Vision transformer based deep learning of topological indicators in Majorana nanowires

One-dimensional superconductor-semiconductor nanowires are leading candidates for topological quantum computation because of their ability to host non-Abelian Majorana zero modes (MZMs). However, 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 studies clearly indicate the need for developing new techniques for identifying and diagnosing MZMs. In this study, we use a generalized vision transformer-based neural network to predict, using tunnel conductance measurements, whether a device manifests a topological MZM phase in the presence of disorder and to map out the entire topological phase diagram. We demonstrate the ability of our method to classify with arbitrary confidence $(P>0.9998)$ whether a device as possesses a a nontrivial MZM-carrying topological phase for a wide variety of disorder parameters. We also show 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 because topology may not be uniquely defined by the scattering invariant in short disordered wires. This work serves as a significant advance, offering a step toward the practical realization of Majorana-based quantum devices, allowing 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 employing this technique for the analysis of experimental data in superconductor-semiconductor hybrid Majorana platforms.