code: def algebra_commutator(
      tape, observables, lie_algebra_basis_names, nqubits
  ):
      """Calculate the Riemannian gradient in the Lie algebra with the parameter shift rule
      (see :meth:`RiemannianGradientOptimizer.get_omegas`).
  
      Args:
          tape (.QuantumTape or .QNode): input circuit
          observables (list[.Observable]): list of observables to be measured. Can be grouped.
          lie_algebra_basis_names (list[str]): List of strings corresponding to valid Pauli words.
          nqubits (int): the number of qubits.
  
      Returns:
          function or tuple[list[QuantumTape], function]:
  
          - If the input is a QNode, an object representing the Riemannian gradient function
            of the QNode that can be executed with the same arguments as the QNode to obtain
            the Lie algebra commutator.
  
          - If the input is a tape, a tuple containing a
            list of generated tapes, together with a post-processing
            function to be applied to the results of the evaluated tapes
            in order to obtain the Lie algebra commutator.
      """
      tapes_plus_total = []
      tapes_min_total = []
      for obs in observables:
          for o in obs:
              # create a list of tapes for the plus and minus shifted circuits
              queues_plus = [
                  qml.queuing.AnnotatedQueue()
                  for _ in lie_algebra_basis_names
              ]
              queues_min = [
                  qml.queuing.AnnotatedQueue()
                  for _ in lie_algebra_basis_names
              ]
  
              # loop through all operations on the input tape
              for op in tape.operations:
                  for t in queues_plus + queues_min:
                      with t:
                          qml.apply(op)
              for i, t in enumerate(queues_plus):
                  with t:
                      qml.PauliRot(
                          np.pi / 2,
                          lie_algebra_basis_names[i],
                          wires=list(range(nqubits)),
                      )
                      qml.expval(o)
              for i, t in enumerate(queues_min):
                  with t:
                      qml.PauliRot(
                          -np.pi / 2,
                          lie_algebra_basis_names[i],
                          wires=list(range(nqubits)),
                      )
                      qml.expval(o)
              tapes_plus_total.extend(
                  [
                      qml.tape.QuantumScript(
                          *qml.queuing.process_queue(q)
                      )
                      for q, p in zip(
                          queues_plus, lie_algebra_basis_names
                      )
                  ]
              )
              tapes_min_total.extend(
                  [
                      qml.tape.QuantumScript(
                          *qml.queuing.process_queue(q)
                      )
                      for q, p in zip(
                          queues_min, lie_algebra_basis_names
                      )
                  ]
              )
      return tapes_plus_total + tapes_min_total
  
file_path: pennylane/pennylane/optimize/riemannian_gradient.py
imports: import warnings
  from typing import Sequence, Callable
  import numpy
  from scipy.sparse.linalg import expm
  import pennylane
  from pennylane import transform
  from pennylane.tape import QuantumTape
  from pennylane.queuing import QueuingManager
label_desc: Use image node_id 2 for calling a global function with example usage: algebra_commutator(tape, observables, lie_algebra_basis_names, nqubits) and returns: unknown