Illustrating Shor’s algorithm with Qiskit code

In this section, we present two Qiskit programs. One program illustrates, in a straightforward manner, the application of Qiskit’s QFT function. The other uses special tricks to construct a circuit that scales for large numbers. Neither program implements Shor’s algorithm in complete detail.

Testing the QFT

We begin this example with the required import statements:

from qiskit import QuantumCircuit, Aer, executefrom qiskit.circuit.library import QFT
from qiskit.tools.visualization import plot_histogram
import numpy as np

With public key 15 and coprime 7, we create a vector containing eight values of 7n % 15:

public_key = 15coprime = 7
#coprime = 11
vector = []
for i in range(8):
    vector.append(coprime**i % public_key)
norm = np.linalg.norm(vector)
statevector = vector / norm
print('vector:')
print(vector)
print()
print('statevector:')
print(statevector)

The...