  The spin-sensitive charge oscillation, controlled by an external magnetic
field, was recently proposed as a mechanism of transformations of qubits,
defined as two-electron spin-charge Wannier molecules in a square quantum dot.
The paper expands this idea by including the effects of Rashba type spin-orbit
coupling. The problem is studied theoretically by mapping the system to an
analytic effective Hamiltonian for 8 low energy states, comprising singlet and
triplet on each dot diagonal. The validity of the mapping is confirmed by
comparing the energy and spin of full and mapped system, and also by the
reproduction of charge-oscillation dynamics in the presence of magnetic flux.
The newly introduced Rashba coupling significantly enriches the system
dynamics, affecting the magnitude of charge oscillations and allowing the
controlled transitions between singlet and triplet states due to the spin
rotations, induced by spin-orbit coupling. The results indicate the possibility
for use of the studied system for quantum information processing, while
possible extensions of the system to serve as a qubit in a universal quantum
computer, fulfilling all five DiVincenzo criteria, are also discussed.
