


"""simple docstring"""



import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute
def      UpperCAmelCase     (       _lowercase :   Union[str, Any] = 3	)						-> qiskit.result.counts.Counts:


	"""simple docstring"""




	if isinstance(_lowercase			,   _lowercase	):
		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(_lowercase	) != number_of_qubits:
		raise ValueError('''number of qubits must be exact integer.'''	)
	if number_of_qubits > 1_0:
		raise ValueError('''number of qubits too large to simulate(>10).'''	)

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

	lowerCAmelCase_      							=			QuantumCircuit(_lowercase			,   _lowercase	)

	lowerCAmelCase_      							=			number_of_qubits

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

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

	# measure all the qubits
	quantum_circuit.measure(_lowercase			,   _lowercase	)
	# simulate with 10000 shots
	lowerCAmelCase_      							=			Aer.get_backend('''qasm_simulator'''	)
	lowerCAmelCase_      							=			execute(_lowercase			,   _lowercase			,   shots=1_0_0_0_0	)

	return job.result().get_counts(_lowercase	)


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

def  __lowerCamelCase					( _lowercase = 50000000			)       ->      int:
     UpperCamelCase						    =					set()
     UpperCamelCase						    =					int((limit - 24) ** (1 / 2)			)

     UpperCamelCase						    =					set(range(3						,     prime_square_limit + 1						,     2			)			)
     primes.add(2			)
     for p in range(3						,     prime_square_limit + 1						,     2			):
          if p not in primes:
               continue
          primes.difference_update(set(range(p * p						,     prime_square_limit + 1						,     _lowercase			)			)			)

     for primea in primes:
          UpperCamelCase						    =					primea * primea
          for primea in primes:
               UpperCamelCase						    =					primea * primea * primea
               if square + cube >= limit - 16:
                    break
               for primea in primes:
                    UpperCamelCase						    =					primea * primea * primea * primea
                    UpperCamelCase						    =					square + cube + tetr
                    if total >= limit:
                         break
                    ret.add(_lowercase			)

     return len(_lowercase			)


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


