Mitigating disorder and optimizing topological indicators with vision-transformer-based neural networks in Majorana nanowires

TL;DR

This paper presents a deep learning approach using vision transformers and an optimization framework to mitigate disorder in Majorana nanowires, enabling the recovery of topological zero modes even in highly disordered systems.

Contribution

It introduces a novel neural network-based method that directly optimizes topological indicators to improve the topological properties of nanowires affected by disorder.

Findings

Deep learning can recover topological MZMs in disordered nanowires.

The method effectively mitigates disorder effects, transforming trivial states into topological ones.

The approach outperforms traditional indirect classification methods.

Abstract

Disorder remains a major obstacle to realizing topological Majorana zero modes (MZMs) in superconductor-semiconductor nanowires, and we show how deep learning can be used to recover topological MZMs mitigating disorder even when the pre-mitigation situation manifests no apparent topology. The disorder potential, as well as the scattering invariant ($T_V$) normally used to classify a device as topologically non-trivial are not directly measurable experimentally. Additionally, the conventional signatures of MZMs have proved insufficient due to their being accidentally replicated by disorder-induced trivial states. Recent advances in machine learning provide a novel method to solve these problems, allowing the underlying topology, suppressed by disorder, to be recovered using effective mitigation procedures. In this work, we leverage a vision transformer neural network trained on conductance measurements along with a CMA-ES optimization framework to dynamically tune gate voltages mitigating disorder effects. Unlike prior efforts that relied on indirect cost functions, our method directly optimizes $T_V$ alongside additional local density of states-based topological indicators. Using a lightweight neural network variant, we demonstrate that even highly disordered nanowires initially lacking any topologically non-trivial regions can be transformed into robust topological devices.