Notebooks/qiskit/Deutsch-Jozsa_algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5: Deutsch-Jozsa algorithm\n",
    "\n",
    "The idea is to find if a binary function:\n",
    "$$f:Z_{2^n} \\to Z_2$$\n",
    "that is known to be *constant* (for every x the result is equal, or 0 or 1) or *balanced* (produces the same number of 0s and 1s), is constant or balanced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start the Engine and allocate an even number of qubits (by default, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 878.92x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leng = 4\n",
    "\n",
    "circuit=QuantumCircuit(leng,leng)\n",
    "circuit.x(3)\n",
    "circuit.h(range(leng))\n",
    "circuit.barrier()\n",
    "\n",
    "# To create an Oracle for the function, it is enough to compute \n",
    "\n",
    "circuit.cx(0,3)\n",
    "circuit.barrier()\n",
    "#\n",
    "#Other oracles you can check\n",
    "#\n",
    "#X|qreg[0] #Constant\n",
    "#All(X)|qreg #Constant\n",
    "#All(Z)|qreg #balanced\n",
    "\n",
    "\n",
    "circuit.h(range(leng))\n",
    "circuit.x(3)\n",
    "circuit.barrier()\n",
    "\n",
    "circuit.measure((0,1,2,3),(0,1,2,3))\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Measure the results. If it is **constant**, the result must be |0000>=|0>. If it is **balanced**, the result is different of |0>"
   ]
  },
  {
   "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": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(circuit,backend=simulator).result()\n",
    "\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us solve this without an ancilla\n",
    "\n",
    "The idea is to encode the function f(x) as  the phase of the action of a certain oracle $U_f$. Namely, suppose you are able to device  \n",
    "\n",
    "$$U_f(|x>) = (-1)^{f(x)} |x>$$\n",
    "\n",
    "Where $$U_f$$ is call oracle. Here we will use a simple case:\n",
    "$$f(x) = x\\%2 $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 758.52x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leng = 4\n",
    "\n",
    "qc=QuantumCircuit(leng,leng)\n",
    "qc.h(range(leng))\n",
    "qc.barrier()\n",
    "\n",
    "# To create an Oracle for the function, it is enought to compute Z applied to first qubit\n",
    "\n",
    "qc.x(0)\n",
    "qc.barrier()\n",
    "#\n",
    "#Other oracles you can check\n",
    "#\n",
    "#X|qreg[0] #Constant\n",
    "#All(X)|qreg #Constant\n",
    "#All(Z)|qreg #balanced\n",
    "\n",
    "qc.h(range(leng))\n",
    "qc.barrier()\n",
    "\n",
    "qc.measure((0,1,2,3),(0,1,2,3))\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qc,backend=simulator).result()\n",
    "\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}