


'''simple docstring'''






def       _snake_case     (  A				,					A				,					A )		->					float:
							lowerCAmelCase__      =			(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
							# formula for sum of series
							return total


def       _snake_case     (  )		->					List[str]:
							print(sum_of_series(1				,					1				,					10 ) )


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''






import numpy as np
import qiskit


def       _snake_case     (  A = 8				,					A = None )		->					str:
							lowerCAmelCase__      =			np.random.default_rng(seed=A )

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

							# Quantum Circuit to simulate BB84
							lowerCAmelCase__      =			qiskit.QuantumCircuit(A				,					name='''BB84''' )

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

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

							bbaa_circ.barrier()
							bbaa_circ.measure_all()

							# Simulate the quantum circuit.
							lowerCAmelCase__      =			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.
							lowerCAmelCase__      =			qiskit.execute(A				,					A				,					shots=1				,					seed_simulator=A )
							# Returns the result of measurement.
							lowerCAmelCase__      =			job.result().get_counts(A ).most_frequent()

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

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


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

		testmod()