Holonomic gates for quantum computation are commonly considered to be robust
against certain kinds of parametric noise, the very motivation of this
robustness being the geometric character of the transformation achieved in the
adiabatic limit. On the other hand, the effects of decoherence are expected to
become more and more relevant when the adiabatic limit is approached. Starting
from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)],
here we discuss the behavior of non ideal holonomic gates at finite operational
time, i.e., far before the adiabatic limit is reached. We have considered
several models of parametric noise and studied the robustness of finite time
gates. The obtained results suggest that the finite time gates present some
effects of cancellation of the perturbations introduced by the noise which
mimic the geometrical cancellation effect of standard holonomic gates.
Nevertheless, a careful analysis of the results leads to the conclusion that
these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on
Phys. Rev.