Day 4 Deutsch Josza algorithm.ipynb

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    "# The Deutsch-Josza Algorithm\n",
    "The Deutsch-Josza algorithm is useful in solving the Deutsch's problem described as follows:\n",
    "Alice selects a number $x$ from $0$ to $2^n-1$ and sends it to Bob who calculates $f(x)$ and sends it back to Alice. The function $f(x)$ attains either the value 0 or 1 for each $x$ and satisfies either one of the following two properties:\n",
    "1. $f(x)$ is *constant* for all values of $x$.\n",
    "2. $f(x)$ is *balanced*, i,e., it attains the value 0 for exactly half of all possible $x$ and 1 for the other half.\n",
    "\n",
    "Alice's job is to determine whether the function is constant or balanced. In the classical situation, where Alice sends n bits to represent her number each time, at worst it would take $\\frac{2^n}{2}+1$ trials for Alice to determine, since a function could attain the same value for the first half of trials and the next trial could still give a different value, if it were balanced.\n",
    "\n",
    "\n",
    "If Alice and Bob use qubits, and Bob uses the unitary operator $U_f$ to calculate $f(x)$ then Alice's number is stored in the $n$ qubit query register and Bob uses the single qubit answer register to store the result of his operator. Alice then follows the described algorithm to carry out the task.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/mnp-club/Quantum_Computing_Workshop_2020/master/images/jozsa.jpg\" width=500 height=400> </img>\n",
    "\n",
    "The input state is $$\\vert \\psi_0 \\rangle = \\vert 0 \\rangle^{\\otimes n}\\vert 1\\rangle.$$\n",
    "After applying the Hadamard transform on all the qubits, the state is:\n",
    "\\begin{align*}\n",
    "\\vert \\psi_1 \\rangle &=\\left(\\frac{\\vert 0 \\rangle + \\vert 1 \\rangle}{\\sqrt{2}}\\right)^{\\otimes n}\\left(\\frac{\\vert 0 \\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right)\\\\\n",
    "&=\\sum\\limits_{x\\in\\{0,1\\}^n}\\frac{\\vert x \\rangle}{\\sqrt{2^n}}\\left(\\frac{\\vert 0 \\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right)\n",
    "\\end{align*}\n",
    "If we apply $U_f$ gate to state $\\vert x \\rangle \\left( \\frac{\\vert 0\\rangle - \\vert 1\\rangle}{\\sqrt{2}}\\right)$, we get the following state\n",
    " \n",
    "\\begin{align*}\n",
    "\\vert x \\rangle\\left(\\frac{\\vert f(x)\\rangle -\\vert 1\\oplus f(x)\\rangle}{\\sqrt{2}}\\right)\n",
    "&=\\begin{cases}\n",
    "\t\t\\vert x \\rangle\\left(\\frac{\\vert 0\\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right) & \\text{if $f(x)=0$}\\\\\n",
    "\t\t\\vert x \\rangle\\left(\\frac{\\vert 1\\rangle -\\vert 0\\rangle}{\\sqrt{2}}\\right) & \\text{if $f(x)=1$}\\\\\n",
    "\t\\end{cases}\\\\\n",
    "&=(-1)^{f(x)}\\vert x \\rangle \\left(\\frac{\\vert 0\\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right)\n",
    "\\end{align*} So, on applying $U_f$ to $\\vert \\psi_1 \\rangle$, we get:\n",
    "$$\\vert \\psi_2 \\rangle=\\sum\\limits_{x}\\frac{(-1)^{f(x)}\\vert x \\rangle}{\\sqrt{2^n}}\\left(\\frac{\\vert 0 \\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right).$$\n",
    "For a single qubit $\\vert x \\rangle,$ $$H\\vert x \\rangle=\\sum\\limits_{z}\\frac{(-1)^{xz}\\vert z \\rangle}{\\sqrt{2}}.$$\n",
    "For $n$ qubits $$H^{\\otimes n}\\vert x_1,...x_n \\rangle=\\sum\\limits_{z_1,...z_n}\\frac{(-1)^{x_1z_1+...x_nz_n}\\vert z_1,...z_n \\rangle}{\\sqrt{2^n}}$$\n",
    "i.e., $$H^{\\otimes n}\\vert x \\rangle=\\sum\\limits_{z}\\frac{(-1)^{x\\cdot z}\\vert z \\rangle}{\\sqrt{2^n}}$$ where $x\\cdot z$ represents the bitwise inner product of $x$ and $z$, modulo 2.\n",
    "\n",
    "Applying Hadamard transform on the query register, we obtain\n",
    "$$\\vert \\psi_3 \\rangle=\\sum\\limits_z\\sum\\limits_{x}\\frac{(-1)^{x.z+f(x)}\\vert z \\rangle}{2^n}\\left(\\frac{\\vert 0 \\rangle -\\vert 1\\rangle}{\\sqrt{2}}\\right).$$\n",
    "\n",
    "The amplitude for the state $\\vert 0 \\rangle^{\\otimes n}$ is $\\displaystyle{\\sum\\limits_{x}\\frac{(-1)^{f(x)}}{2^n}}$.\n",
    "\n",
    "If $f$ is constant, the amplitude will be $\\pm 1$, which means all other amplitudes will be 0, so an observation will yield 0s for all qubits in the query register. If $f$ is balanced, then the positive and negative contributions to the amplitude of the state $\\vert 0 \\rangle^{\\otimes n}$ cancel, leaving an amplitude of 0, and a measurement must yield a result other than 0 on at least one qubit in the query register.\n",
    "\n",
    "Therefore, if on measuring the query register, Alice obtains all 0s  then the function is constant; otherwise the function is balanced. \n",
    "\n",
    "Hence, a quantum computer can solve Deutsch’s problem with one evaluation of the function $f$ compared to the classical requirement for $\\frac{2^n}{2}+1$ evaluations."
   ]
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    "%matplotlib inline\n",
    "# Importing standard Qiskit libraries and configuring account\n",
    "from qiskit import QuantumCircuit, execute, Aer, IBMQ\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "import numpy as np\n",
    "from fractions import Fraction as frac \n",
    "import qiskit.quantum_info as qi\n",
    "# Loading your IBM Q account(s)\n",
    "provider = IBMQ.load_account()"
   ]
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   "source": [
    "## Creating Quantum Oracles\n",
    "Now, we will attempt to construct a circuit in order to demonstrate the above algorithm for a particular case. Before that let's have a look at the internal circuitry of the quantum oracles $U_f$ used to calculate $f(x)$.\n",
    "\n",
    "For a constant function, it is simple:\n",
    "\n",
    "  1. if $f(x)$ = 0, then $\\vert y \\oplus f(x)\\rangle = \\vert y\\rangle$ so apply the  $I$  gate to the qubit in register 2 (i.e., no need to apply any gates).\n",
    "  2. if $f(x)$ = 1, then $\\vert y \\oplus f(x)\\rangle = \\vert y \\oplus 1\\rangle$ so apply the  $X$  gate to the qubit in register 2.\n",
    "  \n",
    "A simple way to create a balanced function is by applying the CNOT gate for each qubit in register 1, with the qubit in register 2 as the target. Shown below is an example of a quantum oracle for a balanced function to be applied to a 3-qubit system:"
   ]
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      "text/plain": [
       "<Figure size 358.792x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc=QuantumCircuit(4)\n",
    "\n",
    "#In this particular oracle, the last qubit is storing the value of the function\n",
    "\n",
    "qc.cx(0,3)\n",
    "qc.cx(1,3)\n",
    "qc.cx(2,3)\n",
    "#The last qubit is 1 if there are odd no. of 1s in the other 3 qubits\n",
    "#and 0 otherwise\n",
    "#Hence it is a balanced function\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
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   "source": [
    "## Example of a quantum circuit for the Deutsch-Josza Algorithm:\n",
    "Here we will take the simple case wherein the number chosen lies in the range 0 to 3 (i.e. $2^2 - 1$ ) and the function is balanced. The part of the quantum circuit between the barriers is one possible representation of the quantum oracle for this function."
   ]
  },
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 719.992x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc1=QuantumCircuit(3)\n",
    "qc1.x(2)\n",
    "qc1.h(0)\n",
    "qc1.h(1)\n",
    "qc1.h(2)\n",
    "\n",
    "qc1.barrier(range(3))\n",
    "qc1.cx(0,2)\n",
    "qc1.cx(1,2)\n",
    "qc1.barrier(range(3))\n",
    "qc1.h(0)\n",
    "qc1.h(1)\n",
    "\n",
    "meas = QuantumCircuit(3, 2)\n",
    "meas.measure(range(2),range(2))\n",
    "\n",
    "# The Qiskit circuit object supports composition using\n",
    "# the addition operator.\n",
    "circ = qc1+meas\n",
    "\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8G95o93ZMAsv"
   },
   "source": [
    "The following is the result obtained on measuring the query register:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZBLhhq4SMAsw"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 1000}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend_sim = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "job_sim = execute(circ, backend_sim, shots=1000)\n",
    "\n",
    "result_sim = job_sim.result()\n",
    "counts = result_sim.get_counts(circ)\n",
    "print(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jW80PBRMMAsy"
   },
   "source": [
    "Since we do not get an output $\\vert 00\\rangle$, the function must be balanced."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MSLCES23MAsz"
   },
   "source": [
    "## Your Task:\n",
    "**(5 points)**\n",
    "\n",
    "Your task is to make a quantum circuit (the rest is done for you, you just need to construct the oracle for the below function) for a 4-qubit query resgister. The function is balanced with outputs for each $x$ as given below:\n",
    "\n",
    "| &nbsp; &nbsp;&nbsp; &nbsp; **$x$ :**  &nbsp;  &nbsp; &nbsp; &nbsp; | &nbsp; &nbsp;&nbsp; &nbsp; **$f(x)$** &nbsp; &nbsp;&nbsp; &nbsp; | &nbsp; &nbsp;&nbsp; &nbsp; **$x$ :**  &nbsp;  &nbsp;&nbsp; &nbsp;| &nbsp; &nbsp;&nbsp; &nbsp; **$f(x)$** &nbsp; &nbsp;&nbsp; &nbsp; |\n",
    "| :-------------: | :----------: | :-------------------: | :----------: |\n",
    "| $\\vert 0000 \\rangle $ | 1 | $\\vert 1000 \\rangle $ | 0 |\n",
    "| $\\vert 0001 \\rangle $ | 0 | $\\vert 1001 \\rangle $ | 1 |\n",
    "| $\\vert 0010 \\rangle $ | 0 | $\\vert 1010 \\rangle $ | 1 |\n",
    "| $\\vert 0011 \\rangle $ | 1 | $\\vert 1011 \\rangle $ | 0 |\n",
    "| $\\vert 0100 \\rangle $ | 0 | $\\vert 1100 \\rangle $ | 1 |\n",
    "| $\\vert 0101 \\rangle $ | 1 | $\\vert 1101 \\rangle $ | 0 |\n",
    "| $\\vert 0110 \\rangle $ | 1 | $\\vert 1110 \\rangle $ | 0 |\n",
    "| $\\vert 0111 \\rangle $ | 0 | $\\vert 1111 \\rangle $ | 1 |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tG-dN9-HMAsz"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1020.99x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2=QuantumCircuit(5)\n",
    "qc2.x(4)\n",
    "qc2.h(0)\n",
    "qc2.h(1)\n",
    "qc2.h(2)\n",
    "qc2.h(3)\n",
    "qc2.h(4)\n",
    "\n",
    "qc2.barrier(range(5))\n",
    "#Your code for the oracle here\n",
    "#YOU ARE PERMITTED TO USE ONLY SINGLE QUBIT GATES AND CNOT(cx) GATES\n",
    "qc2.x(0)        # This is done to flip parity of 4th bit\n",
    "\n",
    "qc2.cx(0,4)\n",
    "qc2.cx(1,4)\n",
    "qc2.cx(2,4)\n",
    "qc2.cx(3,4)\n",
    "\n",
    "qc2.x(0)\n",
    "\n",
    "qc2.barrier(range(5))\n",
    "qc2.h(0)\n",
    "qc2.h(1)\n",
    "qc2.h(2)\n",
    "qc2.h(3)\n",
    "\n",
    "meas2 = QuantumCircuit(5, 4)\n",
    "meas2.measure(range(4),range(4))\n",
    "\n",
    "circ2 = qc2+meas2\n",
    "circ2.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "raw",
    "id": "hi0NJle7MAs2"
   },
   "source": [
    "For demonstrating the values of the function for different inputs, we will use the following circuit. Add and remove $X$ gates as you please, in order to check $f(x)$ for different values of $x$. In this case, $q_4$ will directly give $f(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GAMumA-wMAs2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 719.992x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#verification cell, reinitialising the circuit so that it's easier for you to copy-paste the oracle\n",
    "qc2=QuantumCircuit(5)\n",
    "#Add X gates HERE as required to change the input state\n",
    "qc2.x(0)\n",
    "qc2.x(3)\n",
    "qc2.barrier(range(5))\n",
    "\n",
    "#Copy and paste your code for the oracle from the above cell here\n",
    "qc2.x(0)\n",
    "\n",
    "qc2.cx(0,4)\n",
    "qc2.cx(1,4)\n",
    "qc2.cx(2,4)\n",
    "qc2.cx(3,4)\n",
    "\n",
    "qc2.x(0)\n",
    "\n",
    "qc2.barrier(range(5))\n",
    "\n",
    "measv = QuantumCircuit(5, 1)\n",
    "measv.measure(4,0)\n",
    "\n",
    "circv = qc2+measv\n",
    "circv.draw('mpl')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "VW5CPwMEMAs5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'1': 1000}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#DO NOT RUN THIS CELL WITHOUT EDITING THE ABOVE ONE AS DESIRED\n",
    "#The following code will give you f(x) for the value of x you chose in the above cell\n",
    "backend_sim2 = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "job_sim2 = execute(circv, backend_sim2, shots=1000)\n",
    "\n",
    "result_sim2 = job_sim2.result()\n",
    "counts2 = result_sim2.get_counts(circv)\n",
    "print(counts2)\n",
    "plot_histogram(counts2)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Day 4 Deutsch Josza algorithm.ipynb",
   "provenance": []
  },
  "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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}