qml.liealg.check_commutation_relation

check_commutation_relation(ops1, ops2, vspace)

Helper function to check \([\text{ops1}, \text{ops2}] \subseteq \text{vspace}\).

Warning

This function is expensive to compute.

Parameters:

• ops1 (List[Union[PauliSentence, TensorLike]]) – First set of operators.

• ops2 (List[Union[PauliSentence, TensorLike]]) – Second set of operators.

• vspace (Union[PauliVSpace, List[Union[PauliSentence, TensorLike]]]) – The vector space in form of a PauliVSpace that the operators should map to.

Returns:

Whether or not \([\text{ops1}, \text{ops2}] \subseteq \text{vspace}\).

Return type:

bool

Example

>>> from pennylane.liealg import check_commutation_relation
>>> ops1 = [qml.X(0)]
>>> ops2 = [qml.Y(0)]
>>> vspace1 = [qml.X(0), qml.Y(0)]

Because \([X_0, Y_0] = 2i Z_0\), the commutators do not map to the selected vector space.

>>> check_commutation_relation(ops1, ops2, vspace1)
False

Instead, we need the full \(\mathfrak{su}(2)\) space.

>>> vspace2 = [qml.X(0), qml.Y(0), qml.Z(0)]
>>> check_commutation_relation(ops1, ops2, vspace2)
True

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