


"""simple docstring"""


from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload






class  lowercase:







 '''simple docstring'''





 def __init__(    self:		int,				a_:		Collection[float] | None = None		):




   '''simple docstring'''



   if components is None:
     _snake_case							:		Tuple								=  []
   _snake_case							:		Optional[int]								=  list(_UpperCAmelCase		)


 def __len__(    self:		int		):




   '''simple docstring'''



   return len(self.__components		)


 def __str__(    self:		Tuple		):




   '''simple docstring'''



   return "(" + ",".join(map(_UpperCAmelCase,				self.__components		)		) + ")"


 def __add__(    self:		Optional[Any],				a_:		Vector		):




   '''simple docstring'''



   _snake_case							:		str								=  len(self		)
   if size == len(_UpperCAmelCase		):
     _snake_case							:		Optional[Any]								=  [self.__components[i] + other.component(_UpperCAmelCase		) for i in range(_UpperCAmelCase		)]
     return Vector(_UpperCAmelCase		)
   else:
     raise Exception("""must have the same size"""		)


 def __sub__(    self:		Optional[Any],				a_:		Vector		):




   '''simple docstring'''



   _snake_case							:		str								=  len(self		)
   if size == len(_UpperCAmelCase		):
     _snake_case							:		str								=  [self.__components[i] - other.component(_UpperCAmelCase		) for i in range(_UpperCAmelCase		)]
     return Vector(_UpperCAmelCase		)
   else:  # error case
     raise Exception("""must have the same size"""		)


 @overload
 def __mul__(    self:		List[str],				a_:		float		):




   '''simple docstring'''



   ...


 @overload
 def __mul__(    self:		Optional[Any],				a_:		Vector		):




   '''simple docstring'''



   ...


 def __mul__(    self:		Optional[int],				a_:		float | Vector		):




   '''simple docstring'''



   if isinstance(_UpperCAmelCase,				(float, int)		):
     _snake_case							:		Optional[Any]								=  [c * other for c in self.__components]
     return Vector(_UpperCAmelCase		)
   elif isinstance(_UpperCAmelCase,				_UpperCAmelCase		) and len(self		) == len(_UpperCAmelCase		):
     _snake_case							:		List[Any]								=  len(self		)
     _snake_case							:		Union[str, Any]								=  [self.__components[i] * other.component(_UpperCAmelCase		) for i in range(_UpperCAmelCase		)]
     return sum(_UpperCAmelCase		)
   else:  # error case
     raise Exception("""invalid operand!"""		)


 def 			UpperCamelCase_       (    self:		int		):




   '''simple docstring'''



   return Vector(self.__components		)


 def 			UpperCamelCase_       (    self:		Union[str, Any],				a_:		int		):




   '''simple docstring'''



   if isinstance(_UpperCAmelCase,				_UpperCAmelCase		) and -len(self.__components		) <= i < len(self.__components		):
     return self.__components[i]
   else:
     raise Exception("""index out of range"""		)


 def 			UpperCamelCase_       (    self:		List[str],				a_:		int,				a_:		float		):




   '''simple docstring'''



   assert -len(self.__components		) <= pos < len(self.__components		)
   _snake_case							:		Dict								=  value


 def 			UpperCamelCase_       (    self:		Optional[Any]		):




   '''simple docstring'''



   if len(self.__components		) == 0:
     raise Exception("""Vector is empty"""		)
   _snake_case							:		Tuple								=  [c**2 for c in self.__components]
   return math.sqrt(sum(_UpperCAmelCase		)		)


 def 			UpperCamelCase_       (    self:		Union[str, Any],				a_:		Vector,				a_:		bool = False		):




   '''simple docstring'''



   _snake_case							:		Dict								=  self * other
   _snake_case							:		Optional[int]								=  self.euclidean_length() * other.euclidean_length()
   if deg:
     return math.degrees(math.acos(num / den		)		)
   else:
     return math.acos(num / den		)







def  UpperCAmelCase__	(snake_case__							: Any   ):
  """simple docstring"""

  assert isinstance(lowerCAmelCase_		,       lowerCAmelCase_   )
  return Vector([0] * dimension   )


def  UpperCAmelCase__	(snake_case__							: Tuple		,       snake_case__							: Optional[int]   ):
  """simple docstring"""

  assert isinstance(lowerCAmelCase_		,       lowerCAmelCase_   ) and (isinstance(lowerCAmelCase_		,       lowerCAmelCase_   ))
  _snake_case							:		List[str]								=  [0] * dimension
  _snake_case							:		Optional[Any]								=  1
  return Vector(lowerCAmelCase_   )


def  UpperCAmelCase__	(snake_case__							: str		,       snake_case__							: List[str]		,       snake_case__							: Optional[Any]   ):
  """simple docstring"""

  assert (
      isinstance(lowerCAmelCase_		,       lowerCAmelCase_   )
      and isinstance(lowerCAmelCase_		,       lowerCAmelCase_   )
      and (isinstance(lowerCAmelCase_		,       (int, float)   ))
  )
  return x * scalar + y


def  UpperCAmelCase__	(snake_case__							: List[Any]		,       snake_case__							: List[Any]		,       snake_case__							: List[str]   ):
  """simple docstring"""

  random.seed(lowerCAmelCase_   )
  _snake_case							:		int								=  [random.randint(lowerCAmelCase_		,       lowerCAmelCase_   ) for _ in range(lowerCAmelCase_   )]
  return Vector(lowerCAmelCase_   )






class  lowercase:







 '''simple docstring'''





 def __init__(    self:		Tuple,				a_:		list[list[float]],				a_:		int,				a_:		int		):




   '''simple docstring'''



   _snake_case							:		str								=  matrix
   _snake_case							:		int								=  w
   _snake_case							:		Any								=  h


 def __str__(    self:		Optional[Any]		):




   '''simple docstring'''



   _snake_case							:		Optional[Any]								=  ''
   for i in range(self.__height		):
     ans += "|"
     for j in range(self.__width		):
       if j < self.__width - 1:
         ans += str(self.__matrix[i][j]		) + ","
       else:
         ans += str(self.__matrix[i][j]		) + "|\n"
   return ans


 def __add__(    self:		Dict,				a_:		Matrix		):




   '''simple docstring'''



   if self.__width == other.width() and self.__height == other.height():
     _snake_case							:		Any								=  []
     for i in range(self.__height		):
       _snake_case							:		Optional[Any]								=  [
           self.__matrix[i][j] + other.component(_UpperCAmelCase,				_UpperCAmelCase		)
           for j in range(self.__width		)
       ]
       matrix.append(_UpperCAmelCase		)
     return Matrix(_UpperCAmelCase,				self.__width,				self.__height		)
   else:
     raise Exception("""matrix must have the same dimension!"""		)


 def __sub__(    self:		Any,				a_:		Matrix		):




   '''simple docstring'''



   if self.__width == other.width() and self.__height == other.height():
     _snake_case							:		Tuple								=  []
     for i in range(self.__height		):
       _snake_case							:		int								=  [
           self.__matrix[i][j] - other.component(_UpperCAmelCase,				_UpperCAmelCase		)
           for j in range(self.__width		)
       ]
       matrix.append(_UpperCAmelCase		)
     return Matrix(_UpperCAmelCase,				self.__width,				self.__height		)
   else:
     raise Exception("""matrices must have the same dimension!"""		)


 @overload
 def __mul__(    self:		Union[str, Any],				a_:		float		):




   '''simple docstring'''



   ...


 @overload
 def __mul__(    self:		str,				a_:		Vector		):




   '''simple docstring'''



   ...


 def __mul__(    self:		Dict,				a_:		float | Vector		):




   '''simple docstring'''



   if isinstance(_UpperCAmelCase,				_UpperCAmelCase		):  # matrix-vector
     if len(_UpperCAmelCase		) == self.__width:
       _snake_case							:		str								=  zero_vector(self.__height		)
       for i in range(self.__height		):
         _snake_case							:		Any								=  [
             self.__matrix[i][j] * other.component(_UpperCAmelCase		)
             for j in range(self.__width		)
         ]
         ans.change_component(_UpperCAmelCase,				sum(_UpperCAmelCase		)		)
       return ans
     else:
       raise Exception(
           """vector must have the same size as the """
           """number of columns of the matrix!"""		)
   elif isinstance(_UpperCAmelCase,				(int, float)		):  # matrix-scalar
     _snake_case							:		Any								=  [
         [self.__matrix[i][j] * other for j in range(self.__width		)]
         for i in range(self.__height		)
     ]
     return Matrix(_UpperCAmelCase,				self.__width,				self.__height		)
   return None


 def 			UpperCamelCase_       (    self:		Optional[Any]		):




   '''simple docstring'''



   return self.__height


 def 			UpperCamelCase_       (    self:		Any		):




   '''simple docstring'''



   return self.__width


 def 			UpperCamelCase_       (    self:		int,				a_:		int,				a_:		int		):




   '''simple docstring'''



   if 0 <= x < self.__height and 0 <= y < self.__width:
     return self.__matrix[x][y]
   else:
     raise Exception("""change_component: indices out of bounds"""		)


 def 			UpperCamelCase_       (    self:		str,				a_:		int,				a_:		int,				a_:		float		):




   '''simple docstring'''



   if 0 <= x < self.__height and 0 <= y < self.__width:
     _snake_case							:		Union[str, Any]								=  value
   else:
     raise Exception("""change_component: indices out of bounds"""		)


 def 			UpperCamelCase_       (    self:		List[Any],				a_:		int,				a_:		int		):




   '''simple docstring'''



   if self.__height != self.__width:
     raise Exception("""Matrix is not square"""		)
   _snake_case							:		List[str]								=  self.__matrix[:x] + self.__matrix[x + 1 :]
   for i in range(len(_UpperCAmelCase		)		):
     _snake_case							:		Tuple								=  minor[i][:y] + minor[i][y + 1 :]
   return Matrix(_UpperCAmelCase,				self.__width - 1,				self.__height - 1		).determinant()


 def 			UpperCamelCase_       (    self:		Optional[int],				a_:		int,				a_:		int		):




   '''simple docstring'''



   if self.__height != self.__width:
     raise Exception("""Matrix is not square"""		)
   if 0 <= x < self.__height and 0 <= y < self.__width:
     return (-1) ** (x + y) * self.minor(_UpperCAmelCase,				_UpperCAmelCase		)
   else:
     raise Exception("""Indices out of bounds"""		)


 def 			UpperCamelCase_       (    self:		Dict		):




   '''simple docstring'''



   if self.__height != self.__width:
     raise Exception("""Matrix is not square"""		)
   if self.__height < 1:
     raise Exception("""Matrix has no element"""		)
   elif self.__height == 1:
     return self.__matrix[0][0]
   elif self.__height == 2:
     return (
         self.__matrix[0][0] * self.__matrix[1][1]
         - self.__matrix[0][1] * self.__matrix[1][0]
     )
   else:
     _snake_case							:		List[str]								=  [
         self.__matrix[0][y] * self.cofactor(0,				_UpperCAmelCase		) for y in range(self.__width		)
     ]
     return sum(_UpperCAmelCase		)







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

  _snake_case							:		list[list[float]]								=  [[0] * n for _ in range(lowerCAmelCase_   )]
  return Matrix(lowerCAmelCase_		,       lowerCAmelCase_		,       lowerCAmelCase_   )






def  UpperCAmelCase__	(snake_case__							: Any		,       snake_case__							: Any		,       snake_case__							: Any		,       snake_case__							: Optional[Any]   ):
  """simple docstring"""

  random.seed(lowerCAmelCase_   )
  _snake_case							:		list[list[float]]								=  [
      [random.randint(lowerCAmelCase_		,       lowerCAmelCase_   ) for _ in range(lowerCAmelCase_   )] for _ in range(lowerCAmelCase_   )
  ]
  return Matrix(lowerCAmelCase_		,       lowerCAmelCase_		,       lowerCAmelCase_   )








"""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)}'''
     )


