


import qiskit
from qiskit.providers import Backend





def lowerCamelCase    (    lowerCAmelCase       :			Dict	,	lowerCAmelCase       :			int	):





	"""simple docstring"""







	__magic_name__			,       __magic_name__ :					Union[str, Any]  			=  bin(lowerCAmelCase	)[2:], bin(lowerCAmelCase	)[2:]  # Remove leading '0b'

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

	# 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
	__magic_name__ :					Any  			=  qiskit.QuantumCircuit((len(lowerCAmelCase	) * 3) + 1	,	len(lowerCAmelCase	) + 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(lowerCAmelCase	)	):
		if x[::-1][i] == "1":
			circuit.x(lowerCAmelCase	)
	for j in range(len(lowerCAmelCase	)	):
		if y[::-1][j] == "1":
			circuit.x(len(lowerCAmelCase	) + j	)

	return circuit, x, y





def lowerCamelCase    (    lowerCAmelCase       :			Dict	,	lowerCAmelCase       :			Union[str, Any]	,	lowerCAmelCase       :			int	,	lowerCAmelCase       :			Tuple	,	lowerCAmelCase       :			Union[str, Any]	,	):





	"""simple docstring"""







	circuit.ccx(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)
	circuit.cx(lowerCAmelCase	,	lowerCAmelCase	)
	circuit.ccx(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)
	circuit.cx(lowerCAmelCase	,	lowerCAmelCase	)
	circuit.cx(lowerCAmelCase	,	lowerCAmelCase	)





def lowerCamelCase    (    lowerCAmelCase       :			Tuple	,	lowerCAmelCase       :			Union[str, Any]	,	lowerCAmelCase       :			Dict = qiskit.Aer.get_backend('aer_simulator'	)	,	):





	"""simple docstring"""







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

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

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

	__magic_name__ :					Union[str, Any]  			=  qiskit.execute(lowerCAmelCase	,	lowerCAmelCase	,	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()



'''simple docstring'''

from __future__ import annotations





def lowerCamelCase    (    lowerCAmelCase       :			list[int | float]	,	lowerCAmelCase       :			int	,	lowerCAmelCase       :			int	):





	"""simple docstring"""







	if len(lowerCAmelCase	) == 0:
		raise ValueError('find_min() arg is an empty sequence'	)
	if (
	    left >= len(lowerCAmelCase	)
	    or left < -len(lowerCAmelCase	)
	    or right >= len(lowerCAmelCase	)
	    or right < -len(lowerCAmelCase	)
	):
		raise IndexError('list index out of range'	)
	if left == right:
		return nums[left]
	__magic_name__ :					Tuple  			=  (left + right) >> 1  # the middle
	__magic_name__ :					str  			=  find_min(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)  # find min in range[left, mid]
	__magic_name__ :					Optional[Any]  			=  find_min(lowerCAmelCase	,	mid + 1	,	lowerCAmelCase	)  # find min in range[mid + 1, right]

	return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)