Given two unitaries with the same interaction coefficients but different

local unitary rotations determine the local unitaries that turns one type of gate into another.

1) perform the kak decomp on each unitary and confirm interaction terms are equivalent 2) identify the elements of SU(2) to transform unitary2 into unitary1

unitary1 unitary that we target
unitary2 unitary that we transform the local gates to the target

four 2x2 unitaries. first two are pre-rotations last two are post rotations.