ex1.ipynb

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    "# Exercise 1 - Toffoli gate\n",
    "\n",
    "## Historical background\n",
    "\n",
    "Forty years ago, a ragtag group of 50 thinkers arranged themselves for a photo on the lawn of MIT’s Endicott House. Few at the Physics of Computation Conference, jointly organized by MIT and IBM, thought they were making history in 1981. It was arguably the birthplace of physics of computing, and especially the now-burgeoning field of quantum computing, as a serious subject worthy of a textbook or university course.\n",
    "\n",
    "It was at this conference where Feynman uttered his now-famous quote: “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.”[1] Earlier this month, we celebrated the 40th anniversary of this important conference. You can read more [here](https://youtu.be/GR6ANm6Z0yk).\n",
    "\n",
    "![](resources/conference-photo.jpeg)\n",
    "\n",
    "One of the theme discussed in the conference was reversible computing, which Tommaso Toffoli and Edward Fredkin in MIT have been thinking about in the past few years prior.[2-3] Toffoli came up with a reversible version of AND/NAND gate (which are now called Toffoli gate, or controlled-controlled-NOT gate). Because NAND gate is universal in classical computing, Toffoli gate is a universal reversible logic gate. Quantum computing is a special form of reversible computing; any reversible gate can be implemented on a quantum computer, and hence the Toffoli gate is also a quantum logic gate. However, Toffoli gate alone is not a universal gate for quantum computing. \n",
    "\n",
    "In this exercise, we will explore the Toffoli gate and universal gate sets for quantum computers.\n",
    "\n",
    "### References\n",
    "1. Feynman, Richard P. \"Simulating physics with computers.\" Int. J. Theor. Phys 21.6/7 (1982).\n",
    "1. Toffoli, Tommaso. \"Reversible computing.\" International colloquium on automata, languages, and programming. Springer, Berlin, Heidelberg, 1980.\n",
    "1. Fredkin, Edward, and Tommaso Toffoli. \"Conservative logic.\" International Journal of theoretical physics 21.3 (1982): 219-253."
   ]
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    "## Classical logic gates\n",
    "\n",
    "In classical computation one often used model is Boolean logic or classical logical gates. Such gates represent Boolean functions, functions with only binary (0,1) input and output. One interesting aspect of Boolean logic is, that all possible binary functions can be formed by only using a combination of only a small number of different logic gates. Such sets are called functionally complete sets. One famous such set is AND and NOT. These two gates are enough to express all possible functions. The same is true for OR and NOT. There exists smaller sets, such as the NAND and NOR which alone are universal, nevertheless the functions AND, NOT and OR are often seen as the basic blocks of classical computation.\n",
    "\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Goal**\n",
    "\n",
    "Construct a Toffoli gate using the basis gate set (CX, RZ, SX and X gates) of IBM Quantum systems.\n",
    "\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "This exercise aims to teach you the basic concepts of quantum gates and how to construct quantum circuits\n",
    "1. visually using the Circuit Composer widget\n",
    "1. programmatically using Qiskit. \n",
    "\n",
    "If you are already familiar with quantum gates and Qiskit. You can jump directly to <a href=#problem>the problem</a>.\n",
    "</div>"
   ]
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    "# Getting rid of unnecessary warnings\n",
    "import warnings\n",
    "from matplotlib.cbook import MatplotlibDeprecationWarning\n",
    "warnings.filterwarnings('ignore', category=MatplotlibDeprecationWarning)\n",
    "\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, execute, Aer, IBMQ, QuantumRegister, ClassicalRegister\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from ibm_quantum_widgets import *\n",
    "\n",
    "# Useful to have pi\n",
    "import math\n",
    "pi=math.pi"
   ]
  },
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   "source": [
    "## What are quantum circuits?\n",
    "\n",
    "Quantum circuits are models for quantum computation in which a computation is a sequence of quantum gates. Quantum gates often represent rotations on the Bloch sphere. Let's take a look at some of the popular quantum gates.\n",
    "\n",
    "### X gate \n",
    "\n",
    "The X-gate is represented by the Pauli-X matrix: \n",
    "\n",
    "$X = \\begin{pmatrix}\n",
    "0 & 1 \\\\\n",
    "1 & 0 \\\\\n",
    "\\end{pmatrix}$\n",
    "\n",
    "An X gate equates to a rotation around the X-axis of the Bloch sphere by $\\pi$ radians. 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."
   ]
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   "execution_count": 2,
   "id": "5f676e68",
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      "text/plain": [
       "<Figure size 133.526x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_gate=QuantumCircuit(1) # Create a quantum circuit with 1 qubit\n",
    "x_gate.x(0)\n",
    "x_gate.draw(output='mpl')"
   ]
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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(x_gate, backend).result().get_statevector()\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88764578",
   "metadata": {},
   "source": [
    "### SX gate\n",
    "\n",
    "The SX gate equates to a rotation around the X-axis of the Bloch sphere by $\\pi/2$. It is called SX gate to indicate that it is the square-root of the X gate. Applying this gate twice produces the standard Pauli-X gate. The opposite of the SX is the SX dagger, which is a rotation by $\\pi/2$ in the opposite direction.\n",
    "\n",
    "$SX = \\frac{1}{2}\\begin{pmatrix}\n",
    "1+i & 1-i \\\\\n",
    "1-i & 1+i \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0a5cd6fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAABOCAYAAAATpymVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAESklEQVR4nO3cf0icdRzA8ffN89fUmERqMboDwViZigmR+6FLucjI0OvHnKsZBfujHwyCpoVatrloIPQLJKRsNm1/qIRpMjc5u2VtmKsZVLjmGS1/1NLaDpmJT3+1sjvbaXr39NnnBffP8zw+3w++vS88h5zFMAwDJcKaUA+gVo7GFERjCqIxBdGYgmhMQTSmIBpTEI0piMYURGMKojEF0ZiCaExBNKYgGlMQjSmIxhREYwqiMQXRmIJoTEE0piAaUxCNKYjGFERjCmIN9QCh8m0vXJgMzdpxCXDTnSt/36s25oVJmP4h1FOsLN1mBdGYgmhMQTSmIBpTEI0pyFX7aLJUM7Ne9jY9yMlvupb18z0HVv+rIzRmgI6fbmVL2gPse6wz1KMsSrfZAB3/qo0tafcD8PvcLLvqMqjveGbBNW3uVyndZ+PizHQIJjRpzPb2dlJTU4mMjCQlJYWGhgbKysqw2+0hmefnX88RGx1PdGQsAOHWCCq2H6Lz03pOnekFYGRsiHc+eo5ntx0kNnpdSOY03Tbb3d2N0+kkPz+f2tpavF4v1dXVzMzMEBYWFpQZZi5dxDAM1kbFAdB7qpm8zB0LrrEn3cKjd9dy4HAZbzx1kv3NpRRufJL05JygzOiP6d6ZVVVV2O12urq6KCwspKSkhJ6eHiYmJoKy/omvO9n95iY+/Kz+8rEvv3ORkbzV59qiTU9zY8IGdtWlERZmpeyul4Iy42JMFdPr9TIwMIDT6cRq/WvTsNlsZGdnB2WG2zfcw/a85zk2+B4AZ859QfINGaxZ4/urslgspCfnMu39ifzMhwm3RgRlxsWYKubU1BSGYZCUlORzzt8xfywWS0Cvvj7Xove44+Z7mZga5eyPpzk62IQja6ff60bGhmg+upeHtu6hqedFJqe+D2jGvj5XwHMuhalixsfHY7FYGB8f9znn79hqiQiPYvOtTo58/i7j58+y/roUn2tm5y6xv7mUos27ebzgZTamFvHK4Z3Mz88Hbc5/MlXMmJgYsrKyaG1tZW5u7vLx0dFR+vv7A7qHYRgBvXJycv/1PnmZO/jgk9e5LcXh9/zbXRVYrRE84ngBgCfue42JXzy0flx3xRlzcnIDnnMpTBUToKamBo/HQ0FBAR0dHbS0tOBwOEhMTAzqHOnJuSTE28jN2OZzbnD4GJ0n3qKi5BDWsHAA1kbFsaekiYNHqhkZGwrqrH+ymPErStva2qisrGR4eBibzUZ5eTlutxuXy4XH41mRNQbev/J/Gpz/bYxrr7l+Rdb7u3XrIcv3b+Q/M91zJkBxcTHFxcULjrnd7qDPsRohV5Pptlm1fBpTEFNus/40NjaGegTT03emIBpTEI0piMYURGMKojEF+d88mqy0uAR5a5vys1m1PLrNCqIxBdGYgmhMQTSmIBpTEI0piMYURGMKojEF0ZiCaExBNKYgGlMQjSmIxhREYwqiMQX5A67bTGSP6RdSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 133.526x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sx_gate = QuantumCircuit(1)\n",
    "sx_gate.sx(0)  \n",
    "sx_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3f180f2f",
   "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": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(sx_gate, backend).result().get_statevector()\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ea30c3e",
   "metadata": {},
   "source": [
    "### RZ gate\n",
    "\n",
    "The Rz gate performs a rotation of $\\phi$ around the Z-axis direction (Where $\\phi$ is a real number). It has the matrix below:\n",
    "\n",
    "$RZ = \\begin{pmatrix}\n",
    "1 & 0 \\\\\n",
    "0 & e ^{i \\phi } \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e7a42336",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 133.526x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rz_gate = QuantumCircuit(1)\n",
    "rz_gate.rz(pi/2, 0)\n",
    "rz_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "08691e05",
   "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": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(rz_gate, backend).result().get_statevector()\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68164532",
   "metadata": {},
   "source": [
    "Since the rotation is around the Z-axis one would not see a difference when we apply it to the default state $|0\\rangle$, so we use the state which was generated by applying the SX gate instead and apply the RZ to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "900e713a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 253.926x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rz_gate.sx(0)\n",
    "rz_gate.rz(pi/2, 0)\n",
    "rz_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8f32abf5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(rz_gate, backend).result().get_statevector()\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba61e460",
   "metadata": {},
   "source": [
    "### Hadamard 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 $|+\\rangle$. What the Hadamard does is to transform between the $|0\\rangle$ $|1\\rangle$ and the $|+\\rangle$ $|-\\rangle$ base. \n",
    "\n",
    "$H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}\n",
    "1 & 1 \\\\\n",
    "1 & -1 \\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ac05fd5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 133.526x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do an H-gate on a |0> qubit\n",
    "h_gate = QuantumCircuit(1)\n",
    "h_gate.h(0)\n",
    "h_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2bdb1907",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(h_gate, backend).result().get_statevector()\n",
    "plot_bloch_multivector(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49ff4c4d",
   "metadata": {},
   "source": [
    "### CX gate (CNOT gate)\n",
    "\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. \n",
    "\n",
    "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": 12,
   "id": "14c91df9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cx_gate = QuantumCircuit(2)\n",
    "cx_gate.cx(0,1)\n",
    "cx_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9bf3101",
   "metadata": {},
   "source": [
    "### CCX gate (Toffoli gate)\n",
    "\n",
    "The CCX gate (controlled controlled X Gate) is also called a Toffoli gate. 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. \n",
    "\n",
    "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": 13,
   "id": "510a3b6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.797x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ccx_gate = QuantumCircuit(3)\n",
    "ccx_gate.ccx(0,1,2)\n",
    "ccx_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3fd36ac",
   "metadata": {},
   "source": [
    "## Create logical gates with the help of quantum gates\n",
    "\n",
    "### NOT gate\n",
    "\n",
    "The NOT gate flips the value of a bit and, 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",
    "| Input | Output |\n",
    "| --- | --- | \n",
    "| 1 | 0 |\n",
    "| 0 | 1 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1f0ed8cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 193.726x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_gate=QuantumCircuit(1,1) # Create a quantum circuit with 1 qubit and 1 classical bit\n",
    "not_gate.x(0)\n",
    "not_gate.measure(0,0)\n",
    "not_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33cf186",
   "metadata": {},
   "source": [
    "### AND gate\n",
    "\n",
    "The output of an AND is true if and only if both inputs are true. 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 Toffoli gate, we can get the result of an AND gate by interpreting the two control bits as the input bits and the target bit as the output bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ae2f9706",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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71n9kjfiWux8ZZOyuv7a2loKCAmbMmNHqSMU8xu76L168SF1dXZtfWLbLh3+Je4wN9aGHHsLPz48zZ8606f7a9dtDp9/1d+/enZSUFLKysqiurvb1OOJlRp9M1Z/1R0dHs2jRIqKjoykrK6OgoIA1a9b4ejzxIGN3/QAjR45k3759LFmyhLfffptr164RGRnJ9OnTfT2aeJjRW1R5cBh7jCoPFoUqRlCoYgSFKkZQqGIEhSpGUKhiBIUqRlCoYgSFKkZQqGIEhSpGUKhiBIUqRlCoYgSFKkZQqGIEhSpGUKhiBIUqRlCoYgSFKkZQqGIEhSpGUKhiBIUqRlCoYgSFKkZQqGKE/weIymc3ZQuyBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 206.997x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "and_gate=QuantumCircuit(3,1) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "and_gate.ccx(0,1,2)\n",
    "and_gate.measure(2,0)\n",
    "and_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec84f46",
   "metadata": {},
   "source": [
    "### OR gate\n",
    "\n",
    "An OR gate returns true if at least one of the input gates is true.\n",
    "The truth table for an OR Gate looks like this:\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": 16,
   "id": "cbfe4d81",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 327.397x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "or_gate=QuantumCircuit(3,1) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "or_gate.cx(1,2)\n",
    "or_gate.cx(0,2)\n",
    "or_gate.ccx(0,1,2)\n",
    "or_gate.measure(2,0)\n",
    "or_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00530d92",
   "metadata": {},
   "source": [
    "## Using the Circuit Composer widget\n",
    "\n",
    "You might be familiar with the IBM quantum circuit composer, where you can generate circuits while using a graphical interface. With the new circuit composer widget, the same functionality  can be used in a jupyter notebook. You can learn more about how to use the widget [here](https://quantum-computing.ibm.com/lab/docs/iql/composer-widget)\n",
    "\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Exercise 1a:** Build a NOR (a negated OR) gate using circuit composer\n",
    "    \n",
    "This exercise is intended to encourage you to play around a bit with the composer. It is not graded. You can skip ahead if you want. Executing the cell below will show you a composer, where you can add gates by dragging them onto the correct place.    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1c2d4e08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f6af8dc097e24bf3a234b5d0d113c71e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "CircuitComposer(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7efcab9f0ee0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ibm_quantum_widgets import CircuitComposer\n",
    "editor = CircuitComposer()\n",
    "editor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3be907e",
   "metadata": {},
   "source": [
    "### Use the Circuit Composer widget to work with an existing circuit\n",
    "\n",
    "We can also use the circuit composer to open a previously created circuit. With the code below we will open the circuit created above, which represents the OR gate. You can use this to check if you constructed your OR correctly.\n",
    "\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "You can edit the opened circuit by drag and drop. Try to delete the measurement at the end.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cd044b5a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c92a40ed38d44414983e3f2be3b6ce1b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "CircuitComposer(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7efcab8faac0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ibm_quantum_widgets import CircuitComposer\n",
    "editor2 = CircuitComposer(circuit=or_gate)\n",
    "editor2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49327af4",
   "metadata": {},
   "source": [
    "In the example below we store the last circuit from the composer in the variable qc2 and then apply an X to the output and measure again.\n",
    "\n",
    "Use circuit from last editor and apply an X to the output and measure again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8c1a0418",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 447.797x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2 = editor2.circuit\n",
    "\n",
    "qc2.x(2)\n",
    "qc2.measure((2), (0))\n",
    "\n",
    "qc2.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38eef59",
   "metadata": {},
   "source": [
    "We now have created a NOR the negation of an OR, it should be identical to the circuit you constructed yourself in the first exercise. \n",
    "\n",
    "## Composite quantum gates and their cost\n",
    "\n",
    "A real quantum computer normally does not have physical implementations of all gates. Instead they use a small set of base gates, which form a universal gate set, this is, similar to the classical case, a set of instructions which can be used to implement all possible operations.\n",
    "\n",
    "For this reason, quantum circuits must be transpiled into basis gates before execution. This is usually done automatically by Qiskit transpiler when a quantum circuit is sent to a IBM Quantum system. But for the learning purposes, you are expected to construct the circuit by hand using the basis gates. The basis gates for IBM Quantum system is typically CX, ID, RZ, SX and X gates. You can see [`ibmq_mumbai` system](https://quantum-computing.ibm.com/services?skip=0&systems=all&system=ibmq_mumbai) for an example.\n",
    "\n",
    "Now let’s  take a look at the circuit below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "32c2c2c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.sxdg(0)\n",
    "qc.t(1)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1b9fe7b",
   "metadata": {},
   "source": [
    "Now lets show how a decomposition of the above circuit for a quantum computer, using only the base gates, could look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1c4a08fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.sx(0)\n",
    "qc.sx(0)\n",
    "qc.sx(0)\n",
    "qc.rz(pi/4,1)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c0d00e8",
   "metadata": {},
   "source": [
    "As you can see, we now use only the base gates, but for this reason more total gates are used. The more gates a circuit has, the more complex it is to run. So, when we want to calculate the cost of a circuit, we consider the number of gates used. However, not all gates are considered equal expensive, so when we calculate the cost of a circuit, we use the following formula:\n",
    "\n",
    "$$\n",
    "Cost = 10 N_{CNOT} + N_{other}\n",
    "$$\n",
    "\n",
    "where $N_{CNOT}$ is the number of CNOT gate and $N_{other}$ is the number of other gates.\n",
    "\n",
    "### Hadamard gate\n",
    "\n",
    "As said all operations can be expressed just using the base gates. As an example we show how to construct a Hadamard gate using our base gate set. We don't have a base gate which does a direct rotation around the axis that is in the middle of the X-axis and Z-axis, so we instead use rotations around the X-axis and Z-axis to get the same result. \n",
    "\n",
    "Can you guess what rotations we need to do?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6c9fa7d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 280.469x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q=QuantumRegister(1)\n",
    "c=ClassicalRegister(1)\n",
    "qc=QuantumCircuit(q,c)\n",
    "qc.rz(pi/2, 0)\n",
    "qc.sx(0)\n",
    "qc.rz(pi/2, 0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "671afd9e",
   "metadata": {},
   "source": [
    "As you might remember, this is the circuit we had above, when we visualized the rotation of the RZ gate. Above we saw that the first RZ does nothing, when we are in the $|0\\rangle$ or $|1\\rangle$ states. So it might feel a bit useless. However, if we are in the $|+\\rangle$ and $|-\\rangle$ states the first rotation has an effect. We have the opposite scenario, since after applying the SX gate we are again in the $|0\\rangle$ or $|1\\rangle$ state and then the second RZ has no effect.\n",
    "\n",
    "### Controlled rotation\n",
    "\n",
    "We have seen above the Controlled NOT, lets now show one example on how one can build a controlled rotation around the Y-axis. The rotation $\\theta$ can be any rotation, it does not have to be $\\pi$, this is just an example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7f6ce968",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 327.252x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "theta = pi # Theta can be anything (pi chosen arbitrarily)\n",
    "qc.ry(theta/2,1)\n",
    "qc.cx(0,1)\n",
    "qc.ry(-theta/2,1)\n",
    "qc.cx(0,1)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86137722",
   "metadata": {},
   "source": [
    "When one goes through this circuit, one can see that if the first qubit is 0 then the two rotations cancel each other out and nothing happens. \n",
    "\n",
    "On the other hand, if the first qubit is 1 we will get a state which is equal to applying the rotation $\\theta / 2$ two times which forms our initial rotation $\\theta$. This works since the X-axis and Y-axis are orthogonal. \n",
    "\n",
    "<div class=\"alert alert-block alert-danger\">\n",
    "For rotation around other axes you might need to use other tricks.\n",
    "</div>\n",
    "\n",
    "### Controlled controlled rotation\n",
    "\n",
    "Above we saw an example on how one can do a controlled rotation around the $Y$-axis.\n",
    "Now we assume we have a controlled rotation (around the axis we want) and want to build from that a double controlled rotation, which is only applied if both control qubits are 1 similar to the CCX gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9434680b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 568.197x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(3)\n",
    "theta = pi # Theta can be anything (pi chosen arbitrarily)\n",
    "qc.cp(theta/2,1,2)\n",
    "qc.cx(0,1)\n",
    "qc.cp(-theta/2,1,2)\n",
    "qc.cx(0,1)\n",
    "qc.cp(theta/2,0,2)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f531afef",
   "metadata": {},
   "source": [
    "In this circuit if both the first and second qubit are 0, then nothing happens at all. If only the second qubit is one, first we apply a rotation by $\\pi/2$ and afterwards a rotation by $-\\pi/2$ which cancel each other out. If only the first qubit is 1, then we the second qubit will also be one after the first CX so a rotation by $-\\pi/2$ will be applied and afterwards a rotation by $\\pi/2$ will be applied and these two rotations cancel each other out again.\n",
    "\n",
    "If both the first and the second qubit are 1 then first there will be a rotation by $\\pi/2$ then the second qubit will become 0 so the next rotation does not apply and then it is flipped back to 1. Afterwards another rotation by $\\pi/2$ is applied since the first qubit is 1. So we have two times a rotation of $\\pi/2$ which form together a rotation of $\\pi$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "245b8afe",
   "metadata": {},
   "source": [
    "## The problem\n",
    "\n",
    "<div id='problem'></div>\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "We have seen above how to construct a Hadamard gate with our base set, and now we want to build a Toffoli gate as well. Why the Toffoli gate? As mentioned above, the Toffoli gate is also a universal gate for classical computation the same way the NAND gate is, but it is reversible. Further  it builds a simple universal gate set for quantum computation if combined with the Hadamard gate. \n",
    "\n",
    "We have seen some examples on how to express more complex gates using basis gates, we now want to use the knowledge gained to construct a Toffoli gate only using our basis gates. In order to do solve this exercise the above examples on how to construct and use controlled rotations, will come in handy. The biggest challenge is to construct the needed controlled rotations.\n",
    "    \n",
    "You can use the code below using the composer widget to construct your circuit.\n",
    "    \n",
    "</div>\n",
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-danger\">\n",
    "\n",
    "As a reminder the basis gates for IBM Quantum systems are CX, RZ, SX and X gates, so no other gates are allowed.\n",
    "\n",
    "Of course we want also try to minimize the cost. \n",
    "    \n",
    "$$\n",
    "Cost = 10 N_{CNOT} + N_{other}\n",
    "$$\n",
    "    \n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "752dcd46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "872669b7b6b04629bbe2e13d13e44a72",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "CircuitComposer(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7efca9b18d60>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit import IBMQ, Aer, execute\n",
    "from ibm_quantum_widgets import CircuitComposer\n",
    "editorEx = CircuitComposer() \n",
    "editorEx\n",
    "##### Build your quantum circuit here using the composer widget."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9a81d479",
   "metadata": {},
   "outputs": [],
   "source": [
    "# You can also build your circuit programmatically using Qiskit code\n",
    "\n",
    "circuit = QuantumCircuit(3)\n",
    "\n",
    "# WRITE YOUR CODE BETWEEN THESE LINES - START\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# WRITE YOUR CODE BETWEEN THESE LINES - END"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6c062e71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 929.397x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking the resulting circuit\n",
    "qc = editorEx.circuit \n",
    "#qc = circuit # Uncomment this line if you want to submit the circuit built using Qiskit code\n",
    "\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "641fcb28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grading your answer for ex1. Please wait...\n",
      "\n",
      "Congratulations 🎉! Your answer is correct.\n",
      "Your cost is 73.\n",
      "Feel free to submit your answer.\r\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Check your answer using following code\n",
    "from qc_grader import grade_ex1\n",
    "grade_ex1(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cce2ddad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer for ex1. Please wait...\n",
      "Success 🎉! Your answer has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# Submit your answer. You can re-submit at any time.\n",
    "from qc_grader import submit_ex1\n",
    "submit_ex1(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29294aad",
   "metadata": {},
   "source": [
    "## Additional information\n",
    "\n",
    "**Created by:** Marcel Pfaffhauser, Brahmani Thota, Junye Huang\n",
    "\n",
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