code: def commutation_dag(
      tape: QuantumTape,
  ) -> (Sequence[QuantumTape], Callable):
      r"""Construct the pairwise-commutation DAG (directed acyclic graph) representation of a quantum circuit.
  
      In the DAG, each node represents a quantum operation, and edges represent
      non-commutation between two operations.
  
      This transform takes into account that not all
      operations can be moved next to each other by pairwise commutation.
  
      Args:
          tape (QNode or QuantumTape or Callable): The quantum circuit.
  
      Returns:
          qnode (QNode) or quantum function (Callable) or tuple[List[QuantumTape], function]:
  
          The transformed circuit as described in :func:`qml.transform <pennylane.transform>`. Executing this circuit
          will provide the commutation DAG.
  
      **Example**
  
      >>> dev = qml.device("default.qubit")
  
      .. code-block:: python
  
          @qml.qnode(device=dev)
          def circuit(x, y, z):
              qml.RX(x, wires=0)
              qml.RX(y, wires=0)
              qml.CNOT(wires=[1, 2])
              qml.RY(y, wires=1)
              qml.Hadamard(wires=2)
              qml.CRZ(z, wires=[2, 0])
              qml.RY(-y, wires=1)
              return qml.expval(qml.PauliZ(0))
  
      The commutation dag can be returned by using the following code:
  
      >>> dag_fn = commutation_dag(circuit)
      >>> dag = dag_fn(np.pi / 4, np.pi / 3, np.pi / 2)
  
      Nodes in the commutation DAG can be accessed via the :meth:`~.get_nodes` method, returning a list of
      the  form ``(ID, CommutationDAGNode)``:
  
      >>> nodes = dag.get_nodes()
      >>> nodes
      NodeDataView({0: <pennylane.transforms.commutation_dag.CommutationDAGNode object at 0x7f461c4bb580>, ...}, data='node')
  
      You can also access specific nodes (of type :class:`~.CommutationDAGNode`) by using the :meth:`~.get_node`
      method. See :class:`~.CommutationDAGNode` for a list of available
      node attributes.
  
      >>> second_node = dag.get_node(2)
      >>> second_node
      <pennylane.transforms.commutation_dag.CommutationDAGNode object at 0x136f8c4c0>
      >>> second_node.op
      CNOT(wires=[1, 2])
      >>> second_node.successors
      [3, 4, 5, 6]
      >>> second_node.predecessors
      []
  
      For more details, see:
  
      * Iten, R., Moyard, R., Metger, T., Sutter, D., Woerner, S.
        "Exact and practical pattern matching for quantum circuit optimization" `doi.org/10.1145/3498325
        <https://dl.acm.org/doi/abs/10.1145/3498325>`_
  
      """
  
      def processing_fn(res):
          """Processing function that returns the circuit as a commutation DAG."""
          # Initialize DAG
          dag = CommutationDAG(res[0])
          return dag
  
      return [tape], processing_fn
  
imports: import heapq
  from collections import OrderedDict
  from functools import partial
  from typing import Sequence, Callable
  import networkx
  from networkx.drawing.nx_pydot import to_pydot
  import pennylane
  from pennylane.tape import QuantumTape
  from pennylane.wires import Wires
  from pennylane.transforms import transform
label_desc: Use image node_id 1 for calling a global function with example usage: commutation_dag(tape) and returns: list,  processing_fn, dag