






'''simple docstring'''





import qiskit
from qiskit.providers import Backend
def   lowerCamelCase      (		a_				,		a_			)			->    tuple[qiskit.QuantumCircuit, str, str]:
							lowerCAmelCase_		,     lowerCAmelCase_       		=  bin(a_			)[2:], bin(a_			)[2:]  # Remove leading '0b'

							# Ensure that both strings are of the same length
							if len(a_			) > len(a_			):
														lowerCAmelCase_       		=  y.zfill(len(a_			)			)
							else:
														lowerCAmelCase_       		=  x.zfill(len(a_			)			)

							# We need (3 * number of bits in the larger number)+1 qBits
							# The second parameter is the number of classical registers, to measure the result
							lowerCAmelCase_       		=  qiskit.QuantumCircuit((len(a_			) * 3) + 1				,		len(a_			) + 1			)

							# We are essentially "not-ing" the bits that are 1
							# Reversed because it's easier to perform ops on more significant bits
							for i in range(len(a_			)			):
														if x[::-1][i] == "1":
																					circuit.x(a_			)
							for j in range(len(a_			)			):
														if y[::-1][j] == "1":
																					circuit.x(len(a_			) + j			)

							return circuit, x, y
def   lowerCamelCase      (		a_				,		a_				,		a_				,		a_				,		a_				,		)			->    int:
							circuit.ccx(a_				,		a_				,		a_			)
							circuit.cx(a_				,		a_			)
							circuit.ccx(a_				,		a_				,		a_			)
							circuit.cx(a_				,		a_			)
							circuit.cx(a_				,		a_			)
def   lowerCamelCase      (		a_				,		a_				,		a_ = qiskit.Aer.get_backend('aer_simulator'			)				,		)			->    int:

							if vala < 0 or vala < 0:
														raise ValueError('Both Integers must be positive!'			)

							# Store the Integers
							lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_       		=  store_two_classics(a_				,		a_			)
							for i in range(len(a_			)			):
														full_adder(a_				,		a_				,		len(a_			) + i				,		len(a_			) + len(a_			) + i				,		len(a_			) + len(a_			) + i + 1			)
														circuit.barrier()  # Optional, just for aesthetics

							# Measure the resultant qBits
							for i in range(len(a_			) + 1			):
														circuit.measure([(len(a_			) * 2) + i]				,		[i]			)

							lowerCAmelCase_       		=  qiskit.execute(a_				,		a_				,		shots=1			).result()

							# The result is in binary. Convert it back to int
							return int(list(res.get_counts()			)[0]				,		2			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()











def   lowerCamelCase      (		a_ = 4_000_000			)			->    int:

							if n <= 1:
														return 0
							lowerCAmelCase_       		=  0
							lowerCAmelCase_       		=  2
							lowerCAmelCase_       		=  0
							while 4 * b + a <= n:
														lowerCAmelCase_		,     lowerCAmelCase_       		=  b, 4 * b + a
														count += a
							return count + b


if __name__ == "__main__":
		print(f'''{solution() = }''')



