Shuttling of Majorana zero modes in disordered and noisy topological superconducting wires

An essential ingredient in a number of protocols which braid Majorana zero modes (MZMs) involves their physical transport across topological superconducting wires. Transport occurring over finite time scales can encourage transitions from the ground state subspace into excited states and constitutes a “diabatic error” in the context of quantum computations. In our work, we study the behaviour of the diabatic error as MZMs are shuttled in a wire setting using the “piano key” method, where a series of electric gates are used to tune the chemical potential. It has previously been established that the error from a single piano key can be adequately described by Landau-Zener physics [1] and that the use of multiple piano keys may be optimal in reducing the error in certain situations [2]. We extend upon these studies and consider the response of the error when MZMs are shuttled through wires which contain disorder and are subjected to external noise. Through numerical simulation, we find that the error is generally enhanced in both cases, and we demonstrate that the minimum bulk gap plays a central role in this enhancement.

[1] B. Bauer, T. Karzig, R. V. Mishmash, A. E. Antipov, and J. Alicea, SciPost Phys. 5, 004 (2018)

[2] B. P. Truong, K. Agarwal, T. Pereg-Barnea, Phys. Rev. B 107, 104516 (2023)