


'''simple docstring'''
import qiskit







def       a_				(	UpperCamelCase_						,  UpperCamelCase_ ):
							A_			    =		qiskit.Aer.get_backend("aer_simulator" )

							A_			    =		qiskit.QuantumCircuit(4						,  2 )
							# encode inputs in qubits 0 and 1
							if bita == 1:
														qc_ha.x(0 )
							if bita == 1:
														qc_ha.x(1 )
							qc_ha.barrier()

							# use cnots to write XOR of the inputs on qubit2
							qc_ha.cx(0						,  2 )
							qc_ha.cx(1						,  2 )

							# use ccx / toffoli gate to write AND of the inputs on qubit3
							qc_ha.ccx(0						,  1						,  3 )
							qc_ha.barrier()

							# extract outputs
							qc_ha.measure(2						,  0 )  # extract XOR value
							qc_ha.measure(3						,  1 )  # extract AND value

							# Execute the circuit on the qasm simulator
							A_			    =		qiskit.execute(UpperCamelCase_						,  UpperCamelCase_						,  shots=1_0_0_0 )

							# Return the histogram data of the results of the experiment
							return job.result().get_counts(UpperCamelCase_ )


if __name__ == "__main__":
							__SCREAMING_SNAKE_CASE					:				Tuple									=		half_adder(1, 1)
							print(F"Half Adder Output Qubit Counts: {counts}")









'''simple docstring'''
def       a_				(	UpperCamelCase_ ):

							if length <= 0 or not isinstance(UpperCamelCase_						,  UpperCamelCase_ ):
														raise ValueError("Length must be a positive integer." )
							return [n * (2 * n - 1) for n in range(UpperCamelCase_ )]


if __name__ == "__main__":
							print(hexagonal_numbers(length=5))
							print(hexagonal_numbers(length=10))





