# qml.transforms.split_non_commuting¶

split_non_commuting(tape)[source]

Splits a qnode measuring non-commuting observables into groups of commuting observables.

Parameters

qnode (pennylane.QNode or QuantumTape) – quantum tape or QNode that contains a list of non-commuting observables to measure.

Returns

If a QNode is passed, it returns a QNode capable of handling non-commuting groups. If a tape is passed, returns a tuple containing a list of quantum tapes to be evaluated, and a function to be applied to these tape executions to restore the ordering of the inputs.

Return type

qnode (pennylane.QNode) or tuple[List[QuantumTape], function]

Example

This transform allows us to transform a QNode that measures non-commuting observables to multiple circuit executions with qubit-wise commuting groups:

dev = qml.device("default.qubit", wires=1)

@qml.transforms.split_non_commuting
@qml.qnode(dev)
def circuit(x):
qml.RX(x,wires=0)
return [qml.expval(qml.PauliX(0)), qml.expval(qml.PauliZ(0))]


Instead of decorating the QNode, we can also create a new function that yields the same result in the following way:

@qml.qnode(dev)
def circuit(x):
qml.RX(x,wires=0)
return [qml.expval(qml.PauliX(0)), qml.expval(qml.PauliZ(0))]

circuit = qml.transforms.split_non_commuting(circuit)


Internally, the QNode is split into groups of commuting observables when executed:

>>> print(qml.draw(circuit)(0.5))
0: ──RX(0.50)─┤  <X>
\
0: ──RX(0.50)─┤  <Z>


Note that while internally multiple QNodes are created, the end result has the same ordering as the user provides in the return statement. Here is a more involved example where we can see the different ordering at the execution level but restoring the original ordering in the output:

@qml.transforms.split_non_commuting
@qml.qnode(dev)
def circuit0(x):
qml.RY(x[0], wires=0)
qml.RX(x[1], wires=0)
return [qml.expval(qml.PauliX(0)),
qml.expval(qml.PauliZ(0)),
qml.expval(qml.PauliY(1)),
qml.expval(qml.PauliZ(0) @ qml.PauliZ(1)),
]


Drawing this QNode unveils the separate executions in the background

>>> print(qml.draw(circuit0)([np.pi/4, np.pi/4]))
0: ──RY(0.79)──RX(0.79)─┤  <X>
1: ─────────────────────┤  <Y>
\
0: ──RY(0.79)──RX(0.79)─┤  <Z> ╭<[email protected]>
1: ─────────────────────┤      ╰<[email protected]>


Yet, executing it returns the original ordering of the expectation values. The outputs correspond to $$(\langle \sigma_x^0 \rangle, \langle \sigma_z^0 \rangle, \langle \sigma_y^1 \rangle, \langle \sigma_z^0\sigma_z^1 \rangle)$$.

>>> circuit0([np.pi/4, np.pi/4])
tensor([0.70710678, 0.5       , 0.        , 0.5       ], requires_grad=True)


Internally, this function works with tapes. We can create a tape with non-commuting observables:

with qml.tape.QuantumTape() as tape:
qml.expval(qml.PauliZ(0))
qml.expval(qml.PauliY(0))

tapes, processing_fn = qml.transforms.split_non_commuting(tape)


Now tapes is a list of two tapes, each for one of the non-commuting terms:

>>> [t.observables for t in tapes]
[[expval(PauliZ(wires=[0]))], [expval(PauliY(wires=[0]))]]


The processing function becomes important when creating the commuting groups as the order of the inputs has been modified:

with qml.tape.QuantumTape() as tape:
qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))
qml.expval(qml.PauliX(0) @ qml.PauliX(1))
qml.expval(qml.PauliZ(0))
qml.expval(qml.PauliX(0))

tapes, processing_fn = qml.transforms.split_non_commuting(tape)


In this example, the groupings are group_coeffs = [[0,2], [1,3]] and processing_fn makes sure that the final output is of the same shape and ordering:

>>> processing_fn(tapes)