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  • Letter

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

Jacob R. Taylor and Sankar Das Sarma

Phys. Rev. B 112, L041110 – Published 10 July, 2025

DOI: https://doi.org/10.1103/8p7r-cw9k

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 premitigation situation manifests no apparent topology. The disorder potential, as well as the scattering invariant (TV) normally used to classify a device as topologically nontrivial, 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 Letter, we leverage a vision-transformer neural network trained on conductance measurements along with a covariance matrix adaptation evolution strategy (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 TV 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 nontrivial regions can be transformed into robust topological devices.

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