NB1-QC-Gates-1bit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying Hadamard to Single Qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "# Importing standard Qiskit libraries and configuring account\n",
    "from qiskit import QuantumCircuit, QuantumRegister,ClassicalRegister\n",
    "from qiskit import  execute, Aer, IBMQ\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from qiskit.providers.aer import UnitarySimulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hadamard Gate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algebra:\n",
    "$H = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 244.412x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n =1\n",
    "q = QuantumRegister(n)\n",
    "c = ClassicalRegister(n)\n",
    "circ = QuantumCircuit(q,c)\n",
    "circ.h(q[0])\n",
    "circ.measure(q,c)\n",
    "\n",
    "# Change the background color in mpl\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circ.draw(output='mpl', style = style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Manual approach:\n",
    "Initial state: |0>; \n",
    "After Hadamard Gate: 1√2|0>+1√2|1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Simulation\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(circ, simulator).result()\n",
    "counts = result.get_counts(circ)\n",
    "plot_histogram(counts, title='Bell-State counts')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.+0.j 0.+0.j]\n",
      " [0.+0.j 1.+0.j]]\n"
     ]
    }
   ],
   "source": [
    "#Unitary Matrix representation\n",
    "#Create a new simulator that will display unitary Matrix\n",
    "circ = QuantumCircuit(q,c)\n",
    "simulator1 = Aer.get_backend('unitary_simulator')\n",
    "# Execute and get counts\n",
    "result1 = execute(circ, simulator1).result()\n",
    "unitary = result1.get_unitary(circ)\n",
    "print( unitary)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Aer Simulators:\n",
    "QasmSimulator: Allows ideal and noisy multi-shot execution of qiskit\n",
    "circuits and returns counts or memory.\n",
    "\n",
    "UnitarySimulator: Allows ideal single-shot execution of qiskit\n",
    "circuits and returns the final unitary matrix of the circuit itself.\n",
    "\n",
    "StatevectorSimulator: Allows ideal single-shot execution of qiskit\n",
    "circuits and returns the final statevector of the simulator after \n",
    "application."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": 4
}