Vision transformer based Deep Learning of Topological indicators in Majorana Nanowires

Abstract

1D superconductor-semiconductor nanowires are the leading candidates for topological quantum computation due to their ability to host non-Abelian Majorana zero modes (MZMs). However, the standard methods for identifying MZMs are often inadequate, particularly in the presence of disorder, where many properties considered to be heralds of MZMs are often generated by trivial disorder induced Andreev bound states. Recent works clearly indicate the need for developing new techniques for identifying and diagnosing MZMs. In this study, we utilize a generalized Vision Transformer-based neural network to predict, using tunnel conductance measurements, both whether a device manifests a topological MZMs phase in the presence of disorder, and also to map out the entire topological phase diagram. We show the ability of our method up to arbitrary confidence ($P>0.9998$) in classifying a device as possessing a non-trivial MZM-carrying topological phase for a wide variety of disorder parameters. We demonstrate an ability to predict from conductance measurements alternative (to the extensively used scattering-matrix-invariant topological indicator) Majorana indicators based on local density of states (LDOS). This is relevant since topology may not be uniquely defined by the scattering invariant in short disordered wires. This work serves as a significant advance offering a step towards the practical realization of Majorana-based quantum devices, enabling a deep-learning understanding of the topological properties in disordered nanowire systems. We validate our method using extensive simulated Majorana results in the presence of disorder, and suggest using this technique for the analysis of experimental data in superconductor-semiconductor hybrid Majorana platforms.

21 pages, 12 Figures

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• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
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• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires