Fidelity optimization for holonomic quantum gates in dissipative environments

We analyze the performance of holonomic quantum gates in semiconductor quantum dots, driven by ultrafast lasers, under the effect of a dissipative environment. The environment is modeled as a thermal bath of oscillators linearly coupled with the electron states of the quantum dot. Standard techniques make the problem amenable to a numerical treatment and allow one to determine the fidelity as a function of all the relevant physical parameters. As a consequence of our analysis, we show that the disturbance of the environment can be (approximately) suppressed and the performance of the gate optimized-provided that the thermal bath is purely super-Ohmic. We conclude by showing that such an optimization is impossible for Ohmic environments.