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.


circuit (pennylane.QNode, QuantumTape, or Callable) – A quantum node, tape, or function that applies quantum operations.


Function which accepts the same arguments as the qml.QNode, qml.tape.QuantumTape or quantum function. When called, this function will return the commutation DAG representation of the circuit.

Return type



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.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 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 CommutationDAGNode) by using the get_node() method. See 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


Using PennyLane