
"""simple docstring"""

import numpy as np
import qiskit




def      lowercase__    (       lowerCAmelCase					:       int = 8			,					lowerCAmelCase					:       int | None = None			)			->   str:






    """simple docstring"""




    UpperCAmelCase          =       np.random.default_rng(seed=lowerCAmelCase			)

    # Roughly 25% of the qubits will contribute to the key.
    # So we take more than we need.
    UpperCAmelCase          =       6 * key_len
    # Measurement basis for Alice's qubits.
    UpperCAmelCase          =       rng.integers(2			,					size=lowerCAmelCase			)
    # The set of states Alice will prepare.
    UpperCAmelCase          =       rng.integers(2			,					size=lowerCAmelCase			)
    # Measurement basis for Bob's qubits.
    UpperCAmelCase          =       rng.integers(2			,					size=lowerCAmelCase			)

    # Quantum Circuit to simulate BB84
    UpperCAmelCase          =       qiskit.QuantumCircuit(lowerCAmelCase			,					name='BB84'			)

    # Alice prepares her qubits according to rules above.
    for index, _ in enumerate(lowerCAmelCase			):
        if alice_state[index] == 1:
            bbaa_circ.x(lowerCAmelCase			)
        if alice_basis[index] == 1:
            bbaa_circ.h(lowerCAmelCase			)
    bbaa_circ.barrier()

    # Bob measures the received qubits according to rules above.
    for index, _ in enumerate(lowerCAmelCase			):
        if bob_basis[index] == 1:
            bbaa_circ.h(lowerCAmelCase			)

    bbaa_circ.barrier()
    bbaa_circ.measure_all()

    # Simulate the quantum circuit.
    UpperCAmelCase          =       qiskit.Aer.get_backend('aer_simulator'			)
    # We only need to run one shot because the key is unique.
    # Multiple shots will produce the same key.
    UpperCAmelCase          =       qiskit.execute(lowerCAmelCase			,					lowerCAmelCase			,					shots=1			,					seed_simulator=lowerCAmelCase			)
    # Returns the result of measurement.
    UpperCAmelCase          =       job.result().get_counts(lowerCAmelCase			).most_frequent()

    # Extracting the generated key from the simulation results.
    # Only keep measurement results where Alice and Bob chose the same basis.
    UpperCAmelCase          =       ''.join(
        [
            result_bit
            for alice_basis_bit, bob_basis_bit, result_bit in zip(
                lowerCAmelCase			,					lowerCAmelCase			,					lowerCAmelCase			)
            if alice_basis_bit == bob_basis_bit
        ]			)

    # Get final key. Pad with 0 if too short, otherwise truncate.
    UpperCAmelCase          =       gen_key[:key_len] if len(lowerCAmelCase			) >= key_len else gen_key.ljust(lowerCAmelCase			,					'0'			)
    return key


if __name__ == "__main__":
   print(F'The generated key is : {bbaa(8, seed=0)}')
   from doctest import testmod

   testmod()





"""simple docstring"""

def      lowercase__    (       lowerCAmelCase					:       str			)			->   bool:






    """simple docstring"""




    UpperCAmelCase          =       [int(lowerCAmelCase			) for i in ip_va_address.split('.'			) if i.isdigit()]
    return len(lowerCAmelCase			) == 4 and all(0 <= int(lowerCAmelCase			) <= 254 for octet in octets			)


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE_            =    input().strip()
   SCREAMING_SNAKE_CASE_            =    '''valid''' if is_ip_va_address_valid(ip) else '''invalid'''
   print(F'{ip} is a {valid_or_invalid} IP v4 address.')



