
class       a		:







							def __init__(						self  :  Any      ,				snake_case__  :  list[int] ):
								"""simple docstring"""







								__lowerCAmelCase         =							len(snake_case__ )
								__lowerCAmelCase         =							[0] * len_array

								if len_array > 0:
									__lowerCAmelCase         =							array[0]

								for i in range(1      ,				snake_case__ ):
									__lowerCAmelCase         =							self.prefix_sum[i - 1] + array[i]







							def       UpperCAmelCase__					(						self  :  Union[str, Any]      ,				snake_case__  :  int      ,				snake_case__  :  int ):
								"""simple docstring"""







								if start == 0:
									return self.prefix_sum[end]

								return self.prefix_sum[end] - self.prefix_sum[start - 1]







							def       UpperCAmelCase__					(						self  :  List[Any]      ,				snake_case__  :  int ):
								"""simple docstring"""







								__lowerCAmelCase         =							{0}
								for sum_item in self.prefix_sum:
									if sum_item - target_sum in sums:
										return True

									sums.add(snake_case__ )

								return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()








import numpy as np
import qiskit






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 8			,							UpperCamelCase:     int | None = None  ):






	"""simple docstring"""


	__lowerCAmelCase         =							np.random.default_rng(seed=UpperCamelCase  )

	# 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=UpperCamelCase  )
	# The set of states Alice will prepare.
	__lowerCAmelCase         =							rng.integers(2			,							size=UpperCamelCase  )
	# Measurement basis for Bob's qubits.
	__lowerCAmelCase         =							rng.integers(2			,							size=UpperCamelCase  )

	# Quantum Circuit to simulate BB84
	__lowerCAmelCase         =							qiskit.QuantumCircuit(UpperCamelCase			,							name="BB84"  )

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

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

	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(UpperCamelCase			,							UpperCamelCase			,							shots=1			,							seed_simulator=UpperCamelCase  )
	# Returns the result of measurement.
	__lowerCAmelCase         =							job.result().get_counts(UpperCamelCase  ).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(
	            UpperCamelCase			,							UpperCamelCase			,							UpperCamelCase  )
	        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(UpperCamelCase  ) >= key_len else gen_key.ljust(UpperCamelCase			,							"0"  )
	return key


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

					testmod()






