  An idea for a nanodevice in which an arbitrary sequence of three basic
quantum single qubit gates - negation, Hadamard and phase shift - can be
performed on a single electron spin. The spin state is manipulated using the
spin-orbit coupling and the electron trajectory is controlled by the electron
wave function self-focusing mechanism due to the electron interaction with the
charge induced on metal gates. We present results of simulations based on
iterative solution of the time dependent Schr\"odinger equation in which the
subsequent operations on the electron spin can be followed and controlled.
Description of the moving electron wave packet requires evaluation of the
electric field within the entire nanodevice in each time step.
