A spin-orbit qubit is a hybrid qubit that contains both orbital and spindegrees of freedom of an electron in a quantum dot. Here we study the exchangecoupling between two spin-orbit qubits in a nanowire double quantum dot (DQD)with strong spin-orbit coupling (SOC). We find that while the total tunnelingin the DQD is irrelevant to the SOC, both the spin-conserved and spin-flippedtunnelings are SOC dependent and can compete with each other in the strong SOCregime. Moreover, the Coulomb repulsion between electrons can combine with theSOC-dependent tunnelings to yield an anisotropic exchange coupling between thetwo spin-orbit qubits. Also, we give an explicit physical mechanism for thisanisotropic exchange coupling.
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