Dephasing dynamics of noisy Majorana-based qubits: Topological versus Andreev

Topological quantum computation schemes encode quantum information nonlocally through non-Abelian anyons separated by macroscopic distances $L$, typically spanning the length of the constituent qubit device. This nonlocality renders topological qubits exponentially immune to dephasing from \emph{all} sources of classical noise with operator support local on the scale of $L$. We explore detailed theoretical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits which is designed to validate this coveted topological protection in near-term nanowire devices. By assessing dependence on wire length $L$, our proposed protocol can sharply distinguish a bona fide Majorana qubit from one constructed from Andreev bound states, which can otherwise closely mimic the true Majorana scenario in local probes; for a fixed wire length, the protocol can also inform which scenario is likely realized. This proposed experiment requires no pulsing and only (relatively slow) measurement of two nearby Majorana modes for both initialization and readout---achievable, for example, by tunnel coupling to a nearby quantum dot---and thus serves as an enticing pre-braiding experiment aimed at quantifying the utility of Majorana-based qubits.