code: def are_pauli_words_qwc(lst_pauli_words):
      """Given a list of observables assumed to be valid Pauli words, determine if they are pairwise
      qubit-wise commuting.
  
      This implementation has time complexity ~ O(m * n) for m Pauli words and n wires, where n is the
      number of distinct wire labels used to represent the Pauli words.
  
      Args:
          lst_pauli_words (list[Observable]): List of observables (assumed to be valid Pauli words).
  
      Returns:
          (bool): True if they are all qubit-wise commuting, false otherwise.
      """
      latest_op_name_per_wire = {}
  
      for op in lst_pauli_words:  # iterate over the list of observables
          op_names = (
              [op.name] if not isinstance(op.name, list) else op.name
          )
          op_wires = op.wires.tolist()
  
          for op_name, wire in zip(
              op_names, op_wires
          ):  # iterate over wires of the observable,
              try:
                  if latest_op_name_per_wire[wire] != op_name and (
                      op_name != "Identity"
                      and latest_op_name_per_wire[wire] != "Identity"
                  ):
                      return False
                  if latest_op_name_per_wire[wire] == "Identity":
                      latest_op_name_per_wire[
                          wire
                      ] = op_name  # update name
              except KeyError:
                  latest_op_name_per_wire[
                      wire
                  ] = op_name  # add wire and name for the first time
  
      return True
  
imports: from functools import lru_cache, reduce, singledispatch
  from itertools import product
  from typing import List, Union
  from warnings import warn
  import numpy
  import pennylane
  from pennylane.operation import Tensor
  from pennylane.ops import Hamiltonian, Identity, PauliX, PauliY, PauliZ, Prod, SProd
  from pennylane.tape import OperationRecorder
  from pennylane.wires import Wires
label_desc: Use image node_id 16 for calling a global function with example usage: are_pauli_words_qwc(lst_pauli_words) and returns: True, False