code: def diagonalize_qwc_groupings(qwc_groupings):
      """Diagonalizes a list of qubit-wise commutative groupings of Pauli strings.
  
      Args:
          qwc_groupings (list[list[Observable]]): a list of mutually qubit-wise commutative groupings
              of Pauli string observables
  
      Returns:
          tuple:
  
              * list[list[Operation]]: a list of instances of the qwc_rotation
                template which diagonalizes the qubit-wise commuting grouping,
                order corresponding to qwc_groupings
              * list[list[Observable]]: a list of QWC groupings diagonalized in the
                computational basis, order corresponding to qwc_groupings
  
      **Example**
  
      >>> qwc_group_1 = [qml.PauliX(0) @ qml.PauliZ(1),
                         qml.PauliX(0) @ qml.PauliY(3),
                         qml.PauliZ(1) @ qml.PauliY(3)]
      >>> qwc_group_2 = [qml.PauliY(0),
                         qml.PauliY(0) @ qml.PauliX(2),
                         qml.PauliX(1) @ qml.PauliZ(3)]
      >>> post_rotations, diag_groupings = diagonalize_qwc_groupings([qwc_group_1, qwc_group_2])
      >>> post_rotations
      [[RY(-1.5707963267948966, wires=[0]), RX(1.5707963267948966, wires=[3])],
       [RX(1.5707963267948966, wires=[0]),
        RY(-1.5707963267948966, wires=[2]),
        RY(-1.5707963267948966, wires=[1])]]
      >>> diag_groupings
      [[PauliZ(wires=[0]) @ PauliZ(wires=[1]),
       PauliZ(wires=[0]) @ PauliZ(wires=[3]),
       PauliZ(wires=[1]) @ PauliZ(wires=[3])],
      [PauliZ(wires=[0]),
       PauliZ(wires=[0]) @ PauliZ(wires=[2]),
       PauliZ(wires=[1]) @ PauliZ(wires=[3])]]
      """
  
      post_rotations = []
      diag_groupings = []
      m_groupings = len(qwc_groupings)
  
      for i in range(m_groupings):
          (
              diagonalizing_unitary,
              diag_grouping,
          ) = diagonalize_qwc_pauli_words(qwc_groupings[i])
          post_rotations.append(diagonalizing_unitary)
          diag_groupings.append(diag_grouping)
  
      return post_rotations, diag_groupings
  
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 27 for calling a global function with example usage: diagonalize_qwc_groupings(qwc_groupings) and returns: post_rotations,  diag_groupings