Spin-orbit interaction enabled high-fidelity two-qubit gates

We study the implications of spin-orbit interaction (SOI) for two-qubit gates (TQGs) in semiconductor spin qubit platforms. SOI renders the exchange interaction governing qubit pairs anisotropic, posing a serious challenge for conventional TQGs derived for the isotropic Heisenberg exchange. Starting from microscopic level, we develop a concise computational Hamiltonian that captures the essence of SOI, and use it to derive properties of the rotating-frame time evolutions. Two key findings are made. First, for the controlled-phase/controlled-Z gate, we show and analytically prove the existence of 'SOI nodes' where the fidelity can be optimally enhanced, with only slight modifications in terms of gate time and local phase corrections. Second, we discover and discuss novel two-qubit dynamics that are inaccessible without SOI-the reflection gate and the direct controlled-not gate (CNOT). The relevant conditions and achievable fidelities are explicitly derived for the direct CNOT.