class_docstr: Internal class used to keep track of the required information to translate a ``ParametrizedHamiltonian``
  into hardware.
  
  This class contains the ``coeffs`` and the ``observables`` to construct the :class:`ParametrizedHamiltonian`,
  but on top of that also contains attributes that store parameteres relevant for real hardware execution.
  
  .. warning::
  
      This class should NEVER be initialized directly! Please use the functions
      :func:`rydberg_interaction` and :func:`drive` instead.
  
  .. seealso:: :func:`rydberg_interaction`, :func:`drive`, :class:`ParametrizedHamiltonian`
  
  Args:
      coeffs (Union[float, callable]): coefficients of the Hamiltonian expression, which may be
          constants or parametrized functions. All functions passed as ``coeffs`` must have two
          arguments, the first one being the trainable parameters and the second one being time.
      observables (Iterable[Observable]): observables in the Hamiltonian expression, of same
          length as ``coeffs``
  
  Keyword Args:
      reorder_fn (callable): function for reordering the parameters before calling.
          This allows automatically copying parameters when they are used for different terms,
          as well as allowing single terms to depend on multiple parameters, as is the case for
          drive Hamiltonians. Note that in order to add two HardwareHamiltonians,
          the reorder_fn needs to be matching.
      settings Union[RydbergSettings, TransmonSettings]: Dataclass containing the hardware specific settings. Default is ``None``.
      pulses (list[HardwarePulse]): list of ``HardwarePulse`` dataclasses containing the information about the
          amplitude, phase, drive frequency and wires of each pulse
  
  Returns:
      HardwareHamiltonian: class representing the Hamiltonian of Rydberg or Transmon device.
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code: def __add__(
      self, other
  ):  # pylint: disable=too-many-return-statements
      if isinstance(other, HardwareHamiltonian):
          if not self.reorder_fn == other.reorder_fn:
              raise ValueError(
                  "Cannot add two HardwareHamiltonians with different reorder functions. "
                  f"Received reorder_fns {self.reorder_fn} and {other.reorder_fn}. This is "
                  "likely due to an attempt to add hardware compatible Hamiltonians for "
                  "different target systems."
              )
          if self.settings is None and other.settings is None:
              new_settings = None
          else:
              new_settings = self.settings + other.settings
  
          new_pulses = self.pulses + other.pulses
  
          new_ops = self.ops + other.ops
          new_coeffs = self.coeffs + other.coeffs
          return HardwareHamiltonian(
              new_coeffs,
              new_ops,
              reorder_fn=self.reorder_fn,
              settings=new_settings,
              pulses=new_pulses,
          )
  
      ops = self.ops.copy()
      coeffs = self.coeffs.copy()
      settings = self.settings
      pulses = self.pulses
  
      if isinstance(other, (Hamiltonian, ParametrizedHamiltonian)):
          new_coeffs = coeffs + list(other.coeffs.copy())
          new_ops = ops + other.ops.copy()
          return HardwareHamiltonian(
              new_coeffs,
              new_ops,
              reorder_fn=self.reorder_fn,
              settings=settings,
              pulses=pulses,
          )
  
      if isinstance(other, qml.ops.SProd):  # pylint: disable=no-member
          new_coeffs = coeffs + [other.scalar]
          new_ops = ops + [other.base]
          return HardwareHamiltonian(
              new_coeffs,
              new_ops,
              reorder_fn=self.reorder_fn,
              settings=settings,
              pulses=pulses,
          )
  
      if isinstance(other, Operator):
          new_coeffs = coeffs + [1]
          new_ops = ops + [other]
          return HardwareHamiltonian(
              new_coeffs,
              new_ops,
              reorder_fn=self.reorder_fn,
              settings=settings,
              pulses=pulses,
          )
  
      if isinstance(other, (int, float)):
          if other in (0, 0.0):
              return HardwareHamiltonian(
                  coeffs,
                  ops,
                  reorder_fn=self.reorder_fn,
                  settings=settings,
                  pulses=pulses,
              )
          new_coeffs = coeffs + [other]
          with qml.queuing.QueuingManager.stop_recording():
              new_ops = ops + [qml.Identity(self.wires[0])]
  
          return HardwareHamiltonian(
              new_coeffs,
              new_ops,
              reorder_fn=self.reorder_fn,
              settings=settings,
              pulses=pulses,
          )
  
      return NotImplemented
  
imports: from dataclasses import dataclass
  from typing import Callable, List, Union
  import numpy
  import pennylane
  from pennylane.wires import Wires
  from pennylane.operation import Operator
  from pennylane.ops.qubit.hamiltonian import Hamiltonian
  from .parametrized_hamiltonian import ParametrizedHamiltonian
label_desc: Use image node_id 4 for calling the HardwareHamiltonian obj's underlying member method code with example usage: obj.__add__(other) and returns: NotImplemented, HardwareHamiltonian, HardwareHamiltonian, HardwareHamiltonian, HardwareHamiltonian, HardwareHamiltonian, HardwareHamiltonian