code: def equal(
      op1: Union[Operator, MeasurementProcess, QuantumTape],
      op2: Union[Operator, MeasurementProcess, QuantumTape],
      check_interface=True,
      check_trainability=True,
      rtol=1e-5,
      atol=1e-9,
  ):
      r"""Function for determining operator or measurement equality.
  
      .. Warning::
  
          The ``qml.equal`` function is based on a comparison of the type and attributes
          of the measurement or operator, not a mathematical representation. While
          comparisons between some classes, such as ``Tensor`` and ``Hamiltonian``, are
          supported, mathematically equivalent operators defined via different classes
          may return False when compared via ``qml.equal``.
  
          To be more thorough would require the matrix forms to be calculated, which may
          drastically increase runtime.
  
      .. Warning::
  
          The kwargs ``check_interface`` and ``check_trainability`` can only be set when
          comparing ``Operation`` objects. Comparisons of ``MeasurementProcess``
          or ``Observable`` objects will use the default value of ``True`` for both, regardless
          of what the user specifies when calling the function. For subclasses of ``SymbolicOp``
          or ``CompositeOp`` with an ``Operation`` as a base, the kwargs will be applied to the base
          comparison.
  
      Args:
          op1 (.Operator or .MeasurementProcess or .QuantumTape): First object to compare
          op2 (.Operator or .MeasurementProcess or .QuantumTape): Second object to compare
          check_interface (bool, optional): Whether to compare interfaces. Default: ``True``. Not used for comparing ``MeasurementProcess``, ``Hamiltonian`` or ``Tensor`` objects.
          check_trainability (bool, optional): Whether to compare trainability status. Default: ``True``. Not used for comparing ``MeasurementProcess``, ``Hamiltonian`` or ``Tensor`` objects.
          rtol (float, optional): Relative tolerance for parameters. Not used for comparing ``MeasurementProcess``, ``Hamiltonian`` or ``Tensor`` objects.
          atol (float, optional): Absolute tolerance for parameters. Not used for comparing ``MeasurementProcess``, ``Hamiltonian`` or ``Tensor`` objects.
  
      Returns:
          bool: ``True`` if the operators or measurement processes are equal, else ``False``
  
      **Example**
  
      Given two operators or measurement processes, ``qml.equal`` determines their equality.
  
      >>> op1 = qml.RX(np.array(.12), wires=0)
      >>> op2 = qml.RY(np.array(1.23), wires=0)
      >>> qml.equal(op1, op1), qml.equal(op1, op2)
      (True, False)
  
      >>> T1 = qml.PauliX(0) @ qml.PauliY(1)
      >>> T2 = qml.PauliY(1) @ qml.PauliX(0)
      >>> T3 = qml.PauliX(1) @ qml.PauliY(0)
      >>> qml.equal(T1, T2), qml.equal(T1, T3)
      (True, False)
  
      >>> T = qml.PauliX(0) @ qml.PauliY(1)
      >>> H = qml.Hamiltonian([1], [qml.PauliX(0) @ qml.PauliY(1)])
      >>> qml.equal(T, H)
      True
  
      >>> H1 = qml.Hamiltonian([0.5, 0.5], [qml.PauliZ(0) @ qml.PauliY(1), qml.PauliY(1) @ qml.PauliZ(0) @ qml.Identity("a")])
      >>> H2 = qml.Hamiltonian([1], [qml.PauliZ(0) @ qml.PauliY(1)])
      >>> H3 = qml.Hamiltonian([2], [qml.PauliZ(0) @ qml.PauliY(1)])
      >>> qml.equal(H1, H2), qml.equal(H1, H3)
      (True, False)
  
      >>> qml.equal(qml.expval(qml.PauliX(0)), qml.expval(qml.PauliX(0)))
      True
      >>> qml.equal(qml.probs(wires=(0,1)), qml.probs(wires=(1,2)))
      False
      >>> qml.equal(qml.classical_shadow(wires=[0,1]), qml.classical_shadow(wires=[0,1]))
      True
      >>> tape1 = qml.tape.QuantumScript([qml.RX(1.2, wires=0)], [qml.expval(qml.PauliZ(0))])
      >>> tape2 = qml.tape.QuantumScript([qml.RX(1.2 + 1e-6, wires=0)], [qml.expval(qml.PauliZ(0))])
      >>> qml.equal(tape1, tape2, tol=0, atol=1e-7)
      False
      >>> qml.equal(tape1, tape2, tol=0, atol=1e-5)
      True
  
      .. details::
          :title: Usage Details
  
          You can use the optional arguments to get more specific results. Additionally, they are
          applied when comparing the base of ``SymbolicOp`` and ``CompositeOp`` operators such as
          ``Controlled``, ``Pow``, ``SProd``, ``Prod``, etc., if the base is an ``Operation``. These arguments
          are, however, not used for comparing ``MeasurementProcess``, ``Hamiltonian`` or ``Tensor``
          objects.
  
          Consider the following comparisons:
  
          >>> op1 = qml.RX(torch.tensor(1.2), wires=0)
          >>> op2 = qml.RX(jax.numpy.array(1.2), wires=0)
          >>> qml.equal(op1, op2)
          False
  
          >>> qml.equal(op1, op2, check_interface=False, check_trainability=False)
          True
  
          >>> op3 = qml.RX(np.array(1.2, requires_grad=True), wires=0)
          >>> op4 = qml.RX(np.array(1.2, requires_grad=False), wires=0)
          >>> qml.equal(op3, op4)
          False
  
          >>> qml.equal(op3, op4, check_trainability=False)
          True
  
          >>> qml.equal(Controlled(op3, control_wires=1), Controlled(op4, control_wires=1))
          False
  
          >>> qml.equal(Controlled(op3, control_wires=1), Controlled(op4, control_wires=1), check_trainability=False)
          True
      """
  
      # types don't have to be the same type, they just both have to be Observables
      if not isinstance(op2, type(op1)) and not isinstance(
          op1, Observable
      ):
          return False
  
      if isinstance(op2, (Hamiltonian, Tensor)):
          return _equal(op2, op1)
  
      return _equal(
          op1,
          op2,
          check_interface=check_interface,
          check_trainability=check_trainability,
          atol=atol,
          rtol=rtol,
      )
  
imports: from collections.abc import Iterable
  from functools import singledispatch
  from typing import Union
  import pennylane
  from pennylane.measurements import MeasurementProcess
  from pennylane.measurements.classical_shadow import ShadowExpvalMP
  from pennylane.measurements.mid_measure import MidMeasureMP, MeasurementValue
  from pennylane.measurements.mutual_info import MutualInfoMP
  from pennylane.measurements.vn_entropy import VnEntropyMP
  from pennylane.measurements.counts import CountsMP
  from pennylane.pulse.parametrized_evolution import ParametrizedEvolution
  from pennylane.operation import Observable, Operator, Tensor
  from pennylane.ops import Hamiltonian, Controlled, Pow, Adjoint, Exp, SProd, CompositeOp
  from pennylane.templates.subroutines import ControlledSequence
  from pennylane.tape import QuantumTape
label_desc: Use image node_id 1 for calling a global function with example usage: equal(op1, op2, check_interface, check_trainability, rtol, atol) and returns: _equal, False, _equal