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We present a numerical study of the robustness of a specific class ofnon-abelian holonomic quantum gates . We take into account the parametric noisedue to stochastic fluctuations of the control fields which drive thetime-dependent Hamiltonian along an adiabatic loop. The performance estimatorused is the state fidelity between noiseless and noisy holonomic gates.  We carry over our analysis with different correlation times and we find outthat noisy holonomic gates seem to be close to the noiseless ones for 'short'and 'long' noise correlation times. This result can be interpreted as aconsequence of to the geometric nature of the holonomic operator. Oursimulation have been performed by using parameters relevant to the excitonicproposal for implementation of holonomic quantum computation  [P. Solinas et al. Phys. Rev. B 67, 121307 (2003)]Comment: 7 pages, 13 figures Corrections in the text and substitution of the  figures concerning the comparison between dynamical and geometrical gate

Robustness of non-Abelian holonomic quantum gates against parametric noise