






import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize
def      a_ (      _A  )			->			float:







				"""simple docstring"""
				return np.dot(_A      ,   _A  )


class   __SCREAMING_SNAKE_CASE:
							def __init__(     self:      Any       ,	*,
							    UpperCamelCase:      float = np.inf       ,	UpperCamelCase:      str = "linear"       ,	UpperCamelCase:      float = 0.0       ,	)		->		None:
											snake_case__									=     regularization
											snake_case__									=     gamma
											if kernel == "linear":
															snake_case__									=     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'						)
															snake_case__									=     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:
															snake_case__									=     F'''Unknown kernel: {kernel}'''
															raise ValueError(UpperCamelCase						)
							def lowerCAmelCase_ (     self:      int       ,	UpperCamelCase:      ndarray       ,	UpperCamelCase:      ndarray						)		->		float:
											return np.dot(UpperCamelCase       ,	UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Dict       ,	UpperCamelCase:      ndarray       ,	UpperCamelCase:      ndarray						)		->		float:
											return np.exp(-(self.gamma * norm_squared(vectora - vectora						))						)
							def lowerCAmelCase_ (     self:      Tuple       ,	UpperCamelCase:      list[ndarray]       ,	UpperCamelCase:      ndarray						)		->		None:
											snake_case__									=     observations
											snake_case__									=     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

											((snake_case__						)							,												)									=     np.shape(UpperCamelCase						)

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

											snake_case__									=     LinearConstraint(UpperCamelCase       ,	0       ,	0						)
											snake_case__									=     Bounds(0       ,	self.regularization						)

											snake_case__									=     minimize(
											    UpperCamelCase       ,	np.ones(UpperCamelCase						)       ,	bounds=UpperCamelCase       ,	constraints=[ly_contraint]						).x
											snake_case__									=     l_star

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


							def lowerCAmelCase_ (     self:      int       ,	UpperCamelCase:      ndarray						)		->		int:
											snake_case__									=     sum(
											    self.optimum[n]
											    * self.classes[n]
											    * self.kernel(self.observations[n]       ,	UpperCamelCase						)
											    for n in range(len(self.classes						)						)						)
											return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
							import doctest

							doctest.testmod()












import qiskit
def      a_ (      _A = 2  )			->			qiskit.result.counts.Counts:







				"""simple docstring"""
				snake_case__									=     qubits

				# Using Aer's simulator
				snake_case__									=     qiskit.Aer.get_backend('aer_simulator'  )

				# Creating a Quantum Circuit acting on the q register
				snake_case__									=     qiskit.QuantumCircuit(_A      ,   _A  )

				# Adding a H gate on qubit 0 (now q0 in superposition)
				circuit.h(0  )

				for i in range(1      ,   _A  ):
								# Adding CX (CNOT) gate
								circuit.cx(i - 1      ,   _A  )

				# Mapping the quantum measurement to the classical bits
				circuit.measure(list(range(_A  )  )      ,   list(range(_A  )  )  )

				# Now measuring any one qubit would affect other qubits to collapse
				# their super position and have same state as the measured one.

				# Executing the circuit on the simulator
				snake_case__									=     qiskit.execute(_A      ,   _A      ,   shots=1000  )

				return job.result().get_counts(_A  )


if __name__ == "__main__":
							print(f'''Total count for various states are: {quantum_entanglement(3)}''')




