Qiskit/QiskitShorAequal11.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from qiskit import Aer\n",
    "from qiskit import execute\n",
    "from qiskit.tools.visualization import matplotlib_circuit_drawer as drawer\n",
    "from qiskit import IBMQ\n",
    "from qiskit import compile\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "\n",
    "my_style = {'cregbundle': True}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will try to implement Shor's algorithm for a simple example using Qiskit. Shor's algorithm applies to composite numbers M which are odd and not a prime power. So the smallest meaningful example is M=15.\n",
    "\n",
    "In our implementation, we will actually cheat - we will use knowledge about the factors of M at some points that we would not have for a real example with a large integer M. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start, let us recall that the algorithm picks a number a relatively prime to M and calculates the period of a module M. We will use a = 11. Let us manually determine its period first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a**2:  1\n"
     ]
    }
   ],
   "source": [
    "M = 15\n",
    "a = 11\n",
    "print(\"a**2: \", a*a % M)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the period r is two. How would we find the period using a quantum circuit? For our implementation, it turns out to be most useful to describe Shor's algorithm in terms of the quantum phase estimation. In this description, we apply the quantum phase estimation algorithm to the state $|1 \\rangle$. So let us see how a circuit for this QPE looks like.\n",
    "\n",
    "We start with a very simple version - a one-qubit QPE. Recall that in the QPE algorithm relevant for period finding, we have a primary register p holding the initial state - $|1 \\rangle$ in our case - and an working register w with t qubits (in our case, we start with t = 1). The circuit acts with a Hadamard on each qubit of the working register and prepares the primary register in the state $|1 \\rangle$. We then apply a sequence of t controlled $U^k$ operations, where $U$ is the unitary operator on the primary register given by multiplication with a, i.e. \n",
    "$$\n",
    "|x \\rangle \\mapsto |a x \\rangle\n",
    "$$\n",
    "Thus the first thing that we need is a circuit implementing this controlled operation. However, we are lucky - we only need to implement this for the input $|1 \\rangle$. Then the result is $|11 \\rangle$, and our resulting circuit is very simple - we simply need to toggle qubits 1 and 3 conditional on the working register"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def oneQbitCircuit(p, w, c):\n",
    "    circuit = QuantumCircuit(w,p, c)\n",
    "    # Prepare initial state 1 in primary register\n",
    "    circuit.x(p[0])\n",
    "    circuit.barrier(p)\n",
    "    circuit.barrier(w)\n",
    "    \n",
    "    # Add Hadamard gate to working register\n",
    "    circuit.h(w[0])\n",
    "    # Add conditional multiplication by a to primary register\n",
    "    circuit.cx(w[0], p[1])\n",
    "    circuit.cx(w[0], p[3])\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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JEtxxxx0yVCiOX1FBRG5hs9nw+OOPY/LkyXjrrbcwZ84c7NixA2azGQBw+PBhbN26FWlp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\n",
      "text/plain": [
       "<Figure size 421.4x379.26 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = QuantumRegister(4,\"p\")\n",
    "w = QuantumRegister(1,\"w\")\n",
    "c = ClassicalRegister(1, \"c\")\n",
    "circuit = oneQbitCircuit(p,w,c)\n",
    "drawer(circuit, style=my_style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see what state we expect here. According to the general logic of the QPE circuit, we should be in the state\n",
    "$$\n",
    "\\frac{1}{\\sqrt{2}} \\sum_{s=0}^1 |a^s \\rangle |s \\rangle  =\\frac{1}{\\sqrt{2}} (  |1 \\rangle |0\\rangle + \n",
    "|11\\rangle) |1 \\rangle  = \\frac{1}{\\sqrt{2}} ( |2 \\rangle + \n",
    "|23\\rangle) \n",
    "$$\n",
    "Here we follow the Qiskit convention and write the primary register first, yielding the most significant bits. Let us test this using the state vector simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00000000+0.j,  0.00000000+0.j,  0.70710678+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.70710678+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,\n",
       "        0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j,  0.00000000+0.j])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(circuit, backend)\n",
    "job.result().get_statevector()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice, this is what we expected. Let us now see how we can extend this to two qubits. For that purpose, we need to add a conditional version of $a^2$. But this is trivial, as $a^2$ is already 1 module 15. So our two-qubit circuit is simply the same as the one qubit circuit, with one additional working qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def twoQbitCircuit(p, w, c):\n",
    "    circuit = QuantumCircuit(w,p, c)\n",
    "    # Prepare initial state 1 in primary register\n",
    "    circuit.x(p[0])\n",
    "    circuit.barrier(p)\n",
    "    circuit.barrier(w)\n",
    "    \n",
    "    # Add Hadamard gate to working register\n",
    "    circuit.h(w[0])\n",
    "    circuit.h(w[1])\n",
    "    # Add conditional multiplication by a to primary register\n",
    "    circuit.cx(w[0], p[1])\n",
    "    circuit.cx(w[0], p[3])\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DbDbL2KH/+eqrrxAREYG3337bOfb1119j7ty5+PnPf46hoSEZuyPyrjEdmEajEeXl5ait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\n",
      "text/plain": [
       "<Figure size 421.4x439.46 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = QuantumRegister(4,\"p\")\n",
    "w = QuantumRegister(2,\"w\")\n",
    "c = ClassicalRegister(3, \"c\")\n",
    "circuit = twoQbitCircuit(p,w,c)\n",
    "drawer(circuit, style=my_style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us again test this. We expect the following four basis vectors to show up\n",
    "$$\n",
    "|1\\rangle |0 \\rangle = |4\\rangle\n",
    "$$\n",
    "$$\n",
    "|11\\rangle |1 \\rangle = |45\\rangle\n",
    "$$\n",
    "$$\n",
    "|1\\rangle |2 \\rangle = |6\\rangle\n",
    "$$\n",
    "$$\n",
    "|11\\rangle |3 \\rangle = |47\\rangle\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| 4 > --->  (0.5+0j)\n",
      "| 6 > --->  (0.5+0j)\n",
      "| 45 > --->  (0.5+0j)\n",
      "| 47 > --->  (0.5+0j)\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(circuit, backend)\n",
    "state = np.around(job.result().get_statevector(), 2)\n",
    "for i in range(2**6):\n",
    "    if (state[i] != 0):\n",
    "        print(\"|\",i,\"> ---> \", state[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the last circuit we need is multiplication by $a^4$ modulo 15. But this is again one, so the circuit is the identity. Therefore our three qubit circuit is identical to our two qubit circuit, just with one more qubit in the working register. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def threeQbitCircuit(p, w, c):\n",
    "    circuit = QuantumCircuit(w,p, c)\n",
    "    # Prepare initial state 1 in primary register\n",
    "    circuit.x(p[0])\n",
    "    circuit.barrier(p)\n",
    "    circuit.barrier(w)\n",
    "    \n",
    "    # Add Hadamard gates to working register\n",
    "    circuit.h(w[0])\n",
    "    circuit.h(w[1])\n",
    "    circuit.h(w[2])\n",
    "    # Add conditional multiplication by a to primary register\n",
    "    circuit.cx(w[0], p[1])\n",
    "    circuit.cx(w[0], p[3])\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JHpgTJkzAli1bYLVa8fXXX2P9+vUYMGCA22v9/ve/R0tLi1t/R6FQ4KWXXkJH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\nMTCJiAQxMImIBP0/V8UmIIiu6I8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 421.4x499.66 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = QuantumRegister(4,\"p\")\n",
    "w = QuantumRegister(3,\"w\")\n",
    "c = ClassicalRegister(3, \"c\")\n",
    "circuit = threeQbitCircuit(p,w,c)\n",
    "drawer(circuit, style=my_style)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| 8 > = | 1 >| 0 >\n",
      "| 89 > = | 11 >| 1 >\n",
      "| 10 > = | 1 >| 2 >\n",
      "| 91 > = | 11 >| 3 >\n",
      "| 12 > = | 1 >| 4 >\n",
      "| 93 > = | 11 >| 5 >\n",
      "| 14 > = | 1 >| 6 >\n",
      "| 95 > = | 11 >| 7 >\n"
     ]
    }
   ],
   "source": [
    "#\n",
    "# Print out expected amplitudes up to normalisation\n",
    "# \n",
    "for s in range(2**3):\n",
    "    x = a**s % 15\n",
    "    print(\"|\", x*8 + s, \"> = |\",x,\">|\", s,\">\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| 8 > = | 1 >| 0 > --->  (0.35+0j)\n",
      "| 10 > = | 1 >| 2 > --->  (0.35+0j)\n",
      "| 12 > = | 1 >| 4 > --->  (0.35+0j)\n",
      "| 14 > = | 1 >| 6 > --->  (0.35+0j)\n",
      "| 89 > = | 11 >| 1 > --->  (0.35+0j)\n",
      "| 91 > = | 11 >| 3 > --->  (0.35+0j)\n",
      "| 93 > = | 11 >| 5 > --->  (0.35+0j)\n",
      "| 95 > = | 11 >| 7 > --->  (0.35+0j)\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(circuit, backend)\n",
    "state = np.around(job.result().get_statevector(), 2)\n",
    "for i in range(2**7):\n",
    "    if (state[i] != 0):\n",
    "        print(\"|\",i,\"> = |\", i // 8, \">|\", i % 8,\"> ---> \", state[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our circuit seems to work fine. Let us now combine this into one circuit with the QFT and see what we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nBitQFT(q,c,n=3):\n",
    "    circuit = QuantumCircuit(q,c)\n",
    "    #\n",
    "    # We start with the most significant bit\n",
    "    #\n",
    "    for k in range(n):\n",
    "        j = n - k\n",
    "        # Add the Hadamard to qubit j-1\n",
    "        circuit.h(q[j-1])\n",
    "        #\n",
    "        # there is one conditional rotation for\n",
    "        # each qubit with lower significance\n",
    "        for i in reversed(range(j-1)):\n",
    "            circuit.cu1(2*np.pi/2**(j-i),q[i], q[j-1])\n",
    "    #\n",
    "    # Finally we need to swap qubits\n",
    "    #\n",
    "    for i in range(n//2):\n",
    "        circuit.swap(q[i], q[n-i-1])\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._instructionset.InstructionSet at 0x7fbbc1b6f8d0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = threeQbitCircuit(p,w,c) + nBitQFT(w,c,n=3)\n",
    "circuit.barrier(w)\n",
    "circuit.measure(w,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dO1ZlZWUufRITE5WVlWVRhfCkbt266fnnn3dZZhiGAgMDtXHjRouqapiv1b17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\n",
      "text/plain": [
       "<Figure size 1023.4x499.66 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawer(circuit, style=my_style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we run this, let us try to understand what output we expect. The value in the working register after a measurement will be a multiple or $2^n$ / r. In our case, r=2 and n=3, so the output is a multiple of four. Thus we expect peaks at 000 and 100. Let us see whether this is what we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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erQTEXGByt7FPALf3XTmSpHbRU7vv6/hd2+0hwOyIWEjRmXU08EHgtn6tUJJUi54uUi/r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\nQpJUyoCQJJX6/5zSQXN0dnr5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator') \n",
    "job = execute(circuit, backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before running this on real hardware, let us try to optimize the circuit a bit. For that purpose, we combine the two subcircuits into one function. We can then apply a few optimizations. First, we skip the final swap gates in the QFT circuit - this will change our expected output from 100 to 001, but we can keep track of this manually when setting up the measurement. Next, we have two Hadamard gates on w[2] that cancel at that we can therefore remove. And the Pauli X gate on p[0] is never really used and can be dropped. We then run this once more on the simulator to verify that our circuit still works, and finally do a run on reald hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def shorAlgorithm(n=3):\n",
    "    # Create registers and circuit\n",
    "    p = QuantumRegister(4,\"p\")\n",
    "    w = QuantumRegister(n,\"w\")\n",
    "    c = ClassicalRegister(n, \"c\")\n",
    "    circuit = QuantumCircuit(w,p,c)\n",
    "    # Add Hadamard gates to working register\n",
    "    circuit.h(w[0])\n",
    "    circuit.h(w[1])\n",
    "    # Add conditional multiplication by a to primary register\n",
    "    circuit.cx(w[0], p[1])\n",
    "    circuit.cx(w[0], p[3])\n",
    "    #\n",
    "    # Now build the QFT part. We start with the most significant bit\n",
    "    #\n",
    "    for k in range(n):\n",
    "        j = n - k\n",
    "        # Add the Hadamard to qubit j-1\n",
    "        if (j - 1) != 2:\n",
    "            circuit.h(w[j-1])\n",
    "        #\n",
    "        # there is one conditional rotation for\n",
    "        # each qubit with lower significance\n",
    "        for i in reversed(range(j-1)):\n",
    "            circuit.cu1(2*np.pi/2**(j-i),w[i], w[j-1])\n",
    "    #\n",
    "    # and add the measurements\n",
    "    #\n",
    "    circuit.barrier(w)\n",
    "    circuit.measure(w[0],c[2])\n",
    "    circuit.measure(w[2], c[0])\n",
    "    circuit.measure(w[1], c[1])\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "circuit = shorAlgorithm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RUeX32tvbW6tWrXJjVUDNnTt3TlOnTlVISIjS0tLk7+9f49dNmjRJb7/9tlas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\neDbYYHSsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 842.8x499.66 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawer(circuit, style=my_style)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PklSTVsYgLqdYsntcZh5IsRbTAnzcqCQNS60ExBTgwsxMgMa/FwGT21GYJKlerQTEUmBu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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator') \n",
    "job = execute(circuit, backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LnEuXLmXo0KEMHjyYL3zhC6xdu7bFOTNNnO64PwQmuvsQ4JPo+xRgZZskE5G0VF1dzdSp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\nYlHhEBGRWFQ4REQklv8PBWiKwwZfNvcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "IBMQ.load_accounts()\n",
    "backend = IBMQ.get_backend('ibmq_16_melbourne') \n",
    "job = execute(circuit, backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}