Dynamical signatures of ground-state degeneracy to discriminate against Andreev levels in a Majorana fusion experiment

Detection of the fusion rule of Majora na zero-modes is a near-term milestone on the road to topological quantum computation. An obstacle is that the non-deterministic fusion outcome of topological zero-modes can be mimicked by the merging of non-topological Andreev levels. To distinguish these two scenarios, the dynamical signatures of the ground-state degeneracy that is the defining property of non-Abelian anyons is searched for. By adiabatically traversing parameter space along two different pathways, one can identify ground-state degeneracies from the breakdown of adiabaticity. It is shown that the approach can discriminate against accidental degeneracies of Andreev levels.