Transport of Majorana Bound State in the presence of telegraph noise

TL;DR

This paper investigates how telegraph noise affects the transport of Majorana Bound States in semiconductor-superconductor heterostructures, providing models and scaling laws to understand errors during topological state manipulation.

Contribution

It introduces a unified analytical and numerical framework to analyze noise-induced errors in MBS transport and explores optimal control strategies in noisy environments.

Findings

Noise induces diabatic errors during MBS transport.

Scaling laws relate error rates to drive time and noise characteristics.

Disorder impacts robustness and error scaling in MBS transport.

Abstract

Majorana Bound States (MBS) have emerged as promising candidates for robust quantum computing due to their non-Abelian statistics and topological protection. In this study, we focus on the dynamical transport of MBS in the semiconductor-superconductor (SM-SC) heterostructure via the piano key-type setup, wherein each of the keys of the wire can be tuned from topological to trivial phases. We focus on the transport of MBS under noisy conditions and evaluate the feasibility for realistic scenarios. The central emphasis of our work lies in using both numerical and analytical techniques to understand the effect of noise in inducing diabatic errors during transport and to establish scaling laws that relate these errors to the drive time. To achieve this, we derive an effective model that captures the scaling behavior in both noise-free and noisy scenarios, providing a unified framework for analyzing the transport dynamics. We investigate the optimal number of keys for both noisy and noiseless scenarios. Additionally, we explore the effects of disorder on transport dynamics, highlighting its impact on error scaling and robustness.