code: def is_qwc(pauli_vec_1, pauli_vec_2):
      """Checks if two Pauli words in the binary vector representation are qubit-wise commutative.
  
      Args:
          pauli_vec_1 (Union[list, tuple, array]): first binary vector argument in qubit-wise
              commutator
          pauli_vec_2 (Union[list, tuple, array]): second binary vector argument in qubit-wise
              commutator
  
      Returns:
          bool: returns True if the input Pauli words are qubit-wise commutative, returns False
          otherwise
  
      Raises:
          ValueError: if the input vectors are of different dimension, if the vectors are not of even
              dimension, or if the vector components are not strictly binary
  
      **Example**
  
      >>> is_qwc([1,0,0,1,1,0],[1,0,1,0,1,0])
      False
      >>> is_qwc([1,0,1,1,1,0],[1,0,0,1,1,0])
      True
      """
  
      if isinstance(pauli_vec_1, (list, tuple)):
          pauli_vec_1 = np.asarray(pauli_vec_1)
      if isinstance(pauli_vec_2, (list, tuple)):
          pauli_vec_2 = np.asarray(pauli_vec_2)
  
      if len(pauli_vec_1) != len(pauli_vec_2):
          raise ValueError(
              f"Vectors a and b must be the same dimension, instead got "
              f"shapes {np.shape(pauli_vec_1)} and {np.shape(pauli_vec_2)}."
          )
  
      if len(pauli_vec_1) % 2 != 0:
          raise ValueError(
              f"Symplectic vector-space must have even dimension, instead got vectors of shape {np.shape(pauli_vec_1)}."
          )
  
      if not (
          np.array_equal(pauli_vec_1, pauli_vec_1.astype(bool))
          and np.array_equal(pauli_vec_2, pauli_vec_2.astype(bool))
      ):
          raise ValueError(
              f"Vectors a and b must have strictly binary components, instead got {pauli_vec_1} and {pauli_vec_2}"
          )
  
      n_qubits = int(len(pauli_vec_1) / 2)
  
      for i in range(n_qubits):
          first_vec_ith_qubit_paulix = pauli_vec_1[i]
          first_vec_ith_qubit_pauliz = pauli_vec_1[n_qubits + i]
          second_vec_ith_qubit_paulix = pauli_vec_2[i]
          second_vec_ith_qubit_pauliz = pauli_vec_2[n_qubits + i]
  
          first_vec_qubit_i_is_identity = (
              first_vec_ith_qubit_paulix
              == first_vec_ith_qubit_pauliz
              == 0
          )
          second_vec_qubit_i_is_identity = (
              second_vec_ith_qubit_paulix
              == second_vec_ith_qubit_pauliz
              == 0
          )
          both_vecs_qubit_i_have_same_x = (
              first_vec_ith_qubit_paulix == second_vec_ith_qubit_paulix
          )
          both_vecs_qubit_i_have_same_z = (
              first_vec_ith_qubit_pauliz == second_vec_ith_qubit_pauliz
          )
  
          if not (
              (
                  (first_vec_qubit_i_is_identity)
                  or (second_vec_qubit_i_is_identity)
              )
              or (
                  (both_vecs_qubit_i_have_same_x)
                  and (both_vecs_qubit_i_have_same_z)
              )
          ):
              return False
  
      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 15 for calling a global function with example usage: is_qwc(pauli_vec_1, pauli_vec_2) and returns: True, False