text: import itertools
  import json
  import numpy as np
  from numpy.random import RandomState
  from qiskit import QuantumCircuit, QuantumRegister
  from qiskit.compiler import transpile
  from cvxopt import matrix, solvers  # pylint: disable=import-error
  from .qka import QKA
  
  class FeatureMap:
  
      def __init__(self, feature_dimension, entangler_map=None):
          if isinstance(feature_dimension, int):
              if feature_dimension % 2 == 0:
                  self._feature_dimension = feature_dimension
              else:
                  raise ValueError("Feature dimension must be an even integer.")
          else:
              raise ValueError("Feature dimension must be an even integer.")
  
          self._num_qubits = int(feature_dimension / 2)
  
          if entangler_map is None:
              self._entangler_map = [
                  [i, j]
                  for i in range(self._feature_dimension)
                  for j in range(i + 1, self._feature_dimension)
              ]
          else:
              self._entangler_map = entangler_map
  
          self._num_parameters = self._num_qubits
  
      def construct_circuit(self, x=None, parameters=None, q=None, inverse=False, name=None):
  
          if parameters is not None:
              if isinstance(parameters, (int, float)):
                  raise ValueError("Parameters must be a list.")
              if len(parameters) == 1:
                  parameters = parameters * np.ones(self._num_qubits)
              else:
                  if len(parameters) != self._num_parameters:
                      raise ValueError(
                          "The number of feature map parameters must be {}.".format(
                              self._num_parameters
                          )
                      )
  
          if len(x) != self._feature_dimension:
              raise ValueError(
                  "The input vector must be of length {}.".format(self._feature_dimension)
              )
  
          if q is None:
              q = QuantumRegister(self._num_qubits, name="q")
  
          circuit = QuantumCircuit(q, name=name)
  
          for i in range(self._num_qubits):
              circuit.ry(-parameters[i], q[i])
  
          for source, target in self._entangler_map:
              circuit.cz(q[source], q[target])
  
          for i in range(self._num_qubits):
              circuit.rz(-2 * x[2 * i + 1], q[i])
              circuit.rx(-2 * x[2 * i], q[i])
  
          if inverse:
              return circuit.inverse()
          else:
              return circuit
  
      def to_json(self):
          return json.dumps(
              {"feature_dimension": self._feature_dimension, "entangler_map": self._entangler_map}
          )
  
      @classmethod
      def from_json(cls, data):
          return cls(**json.loads(data))
  
  