




import math

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







def lowerCamelCase__       (      _lowercase = 3				):

     '''simple docstring'''


     if isinstance(UpperCAmelCase_			,						UpperCAmelCase_				):
          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(UpperCAmelCase_				) != 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_      :							List[Any]       =      QuantumRegister(UpperCAmelCase_			,						'''qr'''				)
     UpperCAmelCase_      :							Union[str, Any]       =      ClassicalRegister(UpperCAmelCase_			,						'''cr'''				)

     UpperCAmelCase_      :							Tuple       =      QuantumCircuit(UpperCAmelCase_			,						UpperCAmelCase_				)

     UpperCAmelCase_      :							List[Any]       =      number_of_qubits

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

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

     # measure all the qubits
     quantum_circuit.measure(UpperCAmelCase_			,						UpperCAmelCase_				)
     # simulate with 10000 shots
     UpperCAmelCase_      :							List[str]       =      Aer.get_backend('''qasm_simulator'''				)
     UpperCAmelCase_      :							Optional[int]       =      execute(UpperCAmelCase_			,						UpperCAmelCase_			,						shots=10000				)

     return job.result().get_counts(UpperCAmelCase_				)


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





def lowerCamelCase__       (      _lowercase			,						_lowercase				):

     '''simple docstring'''


     return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2







def lowerCamelCase__       (      _lowercase			,						_lowercase=0				):

     '''simple docstring'''


     return sorted(_lowercase			,						key=lambda _lowercase				: x[column]				)







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase=float('''inf'''				)				):

     '''simple docstring'''


     for i in range(points_counts - 1				):
          for j in range(i + 1			,						_lowercase				):
               UpperCAmelCase_      :							Optional[int]       =      euclidean_distance_sqr(points[i]			,						points[j]				)
               if current_dis < min_dis:
                    UpperCAmelCase_      :							Optional[Any]       =      current_dis
     return min_dis







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase=float('''inf'''				)				):

     '''simple docstring'''


     for i in range(min(6			,						points_counts - 1				)			,						_lowercase				):
          for j in range(max(0			,						i - 6				)			,						_lowercase				):
               UpperCAmelCase_      :							List[str]       =      euclidean_distance_sqr(points[i]			,						points[j]				)
               if current_dis < min_dis:
                    UpperCAmelCase_      :							Optional[int]       =      current_dis
     return min_dis







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase				):

     '''simple docstring'''


     if points_counts <= 3:
          return dis_between_closest_pair(_lowercase			,						_lowercase				)

     # recursion
     UpperCAmelCase_      :							Optional[int]       =      points_counts // 2
     UpperCAmelCase_      :							List[Any]       =      closest_pair_of_points_sqr(
         _lowercase			,						points_sorted_on_y[:mid]			,						_lowercase				)
     UpperCAmelCase_      :							Dict       =      closest_pair_of_points_sqr(
         _lowercase			,						points_sorted_on_y[mid:]			,						points_counts - mid				)
     UpperCAmelCase_      :							Union[str, Any]       =      min(_lowercase			,						_lowercase				)
     UpperCAmelCase_      :							str       =      []
     for point in points_sorted_on_x:
          if abs(point[0] - points_sorted_on_x[mid][0]				) < closest_pair_dis:
               cross_strip.append(_lowercase				)

     UpperCAmelCase_      :							Optional[Any]       =      dis_between_closest_in_strip(
         _lowercase			,						len(_lowercase				)			,						_lowercase				)
     return min(_lowercase			,						_lowercase				)







def lowerCamelCase__       (      _lowercase			,						_lowercase				):

     '''simple docstring'''


     UpperCAmelCase_      :							Tuple       =      column_based_sort(_lowercase			,						column=0				)
     UpperCAmelCase_      :							List[Any]       =      column_based_sort(_lowercase			,						column=1				)
     return (
         closest_pair_of_points_sqr(
             _lowercase			,						_lowercase			,						_lowercase				)
     ) ** 0.5


if __name__ == "__main__":
     __a          =			[(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
     print('Distance:', closest_pair_of_points(points, len(points)))