code: def pauli_to_binary(
      pauli_word, n_qubits=None, wire_map=None, check_is_pauli_word=True
  ):
      # pylint: disable=isinstance-second-argument-not-valid-type
      """Converts a Pauli word to the binary vector representation.
  
      This functions follows convention that the first half of binary vector components specify
      PauliX placements while the last half specify PauliZ placements.
  
      Args:
          pauli_word (Union[Identity, PauliX, PauliY, PauliZ, Tensor]): the Pauli word to be
              converted to binary vector representation
          n_qubits (int): number of qubits to specify dimension of binary vector representation
          wire_map (dict): dictionary containing all wire labels used in the Pauli word as keys, and
              unique integer labels as their values
          check_is_pauli_word (bool): If True (default) then a check is run to verify that pauli_word
              is infact a Pauli word
  
      Returns:
          array: the ``2*n_qubits`` dimensional binary vector representation of the input Pauli word
  
      Raises:
          TypeError: if the input ``pauli_word`` is not an instance of Identity, PauliX, PauliY,
              PauliZ or tensor products thereof
          ValueError: if ``n_qubits`` is less than the number of wires acted on by the Pauli word
  
      **Example**
  
      If ``n_qubits`` and ``wire_map`` are both unspecified, the dimensionality of the binary vector
      will be ``2 * len(pauli_word.wires)``. Regardless of wire labels, the vector components encoding
      Pauli operations will be read from left-to-right in the tensor product when ``wire_map`` is
      unspecified, e.g.,
  
      >>> pauli_to_binary(qml.PauliX('a') @ qml.PauliY('b') @ qml.PauliZ('c'))
      array([1., 1., 0., 0., 1., 1.])
      >>> pauli_to_binary(qml.PauliX('c') @ qml.PauliY('a') @ qml.PauliZ('b'))
      array([1., 1., 0., 0., 1., 1.])
  
      The above cases have the same binary representation since they are equivalent up to a
      relabelling of the wires. To keep binary vector component enumeration consistent with wire
      labelling across multiple Pauli words, or define any arbitrary enumeration, one can use
      keyword argument ``wire_map`` to set this enumeration.
  
      >>> wire_map = {'a': 0, 'b': 1, 'c': 2}
      >>> pauli_to_binary(qml.PauliX('a') @ qml.PauliY('b') @ qml.PauliZ('c'), wire_map=wire_map)
      array([1., 1., 0., 0., 1., 1.])
      >>> pauli_to_binary(qml.PauliX('c') @ qml.PauliY('a') @ qml.PauliZ('b'), wire_map=wire_map)
      array([1., 0., 1., 1., 1., 0.])
  
      Now the two Pauli words are distinct in the binary vector representation, as the vector
      components are consistently mapped from the wire labels, rather than enumerated
      left-to-right.
  
      If ``n_qubits`` is unspecified, the dimensionality of the vector representation will be inferred
      from the size of support of the Pauli word,
  
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(1))
      array([1., 1., 0., 0.])
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(5))
      array([1., 1., 0., 0.])
  
      Dimensionality higher than twice the support can be specified by ``n_qubits``,
  
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(1), n_qubits=6)
      array([1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(5), n_qubits=6)
      array([1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
  
      For these Pauli words to have a consistent mapping to vector representation, we once again
      need to specify a ``wire_map``.
  
      >>> wire_map = {0:0, 1:1, 5:5}
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(1), n_qubits=6, wire_map=wire_map)
      array([1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(5), n_qubits=6, wire_map=wire_map)
      array([1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.])
  
      Note that if ``n_qubits`` is unspecified and ``wire_map`` is specified, the dimensionality of the
      vector representation will be inferred from the highest integer in ``wire_map.values()``.
  
      >>> wire_map = {0:0, 1:1, 5:5}
      >>> pauli_to_binary(qml.PauliX(0) @ qml.PauliX(5),  wire_map=wire_map)
      array([1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.])
      """
  
      if check_is_pauli_word and not is_pauli_word(pauli_word):
          raise TypeError(
              f"Expected a Pauli word Observable instance, instead got {pauli_word}."
          )
  
      if wire_map is None:
          num_wires = len(pauli_word.wires)
          wire_map = {pauli_word.wires[i]: i for i in range(num_wires)}
  
      n_qubits_min = max(wire_map.values()) + 1
      if n_qubits is None:
          n_qubits = n_qubits_min
      elif n_qubits < n_qubits_min:
          raise ValueError(
              f"n_qubits must support the highest mapped wire index {n_qubits_min},"
              f" instead got n_qubits={n_qubits}."
          )
  
      pauli_wires = pauli_word.wires.map(wire_map).tolist()
  
      binary_pauli = np.zeros(2 * n_qubits)
  
      paulis_with_identity = (PauliX, PauliY, PauliZ, Identity)
  
      if isinstance(pauli_word, paulis_with_identity):
          operations_zip = zip(pauli_wires, [pauli_word.name])
      else:
          operations_zip = zip(pauli_wires, pauli_word.name)
  
      for wire, name in operations_zip:
          if name == "PauliX":
              binary_pauli[wire] = 1
  
          elif name == "PauliY":
              binary_pauli[wire] = 1
              binary_pauli[n_qubits + wire] = 1
  
          elif name == "PauliZ":
              binary_pauli[n_qubits + wire] = 1
  
      return binary_pauli
  
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 10 for calling a global function with example usage: pauli_to_binary(pauli_word, n_qubits, wire_map, check_is_pauli_word) and returns: binary_pauli