Lesson 7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e6ca7d2b-7b62-45a1-b94e-bf92c4103a52",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#Libraries needed to implement and simulate quantum circuits\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, qasm2, qasm3\n",
    "from qiskit_aer import Aer\n",
    "from qiskit.primitives import BackendSampler\n",
    "from qiskit.providers.basic_provider import BasicProvider # instead of BasicAer\n",
    "from qiskit.visualization import plot_histogram\n",
    "#Custem functions to simplify answers\n",
    "import Our_Qiskit_Functions as oq #a part of the library presented in arXiv:1903.04359v1.\n",
    "\n",
    "import numpy as np\n",
    "import math as m\n",
    "import scipy as sci\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Initialize backends simulators to visualize circuits\n",
    "S_simulator = Aer.backends(name='statevector_simulator')[0]\n",
    "M_simulator = Aer.backends(name='qasm_simulator')[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "320714a6-04e6-45c6-9bbf-294fbd74c212",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "____ Unitary Matrix ____\n",
      " [[-0.5        0.8660254]\n",
      " [-0.8660254 -0.5      ]]\n",
      "\n",
      " U |u> =  [ 0.61237244+0.35355339j -0.35355339+0.61237244j]\n",
      "e^{2πiφ} |u> =  [ 0.61237244+0.35355339j -0.35355339+0.61237244j]\n"
     ]
    }
   ],
   "source": [
    "alpha = 2*m.pi/3\n",
    "U = np.array([ [ np.cos(alpha) , np.sin(alpha) ],\n",
    "[ -np.sin(alpha) , np.cos(alpha) ] ])\n",
    "#---------------------------------------------------\n",
    "e = 0.5*(-1+m.sqrt(3)*1.0j)\n",
    "v = 1.0/m.sqrt(2)*np.array( [-1.0j,1] )\n",
    "#---------------------------------------------------\n",
    "print('____ Unitary Matrix ____\\n',U)\n",
    "print( '\\n U |u> = ',np.dot(U,v))\n",
    "print( 'e^{2\\u03C0i\\u03C6} |u> = ',e * v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55b36b52-3c15-4377-aafb-1f77b4891c17",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "____ Initial State ____\n",
      "1.0  |011>   \n",
      "\n",
      "____ After QFT† ____\n",
      "0.35355  |000>   -0.35355  |100>   0.35355j |010>   -0.35355j |110>   -0.25-0.25j |001>   0.25+0.25j |101>   0.25-0.25j |011>   -0.25+0.25j |111>   \n",
      "\n",
      " ____ QFT† Expression ____\n",
      "state:  [0, 0, 0]  phase:  (0.3536+0j)\n",
      "state:  [0, 0, 1]  phase:  (-0.25-0.25j)\n",
      "state:  [0, 1, 0]  phase:  0.3536j\n",
      "state:  [0, 1, 1]  phase:  (0.25-0.25j)\n",
      "state:  [1, 0, 0]  phase:  (-0.3536+0j)\n",
      "state:  [1, 0, 1]  phase:  (0.25+0.25j)\n",
      "state:  [1, 1, 0]  phase:  -0.3536j\n",
      "state:  [1, 1, 1]  phase:  (-0.25+0.25j)\n"
     ]
    }
   ],
   "source": [
    "q = QuantumRegister(3,name='q' )\n",
    "qc= QuantumCircuit(q,name='qc')\n",
    "#-------------------------------\n",
    "qc.x( q[1] )\n",
    "qc.x( q[2] )\n",
    "print('____ Initial State ____')\n",
    "oq.Wavefunction(qc)\n",
    "qc.swap( q[0], q[2] )\n",
    "oq.QFT_dgr( qc,q,3 )\n",
    "print('\\n____ After QFT\\u2020 ____')\n",
    "oq.Wavefunction(qc)\n",
    "#======================================\n",
    "print('\\n ____ QFT\\u2020 Expression ____')\n",
    "for k in np.arange( 8 ):\n",
    "    phase = 1.0/(m.sqrt(8)) * np.exp( -1.0j*m.pi*( (3*k)/4 ) )\n",
    "    print( 'state: ',oq.Binary(int(k),8),' phase: ',round(phase.real,4)+round(phase.imag,4)*1.0j )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8f335b40-b6d5-4732-8dd0-3e7e8cf39812",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta =  0.52  n =  3 \n",
      "---------------------------\n",
      "Probability:  0.0036  State:  [0, 0, 0]  Binary Decimal:  0.0\n",
      "Probability:  0.0041  State:  [0, 0, 1]  Binary Decimal:  0.125\n",
      "Probability:  0.0064  State:  [0, 1, 0]  Binary Decimal:  0.25\n",
      "Probability:  0.0187  State:  [0, 1, 1]  Binary Decimal:  0.375\n",
      "Probability:  0.9198  State:  [1, 0, 0]  Binary Decimal:  0.5\n",
      "Probability:  0.0346  State:  [1, 0, 1]  Binary Decimal:  0.625\n",
      "Probability:  0.0083  State:  [1, 1, 0]  Binary Decimal:  0.75\n",
      "Probability:  0.0045  State:  [1, 1, 1]  Binary Decimal:  0.875\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "theta = 0.52\n",
    "print('Theta = ',theta,' n = ',n,'\\n---------------------------')\n",
    "#===================\n",
    "state = []\n",
    "bstate = []\n",
    "bdec = []\n",
    "for i in range(2**n):\n",
    "    state.append(0)\n",
    "    bstate.append(oq.Binary(i,2**n))\n",
    "    bc = 0\n",
    "    for i2 in range(len(bstate[i])):\n",
    "        bc = bc + ( 1.0/(2**(i2+1)))*bstate[i][i2]\n",
    "    bdec.append(bc)\n",
    "#-------------------------------------------------------------\n",
    "for y in range(2**n):\n",
    "    for x in range(2**n):\n",
    "        state[y] = state[y] + 1.0/(2**n) * np.exp( (-2.0j*np.pi*x/(2**n))*(y-2**n*theta) )\n",
    "#--------------------------------------------------------------\n",
    "for j in np.arange(2**n):\n",
    "    print('Probability: ',round( abs(state[j])**2,4 ),' State: ',bstate[j],' Binary Decimal: ',bdec[j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0fe431fe-c3f0-4a21-aa03-49df39c19758",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = []\n",
    "y = []\n",
    "n = 3\n",
    "for k in np.arange( 1000 ):\n",
    "    if( k != 500 ):\n",
    "        phi = -5 + k/100.\n",
    "        x.append( phi )\n",
    "        y.append( 1/(2**(2*n)) * abs( (-1 + np.exp(2.0j*m.pi*phi) )/(-1 + np.exp(2.0j*m.pi*phi/(2**n))) )**2 )\n",
    "    else:\n",
    "        x.append(phi)\n",
    "        y.append(1)\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.axis([-5,5,0,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "758da712-c656-4275-9320-69884ec0b55c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta =  0.52  n =  4 \n",
      "---------------------------\n",
      "Probability:  0.0028  State:  [0, 0, 0, 0]  Binary Decimal:  0.0\n",
      "Probability:  0.0028  State:  [0, 0, 0, 1]  Binary Decimal:  0.0625\n",
      "Probability:  0.0031  State:  [0, 0, 1, 0]  Binary Decimal:  0.125\n",
      "Probability:  0.0037  State:  [0, 0, 1, 1]  Binary Decimal:  0.1875\n",
      "Probability:  0.0049  State:  [0, 1, 0, 0]  Binary Decimal:  0.25\n",
      "Probability:  0.0076  State:  [0, 1, 0, 1]  Binary Decimal:  0.3125\n",
      "Probability:  0.0144  State:  [0, 1, 1, 0]  Binary Decimal:  0.375\n",
      "Probability:  0.0424  State:  [0, 1, 1, 1]  Binary Decimal:  0.4375\n",
      "Probability:  0.7063  State:  [1, 0, 0, 0]  Binary Decimal:  0.5\n",
      "Probability:  0.1571  State:  [1, 0, 0, 1]  Binary Decimal:  0.5625\n",
      "Probability:  0.0265  State:  [1, 0, 1, 0]  Binary Decimal:  0.625\n",
      "Probability:  0.011  State:  [1, 0, 1, 1]  Binary Decimal:  0.6875\n",
      "Probability:  0.0064  State:  [1, 1, 0, 0]  Binary Decimal:  0.75\n",
      "Probability:  0.0044  State:  [1, 1, 0, 1]  Binary Decimal:  0.8125\n",
      "Probability:  0.0035  State:  [1, 1, 1, 0]  Binary Decimal:  0.875\n",
      "Probability:  0.003  State:  [1, 1, 1, 1]  Binary Decimal:  0.9375\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "theta = 0.52\n",
    "print('Theta = ',theta,' n = ',n,'\\n---------------------------')\n",
    "#===================\n",
    "state = []\n",
    "bstate = []\n",
    "bdec = []\n",
    "for i in range(2**n):\n",
    "    state.append(0)\n",
    "    bstate.append(oq.Binary(i,2**n))\n",
    "    bc = 0\n",
    "    for i2 in range(len(bstate[i])):\n",
    "        bc = bc + ( 1.0/(2**(i2+1)))*bstate[i][i2]\n",
    "    bdec.append(bc)\n",
    "#-------------------------------------------------------------\n",
    "for y in range(2**n):\n",
    "    for x in range(2**n):\n",
    "        state[y] = state[y] + 1.0/(2**n) * np.exp( (-2.0j*np.pi*x/(2**n))*(y-2**n*theta) )\n",
    "#--------------------------------------------------------------\n",
    "for j in np.arange(2**n):\n",
    "    print('Probability: ',round( abs(state[j])**2,4 ),' State: ',bstate[j],' Binary Decimal: ',bdec[j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b765539a-0aea-4ef6-a24a-207b6e7f5f7c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Most Probable State: |1000> Probability:  0.6975\n",
      "\n",
      "Corresponding Φ:  0.3256 \n",
      "\n",
      "Approximate θ:  0.52035\n"
     ]
    }
   ],
   "source": [
    "Prob = [ 0.0028,0.0028,0.0031,0.0037,0.0049,0.0076,0.0144,0.0424,0.7063,0.1571,0.0265,0.011,0.0064,0.0044,0.0035,0.003 ]\n",
    "Measured = np.zeros( len(Prob) )\n",
    "trials = 10000\n",
    "n = 4\n",
    "#======================================== Simulate measurements on the final system\n",
    "for t in range(trials):\n",
    "    M = random.random()\n",
    "    p = 0\n",
    "    for s in range( len(Prob) ):\n",
    "        if( p < M < (p + Prob[s]) ):\n",
    "            Measured[s] = Measured[s] + 1\n",
    "        p = p + Prob[s]\n",
    "#---------------------------------------\n",
    "MD = {}\n",
    "for i in range( len(Prob) ):\n",
    "    state = oq.Binary(int(i),2**n)\n",
    "    state_str = ''\n",
    "    for j in range(len(state)):\n",
    "        state_str = state_str+str(state[j])\n",
    "    MD[state_str] = int( Measured[i] )\n",
    "MP = oq.Most_Probable(MD,2)\n",
    "for mp in range(2):\n",
    "    MP[0][mp] = MP[0][mp]/trials\n",
    "#======================================== Compute phi using the most probable state\n",
    "phi,theta = oq.QPE_phi(MP)\n",
    "print('\\nMost Probable State: |'+str(MP[1][0])+'> Probability: ',round(MP[0][0],5))\n",
    "print('\\nCorresponding \\u03A6: ',phi,'\\n\\nApproximate \\u03B8: ',round(theta,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "65aa84c7-6058-4ad7-b0f9-b46d47e11750",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "___ After Control-U Operations ___\n",
      "0.35355  |000>|1>   0.30982+0.17033j |100>|1>   0.34245+0.08793j |010>|1>   0.25773+0.24202j |110>|1>   -0.35077-0.04431j |001>|1>   -0.28603-0.20781j |101>|1>   -0.32873-0.13015j |011>|1>   -0.22536-0.27242j |111>|1>   \n",
      " \n",
      "State:  [0, 0, 0]  Phase:  (0.35355+0j)\n",
      "State:  [0, 0, 1]  Phase:  (-0.35077-0.04431j)\n",
      "State:  [0, 1, 0]  Phase:  (0.34245+0.08793j)\n",
      "State:  [0, 1, 1]  Phase:  (-0.32873-0.13015j)\n",
      "State:  [1, 0, 0]  Phase:  (0.30982+0.17033j)\n",
      "State:  [1, 0, 1]  Phase:  (-0.28603-0.20781j)\n",
      "State:  [1, 1, 0]  Phase:  (0.25773+0.24202j)\n",
      "State:  [1, 1, 1]  Phase:  (-0.22536-0.27242j)\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "q1 = QuantumRegister(n,name='q1')\n",
    "q2 = QuantumRegister(1,name='q2')\n",
    "qc = QuantumCircuit(q1,q2,name='qc')\n",
    "theta = 0.52\n",
    "phi = 2*m.pi*theta\n",
    "#---------------------------------------------------\n",
    "for i in np.arange(n):\n",
    "    qc.h(q1[int(i)])\n",
    "qc.x( q2[0] )\n",
    "for j in np.arange(n):\n",
    "    for k in np.arange(2**j):\n",
    "        qc.cp( phi, q1[int(n-1-j)], q2[0] )\n",
    "print('\\n___ After Control-U Operations ___')\n",
    "oq.Wavefunction( qc, systems=[n,1] )\n",
    "#---------------------------------------------------\n",
    "Phases = [np.exp(4.0j*phi),np.exp(2.0j*phi),np.exp(1.0j*phi)]\n",
    "print(' ')\n",
    "for i in np.arange(8):\n",
    "    state = oq.Binary(int(i),8)\n",
    "    phase = m.sqrt(1/8)\n",
    "    for j in np.arange(3):\n",
    "        if(state[j]==1):\n",
    "            phase = phase*Phases[j]\n",
    "    print('State: ',state,' Phase: ',round(phase.real,5)+round(phase.imag,5)*1.0j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ad6d8429-5903-4ee7-a7bf-78ab09a66273",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "___ After QFT_dgr ___\n",
      "0.06024-0.10796j |000>|1>   0.18789+0.10484j |100>|1>   0.10682-0.03031j |010>|1>   -0.11217-0.39534j |110>|1>   0.08478-0.06705j |001>|1>   0.51766+0.65453j |101>|1>   0.13442+0.0157j |011>|1>   0.02037-0.17442j |111>|1>   \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 3\n",
    "q1 = QuantumRegister(n,name='q1')\n",
    "q2 = QuantumRegister(1,name='q2')\n",
    "c = ClassicalRegister(n,name='c')\n",
    "qc = QuantumCircuit(q1,q2,c,name='qc')\n",
    "theta = 0.666\n",
    "#---------------------------------------------------\n",
    "for i in np.arange(n):\n",
    "    qc.h(q1[int(i)])\n",
    "qc.x( q2[0] )\n",
    "phi = 2*m.pi*theta\n",
    "for j in np.arange(n):\n",
    "    for k in np.arange(2**j):\n",
    "        qc.cp( phi, q1[int(n-1-j)], q2[0] )\n",
    "print('\\n___ After QFT_dgr ___')\n",
    "oq.QFT_dgr( qc,q1,n,swap=True )\n",
    "oq.Wavefunction( qc, systems=[n,1] )\n",
    "#---------------------------------------------------\n",
    "qc.measure(q1,c)\n",
    "#results = oq.execute(qc, BasicProvider().get_backend('qasm_simulator'), shots=10000).result()\n",
    "results = oq.execute(qc, S_simulator, shots=10000).result()\n",
    "plot_histogram({key: value / 10000. for key, value in results.get_counts().items()})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "da2a93d7-c34c-44c7-b77e-6daec2fb0364",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phases:  [4.3515, 0.0808]\n",
      "\n",
      "Combined θ:  0.70542\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1 = 3\n",
    "n2 = 2\n",
    "phases = []\n",
    "for p in np.arange( n2 ):\n",
    "    phases.append( round( 2*m.pi*random.random(),4 ) )\n",
    "theta = round( sum(phases)/(2*m.pi),5)\n",
    "if( theta > 1 ):\n",
    "    theta = round( theta - m.floor(theta),5)\n",
    "#=================================\n",
    "q = QuantumRegister(n1,name='q')\n",
    "qu = QuantumRegister(n2,name='qu')\n",
    "c = ClassicalRegister(n1,name='c')\n",
    "qc = QuantumCircuit(q,qu,c,name='qc')\n",
    "#----------------------------------\n",
    "for i in np.arange(n1):\n",
    "    qc.h( q[int(i)] )\n",
    "for i2 in np.arange(n2):\n",
    "    qc.x( qu[int(i2)] )\n",
    "qc.barrier()\n",
    "for j in np.arange(n1):\n",
    "    for j2 in np.arange(2**j):\n",
    "        for j3 in np.arange(n2):\n",
    "            qc.cp( phases[int(j3)], q[int(n1-1-j)], qu[int(j3)] )\n",
    "    qc.barrier()\n",
    "\n",
    "oq.QFT_dgr( qc,q,n1,swap=True )\n",
    "#---------------------------------------------------\n",
    "print('Phases: ',phases)\n",
    "print('\\nCombined \\u03B8: ',theta)\n",
    "qc.measure(q,c)\n",
    "#results = execute(qc, BasicAer.get_backend('qasm_simulator'), shots=10000).result()\n",
    "results = oq.execute(qc, S_simulator, shots=10000).result()\n",
    "plot_histogram({key: value / 10000. for key, value in results.get_counts().items()})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c874e211-8d56-4236-857b-bd452c588fc6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      ┌───┐ ░                          ░                                     »\n",
      " q_0: ┤ H ├─░──────────────────────────░─────────────────────────────────────»\n",
      "      ├───┤ ░                          ░                                     »\n",
      " q_1: ┤ H ├─░──────────────────────────░──■───────────■───────────■──────────»\n",
      "      ├───┤ ░                          ░  │           │           │          »\n",
      " q_2: ┤ H ├─░──■───────────■───────────░──┼───────────┼───────────┼──────────»\n",
      "      ├───┤ ░  │P(4.3515)  │           ░  │P(4.3515)  │           │P(4.3515) »\n",
      "qu_0: ┤ X ├─░──■───────────┼───────────░──■───────────┼───────────■──────────»\n",
      "      ├───┤ ░              │P(0.0808)  ░              │P(0.0808)             »\n",
      "qu_1: ┤ X ├─░──────────────■───────────░──────────────■──────────────────────»\n",
      "      └───┘ ░                          ░                                     »\n",
      " c: 3/═══════════════════════════════════════════════════════════════════════»\n",
      "                                                                             »\n",
      "«                   ░                                                 »\n",
      "« q_0: ─────────────░──■───────────■───────────■───────────■──────────»\n",
      "«                   ░  │           │           │           │          »\n",
      "« q_1: ─■───────────░──┼───────────┼───────────┼───────────┼──────────»\n",
      "«       │           ░  │           │           │           │          »\n",
      "« q_2: ─┼───────────░──┼───────────┼───────────┼───────────┼──────────»\n",
      "«       │           ░  │P(4.3515)  │           │P(4.3515)  │          »\n",
      "«qu_0: ─┼───────────░──■───────────┼───────────■───────────┼──────────»\n",
      "«       │P(0.0808)  ░              │P(0.0808)              │P(0.0808) »\n",
      "«qu_1: ─■───────────░──────────────■───────────────────────■──────────»\n",
      "«                   ░                                                 »\n",
      "« c: 3/═══════════════════════════════════════════════════════════════»\n",
      "«                                                                     »\n",
      "«                                                       ░                   »\n",
      "« q_0: ─■───────────■───────────■───────────■───────────░──X────────────────»\n",
      "«       │           │           │           │           ░  │                »\n",
      "« q_1: ─┼───────────┼───────────┼───────────┼───────────░──┼───────■────────»\n",
      "«       │           │           │           │           ░  │ ┌───┐ │P(-π/2) »\n",
      "« q_2: ─┼───────────┼───────────┼───────────┼───────────░──X─┤ H ├─■────────»\n",
      "«       │P(4.3515)  │           │P(4.3515)  │           ░    └───┘          »\n",
      "«qu_0: ─■───────────┼───────────■───────────┼───────────░───────────────────»\n",
      "«                   │P(0.0808)              │P(0.0808)  ░                   »\n",
      "«qu_1: ─────────────■───────────────────────■───────────░───────────────────»\n",
      "«                                                       ░                   »\n",
      "« c: 3/═════════════════════════════════════════════════════════════════════»\n",
      "«                                                                           »\n",
      "«                               ┌───┐┌─┐\n",
      "« q_0: ──────■─────────■────────┤ H ├┤M├\n",
      "«      ┌───┐ │         │P(-π/2) └┬─┬┘└╥┘\n",
      "« q_1: ┤ H ├─┼─────────■─────────┤M├──╫─\n",
      "«      └───┘ │P(-π/4)    ┌─┐     └╥┘  ║ \n",
      "« q_2: ──────■───────────┤M├──────╫───╫─\n",
      "«                        └╥┘      ║   ║ \n",
      "«qu_0: ───────────────────╫───────╫───╫─\n",
      "«                         ║       ║   ║ \n",
      "«qu_1: ───────────────────╫───────╫───╫─\n",
      "«                         ║       ║   ║ \n",
      "« c: 3/═══════════════════╩═══════╩═══╩═\n",
      "«                         2       1   0 \n"
     ]
    }
   ],
   "source": [
    "print(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a5e20386-0cd9-4f88-8a12-801a85c4eaac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phases:  [4.4112, 5.7139, 6.2794]  Combined θ:  0.61086\n",
      "\n",
      "Most Probable State: |10100> Probability:  0.4843\n",
      "\n",
      "Second Most Probable: |10011> Probability:  0.3305\n",
      "\n",
      "Corresponding Φ:  0.4524 \n",
      "\n",
      "Approximate θ:  0.61086\n"
     ]
    }
   ],
   "source": [
    "n1 = 5\n",
    "n2 = 3\n",
    "phases = []\n",
    "trials = 10000\n",
    "for p in np.arange( n2 ):\n",
    "    phases.append( round( 2*m.pi*random.random(),4 ) )\n",
    "theta = round( sum(phases)/(2*m.pi),5)\n",
    "if( theta > 1 ):\n",
    "    theta = round( theta - m.floor(theta),5)\n",
    "#================================================================== QPE Circuit\n",
    "q = QuantumRegister(n1,name='q')\n",
    "qu = QuantumRegister(n2,name='qu')\n",
    "c = ClassicalRegister(n1,name='c')\n",
    "qc = QuantumCircuit(q,qu,c,name='qc')\n",
    "#-------------------------------------\n",
    "for i in np.arange(n1):\n",
    "    qc.h( q[int(i)] )\n",
    "for i2 in np.arange(n2):\n",
    "    qc.x( qu[int(i2)] )\n",
    "for j in np.arange(n1):\n",
    "    for j2 in np.arange(2**j):\n",
    "        for j3 in np.arange(n2):\n",
    "            qc.cp( phases[int(j3)], q[int(n1-1-j)], qu[int(j3)] )\n",
    "oq.QFT_dgr( qc,q,n1,swap=True )\n",
    "#==================================================================\n",
    "print('Phases: ',phases,' Combined \\u03B8: ',theta)\n",
    "qc.measure(q,c)\n",
    "M = oq.Measurement( qc,systems=[n1,n2],shots=trials,return_M=True,print_M=False )\n",
    "MP = oq.Most_Probable(M,2)\n",
    "for mp in np.arange(2):\n",
    "    MP[0][mp] = MP[0][mp]/trials\n",
    "phi,theta = oq.QPE_phi(MP)\n",
    "print('\\nMost Probable State: |'+str(MP[1][0])+'> Probability: ',round(MP[0][0],5))\n",
    "print('\\nSecond Most Probable: |'+str(MP[1][1])+'> Probability: ',round(MP[0][1],5))\n",
    "print('\\nCorresponding \\u03A6: ',phi,'\\n\\nApproximate \\u03B8: ',round(theta,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e0b5cb01-3cdc-4021-844b-a3677449d827",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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