"""simple docstring"""





import qiskit



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    qiskit.result.counts.Counts:
							_SCREAMING_SNAKE_CASE		:						Any			  =    qiskit.Aer.get_backend("""aer_simulator"""  )

							# Create a Quantum Circuit acting on the q register
							_SCREAMING_SNAKE_CASE		:						List[str]			  =    qiskit.QuantumCircuit(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )

							# Map the quantum measurement to the classical bits
							circuit.measure([0]     ,	[0]  )

							# Execute the circuit on the simulator
							_SCREAMING_SNAKE_CASE		:						Any			  =    qiskit.execute(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	shots=1_000  )

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


if __name__ == "__main__":
			print(F"Total count for various states are: {single_qubit_measure(1, 1)}")



"""simple docstring"""





from typing import Any

import numpy as np



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    bool:
							return np.array_equal(__SCREAMING_SNAKE_CASE     ,	matrix.conjugate().T  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    Any:
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v.conjugate().T
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v_star.dot(__SCREAMING_SNAKE_CASE  )
							assert isinstance(__SCREAMING_SNAKE_CASE     ,	np.ndarray  )
							return (v_star_dot.dot(__SCREAMING_SNAKE_CASE  )) / (v_star.dot(__SCREAMING_SNAKE_CASE  ))



def      lowerCamelCase_()->    None:
							_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]  )
							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1], [2], [3]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							print(rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )  )

							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							assert rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  ) == float(3  )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			tests()


