Abstract

Majorana zero modes harbored by topological superconductors may be the key ingredient for the realization of fault-tolerant quantum computing and topologically protected quantum devices. Therein, magnet-superconductor hybrid (MSH) systems have proven to be an experimentally versatile platform for quantum engineering the emergence of topological superconductivity and the associated Majorana modes.
In this talk, I will show how topological nodal-point superconductivity (TNPSC), for which strong evidence was observed in recent scanning tunneling microscopy experiments, can be realized in two-dimensional MSH systems using checkerboard and spiral magnetic structures. Due to its symmetry classification, this intriguing topological phase shows unique and edge-dependent low-energy modes, which can be used to identify the underlying topology.
Moreover, I will show how the ability to manipulate the magnetic structure of a 1D MSH network is a powerful tuning knob for the realization of topological quantum gates and algorithms with Majorana zero modes. In particular, I will demonstrate the simulation of the Bernstein-Vazirani algorithm, which lets one extract a hidden number from the topological system. Finally, I will discuss alternative architectures for topological quantum gates in 2D MSH systems and show how transitions between one-dimensional Majorana edge modes and zero-dimensional Majorana zero modes can be facilitated through magnetic vortices.