code: def pauli_mult_with_phase(pauli_1, pauli_2, wire_map=None):
      r"""Multiply two Pauli words together, and return both their product as a Pauli word
      and the global phase.
  
      .. warning::
  
          ``pauli_mult_with_phase`` is deprecated. Instead, you can multiply two Pauli
          words together with ``qml.simplify(qml.prod(pauli_1, pauli_2))``. Note that if
          there is a phase, this will be in ``result.scalar``, and the base will be
          available in ``result.base``.
  
      Two Pauli operations can be multiplied together by taking the additive
      OR of their binary symplectic representations. The phase is computed by
      looking at the number of times we have the products  :math:`XY, YZ`, or :math:`ZX` (adds a
      phase of :math:`i`), or :math:`YX, ZY, XZ` (adds a phase of :math:`-i`).
  
      Args:
          pauli_1 (.Operation): A Pauli word.
          pauli_2 (.Operation): A Pauli word to multiply with the first one.
          wire_map  (dict[Union[str, int], int]): dictionary containing all wire labels used in the Pauli
              word as keys, and unique integer labels as their values. If no wire map is
              provided, the map will be constructed from the set of wires acted on
              by the input Pauli words.
  
      Returns:
          tuple[.Operation, complex]: The product of ``pauli_1`` and ``pauli_2``, and the
          global phase.
  
      **Example**
  
      This function works the same as :func:`~.pauli_mult` but also returns the global
      phase accumulated as a result of the ordering of Paulis in the product (e.g., :math:`XY = iZ`,
      and :math:`YX = -iZ`).
  
      >>> from pennylane.pauli import pauli_mult_with_phase
      >>> pauli_1 = qml.PauliX(0) @ qml.PauliZ(1)
      >>> pauli_2 = qml.PauliY(0) @ qml.PauliZ(1)
      >>> product, phase = pauli_mult_with_phase(pauli_1, pauli_2)
      >>> product
      PauliZ(wires=[0])
      >>> phase
      1j
      """
  
      warn(
          "`pauli_mult_with_phase` is deprecated. Instead, you can multiply two Pauli words "
          "together with `qml.simplify(qml.prod(pauli_1, pauli_2))`. Note that if "
          "there is a phase, this will be in `result.scalar`, and the base will be "
          "available in `result.base`.",
          qml.PennyLaneDeprecationWarning,
      )
  
      if wire_map is None:
          wire_map = _wire_map_from_pauli_pair(pauli_1, pauli_2)
  
      # Get the product; use our earlier function
      pauli_product = pauli_mult(pauli_1, pauli_2, wire_map)
  
      # Get the names of the operations; in cases where only one single-qubit Pauli
      # is present, the operation name is stored as a string rather than a list, so convert it
      pauli_1_string = pauli_word_to_string(pauli_1, wire_map=wire_map)
      pauli_2_string = pauli_word_to_string(pauli_2, wire_map=wire_map)
  
      pos_phases = (("X", "Y"), ("Y", "Z"), ("Z", "X"))
  
      phase = 1
  
      for qubit_1_char, qubit_2_char in zip(
          pauli_1_string, pauli_2_string
      ):
          # If we have identities anywhere we don't pick up a phase
          if qubit_1_char == "I" or qubit_2_char == "I":
              continue
  
          # Likewise, no additional phase if the Paulis are the same
          if qubit_1_char == qubit_2_char:
              continue
  
          # Use Pauli commutation rules to determine the phase
          if (qubit_1_char, qubit_2_char) in pos_phases:
              phase *= 1j
          else:
              phase *= -1j
  
      return pauli_product, phase
  
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 22 for calling a global function with example usage: pauli_mult_with_phase(pauli_1, pauli_2, wire_map) and returns: pauli_product,  phase