Unreasonable effectiveness of unsupervised learning in identifying Majorana topology

TL;DR

This paper demonstrates that combining unsupervised and supervised learning with autoencoders can effectively identify topological phases in Majorana nanowires using unlabeled data, overcoming traditional challenges.

Contribution

It introduces a novel approach that leverages unsupervised learning to detect topological order in Majorana nanowires, including phase crossover points.

Findings

Unsupervised learning can distinguish topological from trivial phases.

The method identifies the crossover point in the phase diagram.

It reduces the need for labeled data in topological phase detection.

Abstract

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool in identifying topological order since topology does not always manifest in obvious physical ways (e.g., topological superconductivity) for its decisive confirmation. The problem, however, is that unsupervised learning is a difficult challenge, necessitating huge computing resources, which may not always work. In the current work, we combine unsupervised and supervised learning using an autoencoder to establish that unlabeled data in the Majorana splitting in realistic short disordered nanowires may enable not only a distinction between `topological' and `trivial', but also where their crossover happens in the relevant parameter space. This may be a useful tool in identifying topology in Majorana nanowires.