Exchange gate between hole spin qubits with Rashba spin-orbit coupling

Hole spin qubits in semiconductor quantum dots have seen rapid progress in recent years. We focus on the Rashba spin-orbit (SO) coupling, which has been used to implement electric dipole spin resonance (EDSR) without microstructures to create local magnetic fields for single-qubit gate operations. We theoretically study the exchange interaction between localized holes in a double quantum dot system in the planar semiconductor heterostructure, elucidating the effects of the Rashba spin-orbit coupling. Effective Hamiltonian of the system and optimal conditions for two-qubit gates based on the exchange interaction between hole spin qubits with the SO coupling are presented.