Optimizing Transport of Majorana Zero Modes in One-Dimensional Topological Superconductors

Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. Braiding protocols involving MZMs are often envisioned on networks of topological superconducting wires with a key ingredient being the way by which MZMs are shuttled. We consider the “piano key” approach [1], where MZMs are transported by using local electric gates to tune sections (“keys”) of a wire between trivial and topological phases. We numerically simulate this transport on a single wire and calculate the diabatic error, defined to be the probability of transitions between the ground state manifold and excited states. We determine that the diabatic error typically improves when transport is facilitated by using multiple keys, however this advantage is lost when an abundance of keys is used. We demonstrate that there exists an optimal number of keys and establish its dependence on parameters. Furthermore, we show that the behaviour of the diabatic error can be adequately described by usual Landau-Zener physics with corrections originating from the specific model used to tune each key.

[1] B. Bauer et al., SciPost Phys. 5, 004 (2018)