We study the implications of spin-orbit interaction (SOI) for two-qubit gates
(TQGs) in semiconductor spin qubit platforms. The exchange interaction
governing qubit pairs is anisotropic under SOI, posing a problem for
conventional TQGs derived under the Heisenberg exchange. After developing a
concise form of the effective two-qubit Hamiltonian under SOI, we use it to
derive properties of rotating-frame evolution. Two main observations are made.
First, in contrary to past belief, we find that an appropriate amount of SOI
can significantly enhance the controlled-phase gate fidelity compared to the
no-SOI case. Second, SOI enables novel two-qubit dynamics, that are
conventionally inaccessible through DC evolution, such as the reflection gate
and the controlled-not gate