


from __future__ import annotations

from cmath import sqrt




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case					)  ->    tuple[complex, complex]:

       if a == 0:
              raise ValueError('Coefficient \'a\' must not be zero.'					)
       lowercase__:       List[str]        =       b * b - 4 * a * c

       lowercase__:       List[Any]        =       (-b + sqrt(snake_case					)) / (2 * a)
       lowercase__:       List[Any]        =       (-b - sqrt(snake_case					)) / (2 * a)

       return (
           root_a.real if not root_a.imag else root_a,
           root_a.real if not root_a.imag else root_a,
       )




def        snake_case_					(  )  ->    Optional[Any]:
       lowercase__      ,						lowercase__:       Dict        =       quadratic_roots(a=5      ,							b=6      ,							c=1					)
       print(f'The solutions are: {solutiona} and {solutiona}'					)


if __name__ == "__main__":
 main()






import math

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




def        snake_case_					(  snake_case = 3					)  ->    qiskit.result.counts.Counts:
       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).'					)

       lowercase__:       str        =       QuantumRegister(snake_case      ,							'qr'					)
       lowercase__:       str        =       ClassicalRegister(snake_case      ,							'cr'					)

       lowercase__:       List[Any]        =       QuantumCircuit(snake_case      ,							snake_case					)

       lowercase__:       int        =       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
       lowercase__:       str        =       Aer.get_backend('qasm_simulator'					)
       lowercase__:       Union[str, Any]        =       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)}'''
 )


