  Robustness of edge states and non-Abelian excitations of topological states
of matter promises quantum memory and quantum processing, which is naturally
immune against microscopic imperfections such as static disorder. However,
topological properties will not in general protect quantum system from
time-dependent disorder or noise. Here we take the example of a network of
Kitaev wires with Majorana edge modes storing qubits to investigate the effects
of classical noise in the crossover from the quasi-static to the fast
fluctuation regime. We present detailed results for the Majorana edge
correlations, and fidelity of braiding operations for both global and local
noise sources preserving parity symmetry, such as random chemical potentials
and phase fluctuations. While in general noise will induce heating and
dephasing, we identify examples of long-lived quantum correlations in presence
of fast noise due to motional narrowing, where external noise drives the system
rapidly between the topological and non-topological phases.
