


import numpy as np





def   _lowerCAmelCase				(   UpperCamelCase__:     int							,					UpperCamelCase__:     Dict							,					UpperCamelCase__:     str							,					UpperCamelCase__:     Tuple							,					UpperCamelCase__:     str						) ->   List[Any]:





	"""simple docstring"""







	A								=				int(np.ceil((x_end - xa) / h						)						)
	A								=				np.zeros((n + 1,)						)
	A								=				ya
	A								=				xa

	for k in range(UpperCamelCase__						):
		A								=				f(UpperCamelCase__							,					y[k]						)
		A								=				f(x + 0.5 * h							,					y[k] + 0.5 * h * ka						)
		A								=				f(x + 0.5 * h							,					y[k] + 0.5 * h * ka						)
		A								=				f(x + h							,					y[k] + h * ka						)
		A								=				y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
		x += h

	return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()







import qiskit





def   _lowerCAmelCase				(   UpperCamelCase__:     int = 2						) ->   qiskit.result.counts.Counts:





	"""simple docstring"""







	A								=				qubits

	# Using Aer's simulator
	A								=				qiskit.Aer.get_backend("""aer_simulator"""						)

	# Creating a Quantum Circuit acting on the q register
	A								=				qiskit.QuantumCircuit(UpperCamelCase__							,					UpperCamelCase__						)

	# Adding a H gate on qubit 0 (now q0 in superposition)
	circuit.h(0						)

	for i in range(1							,					UpperCamelCase__						):
		# Adding CX (CNOT) gate
		circuit.cx(i - 1							,					UpperCamelCase__						)

	# Mapping the quantum measurement to the classical bits
	circuit.measure(list(range(UpperCamelCase__						)						)							,					list(range(UpperCamelCase__						)						)						)

	# Now measuring any one qubit would affect other qubits to collapse
	# their super position and have same state as the measured one.

	# Executing the circuit on the simulator
	A								=				qiskit.execute(UpperCamelCase__							,					UpperCamelCase__							,					shots=10_00						)

	return job.result().get_counts(UpperCamelCase__						)


if __name__ == "__main__":
				print(f'''Total count for various states are: {quantum_entanglement(3)}''')



