Geometric quantum gates that are robust against stochastic control errors

The realistic application of geometric quantum computation is crucially dependent on an unproved robustness conjecture, claiming that geometric quantum gates are more resilient against random noise than dynamic gates. We propose a suitable model that allows a direct and fair comparison between geometrical and dynamical operations. In the presence of stochastic control errors we find that the maximum of gate fidelity corresponds to quantum gates with a vanishing dynamical phase. This is a clear evidence for the robustness of nonadiabatic geometric quantum computation. The predictions here presented can be experimentally tested in almost all of the already existing quantum computer candidates.