Quantum Engineering Topological Superconductivity and Quantum Algorithms in Magnet-Superconductor Hybrid Systems*

The emergence of Majorana zero modes in topological superconductors might hold the key for realizing topological quantum computing and topology-based devices. Magnet-superconductor hybrid (MSH) systems have proven to be experimentally versatile platforms for the quantum engineering of topological superconductivity by custom-designing the complex structure of their magnetic layer. In this talk I will show how intriguing topological phases -- ranging from topological nodal point superconductivity (TNPSC) [1,2] to higher order topological superconductivity (HOTSC) [3] -- can be realized in two-dimensional MSH systems by using checkerboard, spiral, antiferromagnetic or stacked magnetic structures. The nodal electronic structure of TNPSC phases leads to a unique and edge-dependent emergence of low-energy modes, which can be used to identify the underlying topology. Moreover, I will demonstrate that the existence of HOTSC phases, and of the associated Majorana corner modes, sensitively depends on the edge terminations of MSH islands, providing an intriguing ability to tune the system between trivial and topological phases using atomic manipulation techniques. Finally, I will show how the ability to manipulate the magnetic structure in MSH systems can be employed to implement topological quantum algorithms using Majorana zero modes [4].