




import itertools
import math





def __UpperCamelCase			(       _A  ):

						if 1 < number < 4:
												# 2 and 3 are primes
												return True
						elif number < 2 or number % 2 == 0 or number % 3 == 0:
												# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
												return False

						# All primes number are in format of 6k +/- 1
						for i in range(5 ,  int(math.sqrt(_A  ) + 1  ) ,  6  ):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True





def __UpperCamelCase			(       ):
						lowerCAmelCase_      			=  2
						while True:
												if is_prime(_A  ):
																		yield num
												num += 1





def __UpperCamelCase			(       _A = 10001  ):
						return next(itertools.islice(prime_generator() ,  nth - 1 ,  _A  )  )


if __name__ == "__main__":
						print(f"{solution() = }")










import math

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





def __UpperCamelCase			(       _A = 3  ):
						if isinstance(_A ,  _A  ):
												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(_A  ) != 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).'''  )

						lowerCAmelCase_      			=  QuantumRegister(_A ,  '''qr'''  )
						lowerCAmelCase_      			=  ClassicalRegister(_A ,  '''cr'''  )

						lowerCAmelCase_      			=  QuantumCircuit(_A ,  _A  )

						lowerCAmelCase_      			=  number_of_qubits

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

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

						# measure all the qubits
						quantum_circuit.measure(_A ,  _A  )
						# simulate with 10000 shots
						lowerCAmelCase_      			=  Aer.get_backend('''qasm_simulator'''  )
						lowerCAmelCase_      			=  execute(_A ,  _A ,  shots=10000  )

						return job.result().get_counts(_A  )


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




