Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors

TL;DR

This paper investigates the optimal control of Majorana zero modes in topological superconductors using a multi-key approach, revealing a nontrivial optimal number of gates that minimizes diabatic errors during transport.

Contribution

It introduces a detailed numerical analysis of the 'piano key' method for transporting Majorana zero modes, identifying the optimal number of gates to minimize errors.

Findings

Multiple keys reduce diabatic errors up to an optimal point.

Increasing keys beyond the optimal number raises errors due to nonanalytic effects.

Modeling each key as a Landau-Zener process explains the error behavior.

Abstract

Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. A crucial building block of these protocols is the adiabatic shuttling of MZMs through topological superconductors. Here, we consider the "piano key" approach, where MZMs are transported using local electric gates to tune sections ("keys") of a wire between topologically trivial and nontrivial phases. We numerically simulate this transport on a single wire and calculate the diabatic error corresponding to exciting the system. We find that this error is typically reduced when transport is facilitated by using multiple keys as one may expect from modeling each piano key press as an effective Landau-Zener process. However, further increasing the number of keys increases errors; thus, there exists a nontrivial optimal number of keys that minimizes the diabatic error given a fixed total shuttle time. As we show, this optimal number of keys can be explained by modeling each key press as an effective Landau-Zener process while paying careful attention to power-law corrections that arise due to the nonanalytic behavior of the time-dependent modulation of the chemical potential at the beginning and end of each key press.