  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.
