  We consider the electric dipole spin resonance (EDSR) with using the
spin-orbit interaction (SOI) in GaAs and Ge based quantum dots formed in a
quantum well. We use Schrieffer-Wolff transformation and rotating frame to
derive the effective Hamiltonian of EDSR. We treat the couplings of the orbital
motion with the environment with Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)
master equation. We found that the cubic SOI makes the Rabi frequency
non-linear with the applied microwave amplitude. At the same time, the fidelity
of the spin manipulations becomes worse since the residual spin-orbital
couplings induces spin relaxation.
