Environmental noise reduction for holonomic quantum gates

We study the performance of holonomic quantum gates, driven by lasers, under the effect of a dissipative environment modeled as a thermal bath of oscillators. We show how to enhance the performance of the gates by a suitable choice of the loop in the manifold of the controllable parameters of the laser. For a simplified, albeit realistic model, we find the surprising result that for a long time evolution the performance of the gate (properly estimated in terms of average fidelity) increases. On the basis of this result, we compare holonomic gates with the so-called stimulated raman adiabatic passage (STIRAP) gates.