






from __future__ import annotations

class     _SCREAMING_SNAKE_CASE       :





	def __init__(		self				:					List[Any] ,  __lowerCamelCase				:					int	):
		UpperCamelCase     :Tuple          =	order

		# a_{0} ... a_{k}
		UpperCamelCase     :Dict          =	[1.0] + [0.0] * order
		# b_{0} ... b_{k}
		UpperCamelCase     :str          =	[1.0] + [0.0] * order

		# x[n-1] ... x[n-k]
		UpperCamelCase     :List[str]          =	[0.0] * self.order
		# y[n-1] ... y[n-k]
		UpperCamelCase     :List[Any]          =	[0.0] * self.order





	def 						_A (		self				:					Optional[Any] ,  __lowerCamelCase				:					list[float] ,  __lowerCamelCase				:					list[float]	):
		if len(__lowerCamelCase	) < self.order:
			UpperCamelCase     :List[Any]          =	[1.0, *a_coeffs]

		if len(__lowerCamelCase	) != self.order + 1:
			UpperCamelCase     :int          =	(
			    F"""Expected a_coeffs to have {self.order + 1} elements """
			    F"""for {self.order}-order filter, got {len(__lowerCamelCase	)}"""
			)
			raise ValueError(__lowerCamelCase	)

		if len(__lowerCamelCase	) != self.order + 1:
			UpperCamelCase     :int          =	(
			    F"""Expected b_coeffs to have {self.order + 1} elements """
			    F"""for {self.order}-order filter, got {len(__lowerCamelCase	)}"""
			)
			raise ValueError(__lowerCamelCase	)

		UpperCamelCase     :Optional[Any]          =	a_coeffs
		UpperCamelCase     :Dict          =	b_coeffs





	def 						_A (		self				:					List[str] ,  __lowerCamelCase				:					float	):
		UpperCamelCase     :Tuple          =	0.0

		# Start at index 1 and do index 0 at the end.
		for i in range(1 ,  self.order + 1	):
			result += (
			    self.b_coeffs[i] * self.input_history[i - 1]
			    - self.a_coeffs[i] * self.output_history[i - 1]
			)

		UpperCamelCase     :Dict          =	(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

		UpperCamelCase     :int          =	self.input_history[:-1]
		UpperCamelCase     :str          =	self.output_history[:-1]

		UpperCamelCase     :Optional[int]          =	sample
		UpperCamelCase     :List[Any]          =	result

		return result








import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute

def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  int = 3					)		->			qiskit.result.counts.Counts:






	"""simple docstring"""



	if isinstance(__magic_name__	,			__magic_name__					):
		raise TypeError("""number of qubits must be a integer."""					)
	if number_of_qubits <= 0:
		raise ValueError("""number of qubits must be > 0."""					)
	if math.floor(__magic_name__					) != number_of_qubits:
		raise ValueError("""number of qubits must be exact integer."""					)
	if number_of_qubits > 10:
		raise ValueError("""number of qubits too large to simulate(>10)."""					)

	UpperCamelCase     :int          =	QuantumRegister(__magic_name__	,			"""qr"""					)
	UpperCamelCase     :str          =	ClassicalRegister(__magic_name__	,			"""cr"""					)

	UpperCamelCase     :str          =	QuantumCircuit(__magic_name__	,			__magic_name__					)

	UpperCamelCase     :List[Any]          =	number_of_qubits

	for i in range(__magic_name__					):
		quantum_circuit.h(number_of_qubits - i - 1					)
		counter -= 1
		for j in range(__magic_name__					):
			quantum_circuit.cp(np.pi / 2 ** (counter - j)	,			__magic_name__	,			__magic_name__					)

	for k in range(number_of_qubits // 2					):
		quantum_circuit.swap(__magic_name__	,			number_of_qubits - k - 1					)

	# measure all the qubits
	quantum_circuit.measure(__magic_name__	,			__magic_name__					)
	# simulate with 10000 shots
	UpperCamelCase     :str          =	Aer.get_backend("""qasm_simulator"""					)
	UpperCamelCase     :Dict          =	execute(__magic_name__	,			__magic_name__	,			shots=1_0000					)

	return job.result().get_counts(__magic_name__					)


if __name__ == "__main__":
	print(
	    F'''Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}'''
	)
