2.a-One-qubit-circuit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single Qubit Circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from math import pi\n",
    "import numpy as np\n",
    "from qiskit.visualization import *\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Single qubit circuit:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base states : |0>, |1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 184.212x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.h(0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.707+0.j  0.707-0.j]\n",
      " [ 0.707+0.j -0.707+0.j]]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('unitary_simulator')\n",
    "job = execute(qc, backend)\n",
    "result = job.result()\n",
    "print(result.get_unitary(qc, decimals=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1. Gates in series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 244.412x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.h(0)\n",
    "qc.h(0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.-0.j 0.+0.j]\n",
      " [0.+0.j 1.-0.j]]\n"
     ]
    }
   ],
   "source": [
    "# Run the quantum circuit on a unitary simulator backend\n",
    "backend = Aer.get_backend('unitary_simulator')\n",
    "job = execute(qc, backend)\n",
    "result = job.result()\n",
    "\n",
    "# Show the results\n",
    "print(result.get_unitary(qc, decimals=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.99698000e-01+0.j, -1.37436729e-17+0.j],\n",
       "       [-1.37436729e-17+0.j,  9.99698000e-01+0.j]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "np.dot(H,H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 665.812x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(1)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.barrier()\n",
    "qc0 = qc.copy()\n",
    "qc.h(0)\n",
    "qc.barrier()\n",
    "qc1 = qc.copy()\n",
    "qc.x(0)\n",
    "qc.barrier()\n",
    "qc2 = qc.copy()\n",
    "qc.y(0)\n",
    "qc.barrier()\n",
    "qc3 = qc.copy()\n",
    "qc.z(0)\n",
    "qc.barrier()\n",
    "qc4 = qc.copy()\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.-0.707j -0.-0.707j]\n",
      " [-0.-0.707j  0.+0.707j]]\n"
     ]
    }
   ],
   "source": [
    "# Run the quantum circuit on a unitary simulator backend\n",
    "backend = Aer.get_backend('unitary_simulator')\n",
    "job = execute(qc, backend)\n",
    "result = job.result()\n",
    "\n",
    "# Show the results\n",
    "print(result.get_unitary(qc, decimals=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Operator =  Z.Y.X.H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.-0.707j, 0.-0.707j],\n",
       "       [0.-0.707j, 0.+0.707j]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = sigmax()\n",
    "Y = sigmay()\n",
    "Z = sigmaz()\n",
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "np.dot(np.dot(Z,Y),np.dot(X,H))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Why is order reversed?\n",
    "\n",
    "$ZYXH|\\psi_0\\rangle = ZYX|\\psi_1\\rangle = ZY|\\psi_2\\rangle = Z|\\psi_3\\rangle =|\\psi_4\\rangle $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n",
      "[0.70710678+0.j 0.70710678+0.j]\n",
      "[0.70710678+0.j 0.70710678+0.j]\n",
      "[0.-0.70710678j 0.+0.70710678j]\n",
      "[ 0.-0.70710678j -0.-0.70710678j]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "for qc in [qc0,qc1,qc2,qc3,qc4]:\n",
    "    out = execute(qc,backend).result().get_statevector()\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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