
"""simple docstring"""

import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize






def 							A		(       snake_case   :Union[str, Any]	)   ->			Any:
 return np.dot(snake_case       ,      snake_case	)

class __lowerCAmelCase	:





     def __init__(			self			,  *,
         __UpperCAmelCase = np.inf			,  __UpperCAmelCase = "linear"			,  __UpperCAmelCase = 0.0			,  ):

      '''simple docstring'''




      __UpperCamelCase       						= regularization
      __UpperCamelCase       						= gamma
      if kernel == "linear":
       __UpperCamelCase       						= self.__linear
      elif kernel == "rbf":
       if self.gamma == 0:
        raise ValueError('rbf kernel requires gamma'   )
       if not isinstance(self.gamma			,  (float, int)   ):
        raise ValueError('gamma must be float or int'   )
       if not self.gamma > 0:
        raise ValueError('gamma must be > 0'   )
       __UpperCamelCase       						= self.__rbf
       # in the future, there could be a default value like in sklearn
       # sklear: def_gamma = 1/(n_features * X.var()) (wiki)
       # previously it was 1/(n_features)
      else:
       __UpperCamelCase       						= F'Unknown kernel: {kernel}'
       raise ValueError(A_   )





     def 		UpperCAmelCase      (			self			,  __UpperCAmelCase			,  __UpperCAmelCase   ):

      '''simple docstring'''




      return np.dot(A_			,  A_   )





     def 		UpperCAmelCase      (			self			,  __UpperCAmelCase			,  __UpperCAmelCase   ):

      '''simple docstring'''




      return np.exp(-(self.gamma * norm_squared(vectora - vectora   ))   )





     def 		UpperCAmelCase      (			self			,  __UpperCAmelCase			,  __UpperCAmelCase   ):

      '''simple docstring'''




      __UpperCamelCase       						= observations
      __UpperCamelCase       						= classes

      # using Wolfe's Dual to calculate w.
      # Primal problem: minimize 1/2*norm_squared(w)
      #   constraint: yn(w . xn + b) >= 1
      #
      # With l a vector
      # Dual problem: maximize sum_n(ln) -
      #       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
      #   constraint: self.C >= ln >= 0
      #           and sum_n(ln*yn) = 0
      # Then we get w using w = sum_n(ln*yn*xn)
      # At the end we can get b ~= mean(yn - w . xn)
      #
      # Since we use kernels, we only need l_star to calculate b
      # and to classify observations

      ((__UpperCamelCase	)						,				)       						= np.shape(A_   )

      def to_minimize(__UpperCAmelCase   ) -> float:
       __UpperCamelCase       						= 0
       ((__UpperCamelCase	)						,				)       						= np.shape(A_   )
       for i in range(A_   ):
        for j in range(A_   ):
         s += (
             candidate[i]
             * candidate[j]
             * classes[i]
             * classes[j]
             * self.kernel(observations[i]			,  observations[j]   )
         )
       return 1 / 2 * s - sum(A_   )

      __UpperCamelCase       						= LinearConstraint(A_			,  0			,  0   )
      __UpperCamelCase       						= Bounds(0			,  self.regularization   )

      __UpperCamelCase       						= minimize(
          A_			,  np.ones(A_   )			,  bounds=A_			,  constraints=[ly_contraint]   ).x
      __UpperCamelCase       						= l_star

      # calculating mean offset of separation plane to points
      __UpperCamelCase       						= 0
      for i in range(A_   ):
       for j in range(A_   ):
        s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
            observations[i]			,  observations[j]   )
      __UpperCamelCase       						= s / n







     def 		UpperCAmelCase      (			self			,  __UpperCAmelCase   ):

      '''simple docstring'''




      __UpperCamelCase       						= sum(
          self.optimum[n]
          * self.classes[n]
          * self.kernel(self.observations[n]			,  A_   )
          for n in range(len(self.classes   )   )   )
      return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
      import doctest

      doctest.testmod()





"""simple docstring"""

import numpy as np
import qiskit






def 							A		(       snake_case   :int = 8       ,      snake_case   :int | None = None	)   ->			str:
 __UpperCamelCase       						= np.random.default_rng(seed=snake_case	)

 # Roughly 25% of the qubits will contribute to the key.
 # So we take more than we need.
 __UpperCamelCase       						= 6 * key_len
 # Measurement basis for Alice's qubits.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)
 # The set of states Alice will prepare.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)
 # Measurement basis for Bob's qubits.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)

 # Quantum Circuit to simulate BB84
 __UpperCamelCase       						= qiskit.QuantumCircuit(snake_case       ,      name='BB84'	)

 # Alice prepares her qubits according to rules above.
 for index, _ in enumerate(snake_case	):
  if alice_state[index] == 1:
   bbaa_circ.x(snake_case	)
  if alice_basis[index] == 1:
   bbaa_circ.h(snake_case	)
 bbaa_circ.barrier()

 # Bob measures the received qubits according to rules above.
 for index, _ in enumerate(snake_case	):
  if bob_basis[index] == 1:
   bbaa_circ.h(snake_case	)

 bbaa_circ.barrier()
 bbaa_circ.measure_all()

 # Simulate the quantum circuit.
 __UpperCamelCase       						= qiskit.Aer.get_backend('aer_simulator'	)
 # We only need to run one shot because the key is unique.
 # Multiple shots will produce the same key.
 __UpperCamelCase       						= qiskit.execute(snake_case       ,      snake_case       ,      shots=1       ,      seed_simulator=snake_case	)
 # Returns the result of measurement.
 __UpperCamelCase       						= job.result().get_counts(snake_case	).most_frequent()

 # Extracting the generated key from the simulation results.
 # Only keep measurement results where Alice and Bob chose the same basis.
 __UpperCamelCase       						= ''.join(
     [
         result_bit
         for alice_basis_bit, bob_basis_bit, result_bit in zip(
             snake_case       ,      snake_case       ,      snake_case	)
         if alice_basis_bit == bob_basis_bit
     ]	)

 # Get final key. Pad with 0 if too short, otherwise truncate.
 __UpperCamelCase       						= gen_key[:key_len] if len(snake_case	) >= key_len else gen_key.ljust(snake_case       ,      '0'	)
 return key


if __name__ == "__main__":
      print(f'''The generated key is : {bbaa(8, seed=0)}''')
      from doctest import testmod

      testmod()



