code: def pauli_kraus_map(probabilities):
      r
      if len(probabilities) not in [4, 16]:
          raise ValueError("Currently we only support one or two qubits, "
                           "so the provided list of probabilities must have length 4 or 16.")
      if not np.allclose(sum(probabilities), 1.0, atol=1e-3):
          raise ValueError("Probabilities must sum to one.")
  
      paulis = [np.eye(2), np.array([[0, 1], [1, 0]]), np.array([[0, -1j], [1j, 0]]), np.array([[1, 0], [0, -1]])]
  
      if len(probabilities) == 4:
          operators = paulis
      else:
          operators = np.kron(paulis, paulis)
  
      return [coeff * op for coeff, op in zip(np.sqrt(probabilities), operators)]
docs: r"""
      Generate the Kraus operators corresponding to a pauli channel.
  
      :params list|floats probabilities: The 4^num_qubits list of probabilities specifying the desired pauli channel.
      There should be either 4 or 16 probabilities specified in the order I, X, Y, Z for 1 qubit
      or II, IX, IY, IZ, XI, XX, XY, etc for 2 qubits.
  
              For example::
  
                  The d-dimensional depolarizing channel \Delta parameterized as
                  \Delta(\rho) = p \rho + [(1-p)/d] I
                  is specified by the list of probabilities
                  [p + (1-p)/d, (1-p)/d,  (1-p)/d), ... , (1-p)/d)]
  
      :return: A list of the 4^num_qubits Kraus operators that parametrize the map.
      :rtype: list