Optimal Control of Majorana Zero Modes

TL;DR

This paper develops optimal bang-bang control protocols to minimize nonadiabatic errors in finite-time braiding of Majorana zero modes, enhancing topological quantum computing robustness.

Contribution

It introduces a novel control scheme for Majorana braiding that significantly reduces nonadiabatic errors compared to traditional methods.

Findings

Bang-bang protocols outperform naive protocols in error minimization.

Sharp velocity transitions characterize optimal braiding protocols.

Nonadiabatic errors can be reduced by orders of magnitude.

Abstract

Braiding of Majorana zero modes provides a promising platform for quantum information processing, which is topologically protected against errors. Strictly speaking, however, the scheme relies on infinite braiding times as it utilizes the adiabatic limit. Here we show how to minimize nonadiabatic errors for finite braiding times by finding an optimal protocol for the Majorana movement. Interestingly, these protocols are characterized by sharp transitions between Majorana motion at maximal and minimal velocities. We find that these so-called bang-bang protocols can minimize the nonadiabatic transitions of the system by orders of magnitude in comparison with naive protocols.