[BUG] qml.center does not work for all linear combinations of Paulis

[dwierichs]

Expected behavior

qml.center always computes the center of an algebra.

Actual behavior

If the algebra basis is such that the center elements are linear combinations of them, qml.center does not find them.

Additional information

We need to overlap kernels of adjoint representations instead of commuting basis elements alone.

Source code

>>> dla = qml.lie_closure([qml.X(0), qml.X(1), (qml.X(0)@qml.X(1) + qml.Y(0) @ qml.Y(1) + qml.Z(0)@ qml.Z(1))])
>>> print(dla)
[X(0),
 X(1),
 X(0) @ X(1) + Y(0) @ Y(1) + Z(0) @ Z(1),
 Z(0) @ Y(1) + -1.0 * (Y(0) @ Z(1)),
 -1.0 * (Y(0) @ Y(1)) + -1.0 * (Z(0) @ Z(1))]
>>> qml.center(dla)
[] # Should contain X(0) + X(1)

Tracebacks

No response

System information

pl dev

Existing GitHub issues

• I have searched existing GitHub issues to make sure the issue does not already exist.