  We analyse non-adiabatic non-Abelian holonomic transformations of spin-qubits
confined to a linear time dependent harmonic trap with time dependent Rashba
interaction. For this system exact results can be derived for spin rotation
angle which also enables exact treatment of white gate-noise effects. We
concentrate in particular on the reliability of cyclic transformations
quantified by fidelity defined by the probability that the qubit after one full
cycle remains in the ground-state energy manifold. The formalism allows exact
analysis of spin transformations that optimise final fidelity. Various examples
of time dependent fidelity probability distributions are presented and
discussed.
