, you should notice that the carry output, C, is a result of operating an AND gate against A and B, where the output S is a result of operating an XOR against A and B.\n",
    "As we have already created the AND and XOR gates, we can combine these gates and create a half adder as follows.\n",
    "\n",
    "We denote our quantum register as 'q', classical registers as 'c', assign inputs A and B to q[0] and q[1], the sum output S and  carry output C to q[2] and q[3]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'00': 1000}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 534.395x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Define registers and a quantum circuit\n",
    "q = QuantumRegister(4)\n",
    "c = ClassicalRegister(2)\n",
    "qc = QuantumCircuit(q,c)\n",
    "\n",
    "#XOR\n",
    "qc.cx(q[1], q[2])\n",
    "qc.cx(q[0], q[2])\n",
    "qc.barrier()\n",
    "\n",
    "#AND\n",
    "qc.ccx(q[0], q[1], q[3])\n",
    "qc.barrier()\n",
    "\n",
    "#Sum\n",
    "qc.measure(q[2], c[0])\n",
    "#Carry out\n",
    "qc.measure(q[3], c[1])\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(qc, backend, shots=1000)\n",
    "result = job.result()\n",
    "count =result.get_counts()\n",
    "print(count)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color: red; \">IMPORTANT: How to calculate Quantum Costs using an Unroller</span>\n",
    "There are several ways to evaluate an efficiency of a program (quantum circuit). Such as:\n",
    "\n",
    "1. Number of quantum bits\n",
    "2. Depth\n",
    "3. Program execution speed (Runtime)\n",
    "4. Number of instructions\n",
    "\n",
    "These are all important factors that impact the results and throughput of quantum computation. In this particular challenge, we will use the number of instructions to evaluate the efficiency of our program. We will call the number of instructions \"cost\" throughout this challenge and will use the following formula to evaluate the cost of a circuit.\n",
    "\n",
    "Cost $=$ Single-qubit gates $+$ CX gates $\\times 10$\n",
    "\n",
    "Any given quantum circuit can be decomposed into single-qubit gates (an instruction given to a single qubit) and two-qubit gates. With the current Noisy Intermediate-Scale Quantum (NISQ) devices, CX gate error rates are generally 10x higher than a single qubit gate. Therefore, we will weigh CX gates 10 times more than a single-qubit gate for cost evaluation.\n",
    "\n",
    "You can evaluate gate costs by yourself by using a program called \"Unroller.\"\n",
    "To elaborate on this, let's take a look at the example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400.578x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit import BasicAer, execute\n",
    "from qiskit.quantum_info import Pauli, state_fidelity, process_fidelity\n",
    "q = QuantumRegister(4, 'q0')\n",
    "c = ClassicalRegister(1, 'c0')\n",
    "qc = QuantumCircuit(q, c)\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.cx(q[3], q[1])\n",
    "qc.h(q[3])\n",
    "qc.ccx(q[3], q[2], q[1])\n",
    "qc.measure(q[3],c[0])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('ccx', 2), ('cx', 1), ('h', 1), ('measure', 1)])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.count_ops()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this quantum circuit contains a Hadamard gate, a CX gate and CCX gates. By using qiskit.transpiler and importing PassManager, we can decompose this circuit into gates specified by the Unroller as shown below. In this case, into U3 gates and CX gates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1544.38x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.transpiler import PassManager\n",
    "from qiskit.transpiler.passes import Unroller\n",
    "pass_ = Unroller(['u3', 'cx'])\n",
    "pm = PassManager(pass_)\n",
    "new_circuit = pm.run(qc) \n",
    "new_circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('u3', 19), ('cx', 13), ('measure', 1)])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_circuit.count_ops()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the cost of this circuit is $19+13\\times10=149$.\n",
    "\n",
    "You can easily check how any arbitrary gate can be decomposed by using the Unroller. So, if you are interested in how a particular two-qubit gate or three-qubit gate can be decomposed, we encourage you to try it yourself. In the example below, we used the Unroller to decompose a CCX gate into U3 gates and CX gates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 159.778x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3, 'q0')\n",
    "c = ClassicalRegister(1, 'c0')\n",
    "qc = QuantumCircuit(q, c)\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 761.778x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pass_ = Unroller(['u3', 'cx'])\n",
    "pm = PassManager(pass_)\n",
    "new_circuit = pm.run(qc) \n",
    "new_circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('u3', 9), ('cx', 6)])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_circuit.count_ops()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the total cost of a CCX gate can be calculated as $9+6\\times10=69$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Exercise I-A\n",
    "The full adder takes two binary numbers plus an overflow bit, which we will call X, as its input.\n",
    "Create a full adder with input data:\n",
    "\n",
    "$A=1$, $B=0$, $X=1$\n",
    ". \n",
    "\n",
    "The truth table for the full adder is given below.\n",
    "\n",
    "|A(input)|B(input)|X(carry input)|S(sum)|C(carry out)|\n",
    "|--|--|--|--|--|\n",
    "|0|0|0|0|0|\n",
    "|0|0|1|1|0|\n",
    "|0|1|0|1|0|\n",
    "|0|1|1|0|1|\n",
    "|1|0|0|1|0|\n",
    "|1|0|1|0|1|\n",
    "|1|1|0|0|1|\n",
    "|1|1|1|1|1|\n",
    "\n",
    "Call your quantum register 'q' and classical register 'c'. Assign inputs A, B and X to q[0], q[1] and q[2] respectively, the sum output S to c[0] and carry output C to c[1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit import IBMQ, Aer, execute\n",
    "\n",
    "##### build your quantum circuit here\n",
    "\n",
    "# execute the circuit by qasm_simulator\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(qc, backend, shots=1000)\n",
    "result = job.result()\n",
    "count =result.get_counts()\n",
    "print(count)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check your answer using following code\n",
    "from qc_grader import grade_ex1a\n",
    "grade_ex1a(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Submit your answer. You can re-submit at any time.\n",
    "from qc_grader import submit_ex1a\n",
    "submit_ex1a(qc)"
   ]
  }
 ],
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