




"""simple docstring"""


import math

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


def  UpperCAmelCase__	(snake_case__							: int = 3   ):
		"""simple docstring"""

		if isinstance(snake_case__		,       snake_case__   ):
				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(snake_case__   ) != 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)."""   )

		_snake_case							:		Optional[int]								=  QuantumRegister(snake_case__		,       """qr"""   )
		_snake_case							:		List[Any]								=  ClassicalRegister(snake_case__		,       """cr"""   )

		_snake_case							:		Optional[int]								=  QuantumCircuit(snake_case__		,       snake_case__   )

		_snake_case							:		Dict								=  number_of_qubits

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

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

		# measure all the qubits
		quantum_circuit.measure(snake_case__		,       snake_case__   )
		# simulate with 10000 shots
		_snake_case							:		Optional[int]								=  Aer.get_backend("""qasm_simulator"""   )
		_snake_case							:		Optional[int]								=  execute(snake_case__		,       snake_case__		,       shots=1_00_00   )

		return job.result().get_counts(snake_case__   )


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








"""simple docstring"""


def  UpperCAmelCase__	(snake_case__							: int = 1_00_00_00   ):
  """simple docstring"""

  _snake_case							:		Dict								=  [i - 1 for i in range(limit + 1   )]

  for i in range(2		,       limit + 1   ):
    if phi[i] == i - 1:
      for j in range(2 * i		,       limit + 1		,       snake_case__   ):
        phi[j] -= phi[j] // i

  return sum(phi[2 : limit + 1]   )


if __name__ == "__main__":
     print(solution())


