shor_algorithm_quantum_qiskit.py

# -*- coding: utf-8 -*-

"""
    Programa desarrollado por el Licenciado César Cordero Rodríguez.
    Bajo licencia GPLv3.
    Puede ser modificado, copiado y distribuido.
    Se desarrolló con fines educativos.
"""

#Read more here: https://learn.qiskit.org/course/ch-algorithms/shors-algorithm

#TO INSTALL:
#pip3 install qiskit
#pip3 install matplotlib
#pip3 install pylatexenc
#pip3 install numpy pandas

import matplotlib.pyplot as plt
import numpy as np
from qiskit import QuantumCircuit, BasicAer, Aer, transpile
from qiskit.visualization import plot_histogram
from math import gcd
from numpy.random import randint
import pandas as pd
from fractions import Fraction
print("Imports Successful")

def c_amod15(a, power):
    """Controlled multiplication by a mod 15"""
    if a not in [2,4,7,8,11,13]:
        raise ValueError("'a' must be 2,4,7,8,11 or 13")
    U = QuantumCircuit(4)
    for _iteration in range(power):
        if a in [2,13]:
            U.swap(2,3)
            U.swap(1,2)
            U.swap(0,1)
        if a in [7,8]:
            U.swap(0,1)
            U.swap(1,2)
            U.swap(2,3)
        if a in [4, 11]:
            U.swap(1,3)
            U.swap(0,2)
        if a in [7,11,13]:
            for q in range(4):
                U.x(q)
    U = U.to_gate()
    U.name = f"{a}^{power} mod 15"
    c_U = U.control()
    return c_U

def qft_dagger(n):
    """n-qubit QFTdagger the first n qubits in circ"""
    qc = QuantumCircuit(n)
    # Don't forget the Swaps!
    for qubit in range(n//2):
        qc.swap(qubit, n-qubit-1)
    for j in range(n):
        for m in range(j):
            qc.cp(-np.pi/float(2**(j-m)), m, j)
        qc.h(j)
    qc.name = "QFT†"
    return qc

# Specify variables
N_COUNT = 8  # number of counting qubits
a = 7

# Create QuantumCircuit with N_COUNT counting qubits
# plus 4 qubits for U to act on
qc = QuantumCircuit(N_COUNT + 4, N_COUNT)

# Initialize counting qubits
# in state |+>
for q in range(N_COUNT):
    qc.h(q)

# And auxiliary register in state |1>
qc.x(N_COUNT)

# Do controlled-U operations
for q in range(N_COUNT):
    qc.append(c_amod15(a, 2**q),
             [q] + [i+N_COUNT for i in range(4)])

# Do inverse-QFT
qc.append(qft_dagger(N_COUNT), range(N_COUNT))

# Measure circuit
qc.measure(range(N_COUNT), range(N_COUNT))
qc.draw(fold=-1)  # -1 means 'do not fold'

aer_sim = Aer.get_backend('aer_simulator')
t_qc = transpile(qc, aer_sim)
counts = aer_sim.run(t_qc).result().get_counts()
plot_histogram(counts)

rows, measured_phases = [], []
for output in counts:
    decimal = int(output, 2)  # Convert (base 2) string to decimal
    phase = decimal/(2**N_COUNT)  # Find corresponding eigenvalue
    measured_phases.append(phase)
    # Add these values to the rows in our table:
    rows.append([f"{output}(bin) = {decimal:>3}(dec)",
                 f"{decimal}/{2**N_COUNT} = {phase:.2f}"])
# Print the rows in a table
headers=["Register Output", "Phase"]
df = pd.DataFrame(rows, columns=headers)
print(df)

plt.show()

def a2jmodN(a, j, N):
    """Compute a^{2^j} (mod N) by repeated squaring"""
    for _ in range(j):
        a = np.mod(a**2, N)
    return a

print(a2jmodN(7, 2049, 53))

N = 15

np.random.seed(1) # This is to make sure we get reproduceable results
a = randint(2, N)
print(a)

from math import gcd # greatest common divisor
gcd(a, N)

def qpe_amod15(a):
    """Performs quantum phase estimation on the operation a*r mod 15.
    Args:
        a (int): This is 'a' in a*r mod 15
    Returns:
        float: Estimate of the phase
    """
    N_COUNT = 8
    qc = QuantumCircuit(4+N_COUNT, N_COUNT)
    for q in range(N_COUNT):
        qc.h(q)     # Initialize counting qubits in state |+>
    qc.x(3+N_COUNT) # And auxiliary register in state |1>
    for q in range(N_COUNT): # Do controlled-U operations
        qc.append(c_amod15(a, 2**q),
                 [q] + [i+N_COUNT for i in range(4)])
    qc.append(qft_dagger(N_COUNT), range(N_COUNT)) # Do inverse-QFT
    qc.measure(range(N_COUNT), range(N_COUNT))
    # Simulate Results
    aer_sim = Aer.get_backend('aer_simulator')
    # `memory=True` tells the backend to save each measurement in a list
    job = aer_sim.run(transpile(qc, aer_sim), shots=1, memory=True)
    readings = job.result().get_memory()
    print("Register Reading: " + readings[0])
    phase = int(readings[0],2)/(2**N_COUNT)
    print(f"Corresponding Phase: {phase}")
    return phase

phase = qpe_amod15(a) # Phase = s/r
Fraction(phase).limit_denominator(15)

frac = Fraction(phase).limit_denominator(15)
s, r = frac.numerator, frac.denominator
print(r)

guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]
print(guesses)

a = 7
FACTOR_FOUND = False
ATTEMPT = 0
while not FACTOR_FOUND:
    ATTEMPT += 1
    print(f"\nATTEMPT {ATTEMPT}:")
    phase = qpe_amod15(a) # Phase = s/r
    frac = Fraction(phase).limit_denominator(N)
    r = frac.denominator
    print(f"Result: r = {r}")
    if phase != 0:
        # Guesses for factors are gcd(x^{r/2} ±1 , 15)
        guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]
        print(f"Guessed Factors: {guesses[0]} and {guesses[1]}")
        for guess in guesses:
            if guess not in [1,N] and (N % guess) == 0:
                # Guess is a factor!
                print("*** Non-trivial factor found: {guess} ***")
                FACTOR_FOUND = True