code: def transmon_interaction(
      qubit_freq: Union[float, list],
      connections: list,
      coupling: Union[float, list],
      wires: list,
      anharmonicity=None,
      d=2,
  ):
      r"""Returns a :class:`ParametrizedHamiltonian` representing the circuit QED Hamiltonian of a
      superconducting transmon system.
  
      The Hamiltonian is given by
  
      .. math::
  
          H = \sum_{q\in \text{wires}} \omega_q b^\dagger_q b_q
          + \sum_{(i, j) \in \mathcal{C}} g_{ij} \left(b^\dagger_i b_j + b_j^\dagger b_i \right)
          + \sum_{q\in \text{wires}} \alpha_q b^\dagger_q b^\dagger_q b_q b_q
  
      where :math:`[b_p, b_q^\dagger] = \delta_{pq}` are creation and annihilation operators.
      The first term describes the effect of the dressed qubit frequencies ``qubit_freq`` :math:`= \omega_q/ (2\pi)`,
      the second term their ``coupling`` :math:`= g_{ij}/(2\pi)` and the last the
      ``anharmonicity`` :math:`= \alpha_q/(2\pi)`, which all can vary for
      different qubits. In practice, these operators are restricted to a finite dimension of the
      local Hilbert space (default ``d=2`` corresponds to qubits).
      In that case, the anharmonicity is set to :math:`\alpha=0` and ignored.
  
      The values of :math:`\omega` and :math:`\alpha` are typically around :math:`5 \times 2\pi \text{GHz}`
      and :math:`0.3 \times 2\pi \text{GHz}`, respectively.
      It is common for different qubits to be out of tune with different energy gaps. The coupling strength
      :math:`g` typically varies between :math:`[0.001, 0.1] \times 2\pi \text{GHz}`. For some example parameters,
      see e.g. `arXiv:1804.04073 <https://arxiv.org/abs/1804.04073>`_,
      `arXiv:2203.06818 <https://arxiv.org/abs/2203.06818>`_, or `arXiv:2210.15812 <https://arxiv.org/abs/2210.15812>`_.
  
      .. note:: Currently only supporting ``d=2`` with qudit support planned in the future. For ``d=2``, we have :math:`b:=\frac{1}{2}(\sigma^x + i \sigma^y)`.
  
      .. seealso::
  
          :func:`~.transmon_drive`
  
      Args:
          qubit_freq (Union[float, list[float], Callable]): List of dressed qubit frequencies. This should be in units
              of frequency (GHz), and will be converted to angular frequency :math:`\omega` internally where
              needed, i.e. multiplied by :math:`2 \pi`. When passing a single float all qubits are assumed to
              have that same frequency. When passing a parametrized function, it must have two
              arguments, the first one being the trainable parameters and the second one being time.
          connections (list[tuple(int)]): List of connections ``(i, j)`` between qubits i and j.
              When the wires in ``connections`` are not contained in ``wires``, a warning is raised.
          coupling (Union[float, list[float]]): List of coupling strengths. This should be in units
              of frequency (GHz), and will be converted to angular frequency internally where
              needed, i.e. multiplied by :math:`2 \pi`. Needs to match the length of ``connections``.
              When passing a single float need explicit ``wires``.
          anharmonicity (Union[float, list[float]]): List of anharmonicities. This should be in units
              of frequency (GHz), and will be converted to angular frequency internally where
              needed, i.e. multiplied by :math:`2 \pi`. Ignored when ``d=2``.
              When passing a single float all qubits are assumed to have that same anharmonicity.
          wires (list): Needs to be of the same length as qubit_freq. Note that there can be additional
              wires in the resulting operator from the ``connections``, which are treated independently.
          d (int): Local Hilbert space dimension. Defaults to ``d=2`` and is currently the only supported value.
  
      Returns:
          :class:`~.ParametrizedHamiltonian`: a :class:`~.ParametrizedHamiltonian` representing the transmon interaction
  
      **Example**
  
      We can set up the transmon interaction Hamiltonian with uniform coefficients by passing ``float`` values.
  
      .. code-block::
  
          connections = [[0, 1], [1, 3], [2, 1], [4, 5]]
          H = qml.pulse.transmon_interaction(qubit_freq=0.5, connections=connections, coupling=1., wires=range(6))
  
      The resulting :class:`~.HardwareHamiltonian:` consists of ``4`` coupling terms and ``6`` qubits
      because there are six different wire indices in ``connections``.
  
      >>> print(H)
      HardwareHamiltonian: terms=10
  
      We can also provide individual values for each of the qubit energies and coupling strengths,
      here of order :math:`0.1 \times 2\pi\text{GHz}` and :math:`1 \times 2\pi\text{GHz}`, respectively.
  
      .. code-block::
  
          qubit_freqs = [0.5, 0.4, 0.3, 0.2, 0.1, 0.]
          couplings= [1., 2., 3., 4.]
          H = qml.pulse.transmon_interaction(qubit_freq=qubit_freqs,
                                             connections=connections,
                                             coupling=couplings,
                                             wires=range(6))
  
      The interaction term is dependent only on the typically fixed transmon energies and coupling strengths.
      Executing this as a pulse program via :func:`~.evolve` would correspond to all driving fields being turned off.
      To add a driving field, see :func:`~.transmon_drive`.
  
      """
      if d != 2:
          raise NotImplementedError(
              "Currently only supporting qubits. Qutrits and qudits are planned in the future."
          )
  
      # if wires is None and qml.math.ndim(omega) == 0:
      #     raise ValueError(
      #         f"Cannot instantiate wires automatically. Either need specific wires or a list of omega."
      #         f"Received wires {wires} and omega of type {type(omega)}"
      #     )
  
      # wires = wires or list(range(len(omega)))
  
      n_wires = len(wires)
  
      if not Wires(wires).contains_wires(
          Wires(np.unique(connections).tolist())
      ):
          warnings.warn(
              f"Caution, wires and connections do not match. "
              f"I.e., wires in connections {connections} are not contained in the wires {wires}"
          )
  
      # Prepare coefficients
      if anharmonicity is None:
          anharmonicity = [0.0] * n_wires
  
      # TODO: make coefficients callable / trainable. Currently not supported
      if callable(qubit_freq) or qml.math.ndim(qubit_freq) == 0:
          qubit_freq = [qubit_freq] * n_wires
      elif len(qubit_freq) != n_wires:
          raise ValueError(
              f"Number of qubit frequencies in {qubit_freq} does not match the provided wires = {wires}"
          )
  
      if qml.math.ndim(coupling) == 0:
          coupling = [coupling] * len(connections)
      if len(coupling) != len(connections):
          raise ValueError(
              f"Number of coupling terms {coupling} does not match the provided connections = {connections}"
          )
  
      settings = TransmonSettings(
          connections, qubit_freq, coupling, anharmonicity=anharmonicity
      )
  
      omega = [
          callable_freq_to_angular(f)
          if callable(f)
          else (2 * np.pi * f)
          for f in qubit_freq
      ]
      g = [
          callable_freq_to_angular(c)
          if callable(c)
          else (2 * np.pi * c)
          for c in coupling
      ]
  
      # qubit term
      coeffs = list(omega)
      observables = [ad(i, d) @ a(i, d) for i in wires]
  
      # coupling term
      coeffs += list(g)
      observables += [
          ad(i, d) @ a(j, d) + ad(j, d) @ a(i, d)
          for (i, j) in connections
      ]
  
      # TODO Qudit support. Currently not supported but will be in the future.
      # if d>2:
      #     if qml.math.ndim(anharmonicity)==0:
      #         anharmonicity = [anharmonicity] * n_wires
      #     if len(anharmonicity) != n_wires:
      #         raise ValueError(f"Number of qubit anharmonicities anharmonicity = {anharmonicity} does not match the provided wires = {wires}")
      #     # anharmonicity term
      #     alpha = [2 * np.pi * a for a in anharmonicity]
      #     coeffs += list(alpha)
      #     observables += [ad(i, d) @ ad(i, d) @ a(i, d) @ a(i, d) for i in wires]
  
      return HardwareHamiltonian(
          coeffs,
          observables,
          settings=settings,
          reorder_fn=_reorder_AmpPhaseFreq,
      )
  
imports: import warnings
  from dataclasses import dataclass
  from typing import Callable, List, Union
  import numpy
  import pennylane
  from pennylane.pulse import HardwareHamiltonian
  from pennylane.pulse.hardware_hamiltonian import HardwarePulse
  from pennylane.typing import TensorLike
  from pennylane.wires import Wires
label_desc: Use image node_id 3 for calling a global function with example usage: transmon_interaction(qubit_freq, connections, coupling, wires, anharmonicity, d) and returns: HardwareHamiltonian