Robustness of Kitaev Honeycomb Ground State in Presence of a Quench

Motivated by the importance of stability of quantum computation against perturbations and external noise, we study the Kitaev honeycomb model, a system of interest for topological quantum computing, when it is subjected to different quenches. Particularly, we put our focus on the long-time behaviors of the Loschmidt echo and Uhlmann fidelity for the Kitaev ground state when the system is subjected to a uniform magnetic field and local impurities. We compare the cases without and with noise. We focus on Gaussian white noise modelled by a Lindblad Master Equation approach. We find that in the gapped phase, the Kitaev ground state is robust to perturbations, further motivating the potential usefulness of a gapped Kitaev-like system in quantum computing. This result stands in contrast to the other cases we study where we find an exponential decay that appears to be a manifestation of the orthogonality catastrophe.