from qiskit import Aer, QuantumCircuit, transpile, assemble, execute
from math import gcd
from numpy.random import randint

def a_mod_N(a, power, N, quantum_reg):
    # Function to perform modular exponentiation using quantum gates
    circuit = QuantumCircuit(quantum_reg, 1)
    circuit.x(quantum_reg[0])  # Set the last qubit to |1>
    circuit.h(quantum_reg[1]).c_if(quantum_reg[1], 1)  # Conditional H gate
    circuit.h(quantum_reg[0]).c_if(quantum_reg[0], 1)  # Conditional H gate
    circuit.x(quantum_reg[0]).c_if(quantum_reg[0], 1)  # Conditional X gate
    circuit.cx(quantum_reg[0], quantum_reg[1])  # Conditional CX gate
    circuit.x(quantum_reg[0]).c_if(quantum_reg[0], 1)  # Conditional X gate
    circuit.x(quantum_reg[1]).c_if(quantum_reg[1], 1)  # Conditional X gate
    circuit.measure(quantum_reg[1], 0)  # Measure the result

    # Execute the quantum circuit on the simulator
    backend = Aer.get_backend('qasm_simulator')
    result = execute(circuit, backend, shots=1).result()
    outcome = int(result.get_counts().popitem()[0])

    return outcome

def shors_algorithm_quantum(N):
    a = randint(2, N)  # Choose a random integer a between 2 and N-1

    # Check if the chosen 'a' shares a non-trivial factor with N
    if gcd(a, N) > 1:
        return gcd(a, N)

    r = 2  # Initialize a guess for the period
    quantum_reg = QuantumCircuit(4, 2)  # Quantum register with 4 qubits

    # Modify the a_mod_N function to use the quantum version
    while True:
        outcome = a_mod_N(a, r, N, quantum_reg)
        if outcome == 1:
            break
        r += 1

    # ... (continue with the rest of the code)

# Test Shor's algorithm with a sample number N
N = 21
result = shors_algorithm_quantum(N)
print(f"Non-trivial factor of {N}: {result}")
