A single electron spin in a double quantum dot in a magnetic field is considered in terms of a four-level system. By describing the electron motion between the potential minima by spin-conserving tunneling and spin flip caused by a spin-orbit coupling, we inversely engineer faster-than-adiabatic state manipulation operations based on the geometry of four-dimensional (4D) rotations. In particular, we show how to transport a qubit among the quantum dots performing simultaneously a required spin rotation.
@article{arxiv.1809.08952,
title = {Qubit gates with simultaneous transport in double quantum dots},
author = {Yi-Chao Li and Xi Chen and J. G. Muga and E. Ya. Sherman},
journal= {arXiv preprint arXiv:1809.08952},
year = {2018}
}