  We analyze the performance of holonomic quantum gates in semi-conductor
quantum dots, driven by ultrafast lasers, under the effect of a dissipative
environment. In agreement with the standard practice, the environment is
modeled as a thermal bath of oscillators linearly coupled with the excitonic
states of the quantum dot. Standard techniques of quantum dissipation make the
problem amenable to a numerical treatment and allow to determine the fidelity
(the common gate-performance estimator), as a function of all the relevant
physical parameters. As a consequence of our analysis, we show that, by varying
in a suitable way the controllable parameters, the disturbance of the
environment can be (approximately) suppressed, and the performance of the gate
optimized--provided that the thermal bath is purely superhomic. We conclude by
showing that such an optimization it is impossible for ohmic environments.
