Refocusing schemes for holonomic quantum computation in presence of dissipation

The effects of dissipation on a holonomic quantum computation scheme are analyzed within the quantum-jump approach. We extend to the non-Abelian case the refocusing strategies formerly introduced for (Abelian) geometric computation. We show how double loop symmetrization schemes allow one to get rid of the unwanted influence of dissipation in the no-jump trajectory.