Numerical simulation of spin-qubit operation in coupled quantum dots

Electronic states and spin operation in coupled quantum dots are numerically studied, considering realistic shape of quantum dots and electron-electron interaction, (i) We evaluate the spin coupling J between two electron spins, as a function of magnetic field perpendicular to the quantum dots. We observe a transition from antiferromagnetic coupling (J > 0) to ferromagnetic coupling (J < 0) at magnetic field of a few Tesla. The spin coupling is hardly influenced by the size difference between the quantum dots if the energy levels are matched, (ii) We simulate SWAP gate operations by calculating the time development of two electron spins. We show that a sudden change of tunnel barrier may result in the gate errors. The spin exchange is incomplete in the presence of strong spin-orbit interaction in InGaAs.