text: # This code is part of Qiskit.
  #
  # (C) Copyright IBM 2018, 2021.
  #
  # This code is licensed under the Apache License, Version 2.0. You may
  # obtain a copy of this license in the LICENSE.txt file in the root directory
  # of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
  #
  # Any modifications or derivative works of this code must retain this
  # copyright notice, and modified files need to carry a notice indicating
  # that they have been altered from the originals.
  
  """
  The Multivariate Uniform Distribution.
  """
  
  from typing import Optional, List, Union
  import numpy as np
  from .multivariate_distribution import MultivariateDistribution
  
  
  class MultivariateUniformDistribution(MultivariateDistribution):
      """
      The Multivariate Uniform Distribution.
  
      Although this just results in a Hadamard gate on all involved qubits, the lower and upper
      bounds and the assignment of the qubits to the different dimensions is important if used in
      a particular application.
      """
  
      def __init__(self,
                   num_qubits: Union[List[int], np.ndarray],
                   low: Optional[Union[List[float], np.ndarray]] = None,
                   high: Optional[Union[List[float], np.ndarray]] = None) -> None:
          """
          Args:
              num_qubits: List with the number of qubits per dimension
              low: List with the lower bounds per dimension, set to 0 for each dimension if None
              high: List with the upper bounds per dimension, set to 1 for each dimension if None
          """
          if low is None:
              low = np.zeros(num_qubits)  # type: ignore
          if high is None:
              high = np.ones(num_qubits)  # type: ignore
  
          num_values = np.prod([2**n for n in num_qubits])
          probabilities = np.ones(num_values)  # type: ignore
          super().__init__(num_qubits, probabilities, low, high)  # type: ignore
  
      @staticmethod
      def _replacement():
          return 'qiskit.circuit.library.UniformDistribution'
  
      def build(self, qc, q, q_ancillas=None, params=None):
          if params is None or params['i_state'] is None:
              for i in range(sum(self.num_qubits)):
                  qc.h(q[i])
          else:
              for qubits in params['i_state']:
                  for i in qubits:
                      qc.h(q[i])
  