Machzhender.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "92c123dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randrange\n",
    "from math import pi\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute, Aer, assemble\n",
    "from qiskit.visualization import plot_histogram, plot_bloch_multivector, array_to_latex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee8af9f",
   "metadata": {},
   "source": [
    "### Initialize the Quantum Register for how many qubits you need. \n",
    "\n",
    "#### Since the input source uses only one vaccum state $|0\\rangle$ then we register only qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "db0f85ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "qreg =  QuantumRegister(1,\"qreg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42729011",
   "metadata": {},
   "source": [
    "### One Classical Register for one classical bit for measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "18f4d107",
   "metadata": {},
   "outputs": [],
   "source": [
    "creg = ClassicalRegister(1,\"creg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30d5cf17",
   "metadata": {},
   "source": [
    "## Now initialize Quantum Circuit using both quantum register and classical register."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c578324d",
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = QuantumCircuit(qreg,creg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1e4963d",
   "metadata": {},
   "source": [
    "#### Suppose initially we have |0> photon Fock state and it passes through a beam splitter which transforms the $|0\\rangle$ $\\rightarrow$ $\\frac{1}{\\sqrt{2}}\\left(|0\\rangle + |1\\rangle\\right)$.\n",
    "#### In Qiskit we use the Hadamard gate for the transformation of $|0\\rangle$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e088770e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 168.141x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#first beam splitter transformation\n",
    "qc.h(qreg[0])\n",
    "display(qc.draw(output=\"mpl\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd99311e",
   "metadata": {},
   "source": [
    "* Now there is a phase rotator on one arm named $\\phi$ = $0,\\pi, \\pi/2$\n",
    "* Apply rotation gate $R_{y}$\n",
    "* Describe which detector it will click after passing throught beam splitter 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "95cfdbba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALoAAAB7CAYAAADDuprgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAL9klEQVR4nO3dfUxUVxoG8GcYEZCRYWYIH4M4FERXq7K2iAYWAW1pnRC1IFpxG6DtdmtSMctENOXDwXXLV60kdVUEXXZbXRWr1aK162oxpLIoWhXbXYoIWKGAOgzroKgwZ/8gTnY6VlEG7sB5fwkJnHvuue9NHq7n3rlyRIwxBkJGODuhCyBkKFDQCRco6IQLFHTCBQo64QIFnXCBgk64QEEnXKCgEy5Q0AkXKOiECxR0wgUKOuECBZ1wgYJOuEBBJ1ygoBMuUNAJFyjohAsUdMIFCjrhAgWdcIGCTrhAQSdcoKATLlDQCRdGCV3ASHegGmjuEObY3jIgJujZ9q09Cdxut249/THWHZg01/rjUtAHWXMHUC9AYAbqdjugvy50FdZDUxfCBQo64QIFnXCBgk64QDej5Jlptkbg302VEIvtYWcnhqfsOcTPS0N4YJzQpVmgoJMBWf5SBpa/lI7e3h4cOr0Z2bvjMcF7BrzdJghdmhmauhCrEItHYf6s36HX2IP6lgtCl2OBgk6s4kHPfZSd3goAGOc2UeBqLFHQyYDsPvEnLMpwRfT7TvjLV+lIiSuGn3I6AOCDXfH41/dlpr7rShahuvYfgtQ5IoLe09OD3t5eocuwmv0bInDm8w39bhdS/Lw0fP5HPfZrbyL4V2pcvPK1aduKhQUo+SoDd+8ZUFFzAM6OUgRNihKkTpsL+sGDBzF16lQ4ODhg4sSJKC4uRmJiInx9fQEAjY2NEIlEKCgoQHp6Onx8fODg4ICrV68CAI4cOYKwsDBIJBJIJBLMnz8fly9fNjuG0WiEVquFt7c3nJycEBISgqqqKvj6+iIxMXGIz3hkGDtGhpS4YlT95whOXz4EAJBJ3PHab1bhz4eSsfvEBry7YJNg9dlU0I8dO4bY2FgolUqUlpYiKysLeXl5OHHihEXf/Px8fPvtt9i8eTMOHz4MhUKBnTt3Ijo6GuPHj8eePXvwySefQKfTISwsDE1NTaZ9169fj6ysLMTFxeHQoUOIj4/HkiVLoNfrh/BsRx6XMXLEhqVg57H3YTQaAQCvzEzE9Rs/YFFoMlzGyAWrzaYeL2ZmZsLX1xdHjx7FqFF9pYWEhCAgIABKpdKsr0wmwxdffAE7u77f1a6uLmg0GixduhS7du0y9YuMjIS/vz9yc3OxZcsW6PV6bNy4EUlJSSgoKAAAREVFwcPDA0uWLBmaEx3BXgtbhQMVm3D83N/wysxEAIBSMUHwx402E/Suri5UV1dDo9GYQg4AKpUKISEhaGxsNOu/YMECU8gBoLKyEnq9Hm+88QZ6enpM7RKJBCEhITh16hQAoKamBgaDAXFx5h9qxMTEmB23P0Qi0RP7xKZ9jXGTI55qXAA4c+hPOHf0Q7O2B90GjJ/6Ur/HOHWqHMlRkU99bAD48N2vEegf8dg+G1eUW7Q5O7rgwHrdMx0T6Kt55rL+19zfhc9tJugdHR1gjMHT09Nim6enp0XQvby8zH5ua2sDAERHRz9yfHd3dwBAS0uL2c8PicViKBSKZ6p9MAQvTEPwonSztv0bIoQpZgSwmaDLZDKIRCK0trZabHtU28+vpg9DWlhYiBdeeMGiv729PQCYpkDt7eYviff29uLWrVtPVXN/riYfHxfuffTw8Ajs39C/K97PVe+x3vvoqa+X9LtveHgE2NZnq/lxbOZm1NnZGUFBQfjss8/Mph5NTU04ffr0E/cPDQ2Fi4sLamtrERQUZPEVGBgIAJg2bRokEglKS0vN9j9w4IDZccnIYjNXdKDvaYharYZarcbKlSthMBig1Wrh4eHxxH3Hjh2LgoICvP3227h16xYWLlwIuVyO1tZWVFZWwtvbG6tXr4arqys0Gg2ysrIglUqhVqtRW1uLvLw8SKVSs3k/GTlsKuivvvoq9u/fj4yMDMTGxkKlUmHt2rWoqKhAeXn5E/dPSkqCj48P8vLykJSUhO7ubnh5eWHWrFlmN5+ZmZlgjKGoqAhbt25FYGAg9u7di/nz58PV1XXwTrCfFqeXP1U7eTIR6+9tq4ASExNRXl5ucUNqTVVVVZg9ezY+/fRTLF++3GrjCjlH93cHVr78bPtac47+NFzHAUGvW39cm7qiD5Xq6mocPHgQs2fPhkQiweXLl5GTkwN/f3/ExMQIXd6wd7OzGfvK8xE5Yxm2Hf4DRCI7TPKZiRUCfjLKZdCdnZ1RWVmJwsJCdHZ2Qi6XIyoqCjk5OXBychK6vGHv3A/H8eLEl+HhqkL+709itL0jsncvR8NPNXjOa5ogNQ2LoJeUlFh1vMmTJ+PkyZNWHZNXF+vLof3ra/DzCkSrrgH+yl9j7Bg53lv0MZwcJKZ+Yru+/4UkFHrEQAZk2nNzMMknGBtXlGO6XziSY7ag+36XWcivtlxCZ9cNqDymCFYnBZ0MyE+6q/CS+wEAbnT+CL3hBvyUgabt/72jw+bP34MmbodQJQKgoJMBamr9DirP59Fr7IVIZIfzdcfxYkDfo57e3h7k/P23eCf6Q8hdLF/tGEoUdDIgjW3fwdfjeTzouQe9oR3n6/6JieP6/uDjqUul+OHHsyg6kgrN1gh831gpWJ3D4maU2K74ee+bvi/S1ODUxX2mT5fnzliGuTOWCVWaGbqiE6sKD7TNd/rpij7IvGXD89hj3Z/cZzAM1nGHxSsAhAwUTV0IFyjohAsUdMIFCjrhAgWdcIGCTrhAQSdcoKATLlDQCRco6IQLFHTCBQo64QIFnXCBgk64QEEnXKCgEy5Q0AkXKOiECxR0wgUKOuECBZ1wgYJOuEBBJ1ygoBMujJig37t3T+gSiA2z2aDX1NQgNjYWbm5ucHR0REBAANLS0gD0Ld7l5uaG6upqhIeHw9nZGW+++SaAvhWok5OT4ePjg9GjR8PPzw/Z2dkwGo1m41+6dAmRkZFwcnKCl5cX1qxZg6KiIohEokFdFIwIwyb/9uK5c+cwZ84c+Pj4ID8/HyqVCg0NDWYL6965cweLFy/GqlWroNVqMWrUKBgMBoSFhUGn0yE9PR2TJk3CN998A61Wi/b2dmza1LdYlE6nQ2RkJORyOXbs2AGpVIrCwkLs2bPnqepcm7vdqudNnl7Omnf61c8mg67RaODs7IyqqipIpVJT+1tvvWX6/u7du8jNzcXSpUtNbR988AFqa2tx/vx5TJvWtyjUvHnzIBKJsH79eqxevRpKpRIfffQROjs7cfbsWfj59a3WoFarMX369CE6QzLkmI3p6upidnZ2LDk5+Rf7JCQkMJFIxLq7u83aQ0NDWXBwMHvw4IHZ15kzZxgAtm/fPsYYY3PnzmXBwcEW42q1WgaANTQ0WPWciPBs7ore0dEBo9GIcePGPbafTCaDg4ODWVtbWxuuXLkCe3v7R+5z8+ZNAEBLSwsmTJhgsb0/S7H/P5q6CG/YTl1kMhns7OzQ3Nz82H4ikciiTaFQQCqVYtu2bY/cR6VSAQCUSiXa2y2Xc25ra3uGismwIPQ/KY8SERHB3N3dWWdn5yO3JyQkMIVCYdGelZXFXFxc2PXr1x87flpaGhOLxay+vt7UZjQa2dSpU2nqMkLZ5EIAD5+6qFQqpKamQqVS4dq1a6ioqEBxcTESExNRVlZmmoo8dPv2bYSGhsJgMCAlJQVTpkxBd3c36uvrUVZWhtLSUri4uECn0yEgIAAKhQJarRZSqRTbt2/HhQsXcO3aNTQ1NWH8+PECnT0ZFEL/pv2SixcvsgULFjBXV1fm6OjIAgICWEZGBmPsl6/ojDHW2dnJUlNTmb+/P7O3t2dyuZzNnDmTrVu3jt2/f9/U78KFCyw8PJw5ODgwd3d3lpKSwnJzcxkAptfrh+QcydCxySu6UNRqNerq6lBXVyd0KcTKbO5mdKhkZmbC19cXfn5+0Ov12Lt3L7788kts305PUkYiboMuFouRnZ2N5uZmMMYwefJklJSUICEhQejSyCCgqQvhgs2+1EWINVHQCRco6IQLFHTCBQo64QIFnXCBgk64QEEnXKCgEy5Q0AkXKOiECxR0wgUKOuECBZ1wgYJOuEBBJ1ygoBMuUNAJFyjohAsUdMIFCjrhAgWdcIGCTrhAQSdcoKATLvwPuGB6cHdGrKsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 228.341x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rotation = pi/2\n",
    "qc.ry(rotation,qreg[0])\n",
    "display(qc.draw(output=\"mpl\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc233685",
   "metadata": {},
   "source": [
    "#### We have set the rotation angle.\n",
    "* Now we pass the statevector $\\psi$ through the second beam splitter using Hadamard gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e1b270ad",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288.541x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc.h(qreg[0])\n",
    "display(qc.draw(output=\"mpl\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f102657c",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = \"Beeps on either detector 1 and detector 2 with equal probabilities\"\n",
    "    \n",
    "b = \"Beeps on detector 1\"\n",
    "    \n",
    "c = \"Beeps on detector 2\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20b757b4",
   "metadata": {},
   "source": [
    "#### Perform meaurement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc4f1cc4",
   "metadata": {},
   "source": [
    "* Now set the conditions i.e. which detector will click based on the rotation angle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a9d846c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 348.741x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc.measure(qreg,creg)\n",
    "display(qc.draw(output=\"mpl\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21d77575",
   "metadata": {},
   "source": [
    "* Save the statevector and Print it in hard form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "53fe9419",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector = }\n",
       "\\begin{bmatrix}\n",
       "0 & -1  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.save_statevector()\n",
    "qobj = assemble(qc)\n",
    "svsim = Aer.get_backend('aer_simulator')\n",
    "result = svsim.run(qobj).result()\n",
    "# Print the statevector neatly:\n",
    "final_state = result.get_statevector()\n",
    "array_to_latex(final_state, prefix=\"\\\\text{Statevector = }\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daed679b",
   "metadata": {},
   "source": [
    "### CASE 1: When $\\phi = 0$\n",
    "\n",
    "* It clicks the detector D1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "31f41538",
   "metadata": {},
   "outputs": [],
   "source": [
    "if rotation==0:\n",
    "    print(b)\n",
    "    job = execute(qc,Aer.get_backend('qasm_simulator'),shots=1000)\n",
    "    counts = job.result().get_counts(qc)\n",
    "    \n",
    "    print(counts)\n",
    "    print()\n",
    "    \n",
    "    n_zeros = counts['0']\n",
    "#    n_ones = counts3['1']\n",
    "    print(\"State 0 is observed with frequency %\",100*n_zeros/(n_zeros))\n",
    "#    print(\"State 1 is observed with frequency %\",100*n_ones/(n_zeros+n_ones))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13625f8d",
   "metadata": {},
   "source": [
    "### CASE 2: When $\\phi = \\pi$\n",
    "\n",
    "* It clicks the detector D2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fd280303",
   "metadata": {},
   "outputs": [],
   "source": [
    "if rotation==pi:\n",
    "    print(c)\n",
    "    job = execute(qc,Aer.get_backend('qasm_simulator'),shots=1000)\n",
    "    counts = job.result().get_counts(qc)\n",
    "    \n",
    "    print(counts)\n",
    "    print()\n",
    "    \n",
    "#    n_zeros = counts3['0']\n",
    "    n_ones = counts['1']\n",
    "#    print(\"State 0 is observed with frequency %\",100*n_zeros/(n_zeros))\n",
    "    print(\"State 1 is observed with frequency %\",100*n_ones/(n_ones))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f1d34ac",
   "metadata": {},
   "source": [
    "### CASE 3: When $\\phi = \\frac{\\pi}{2}$\n",
    "\n",
    "* It either clicks the detector D1 or D2 with equal probabilties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a37ff9a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beeps on either detector 1 and detector 2 with equal probabilities\n",
      "{'1': 526, '0': 474}\n",
      "\n",
      "State 0 is observed with frequency % 47.4\n",
      "State 1 is observed with frequency % 52.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "if rotation==pi/2:\n",
    "    print(a)\n",
    "    job = execute(qc,Aer.get_backend('qasm_simulator'),shots=1000)\n",
    "    counts = job.result().get_counts(qc)\n",
    "    \n",
    "    print(counts)\n",
    "    print()\n",
    "    \n",
    "    n_zeros = counts['0']\n",
    "    n_ones = counts['1']\n",
    "    print(\"State 0 is observed with frequency %\",100*n_zeros/(n_zeros+n_ones))\n",
    "    print(\"State 1 is observed with frequency %\",100*n_ones/(n_zeros+n_ones))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6891f6b4",
   "metadata": {},
   "source": [
    "## Plot Probabilities on Histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e32bab8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba174b09",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}