Majorana-based Topological Quantum Algorithms in Magnet-Superconductor Hybrid Structures

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. 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 dissertation, I will show how the exotic phase of topological nodal-point superconductivity can be realized in two-dimensional MSH systems using a checkerboard and spiral magnetic structures. 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 can be employed to simulate topological quantum gates and algorithms with Majorana zero modes. In particular, I will demonstrate the simulation of the Clifford gates as well as the Bernstein-Vazirani algorithm, which lets one extract a hidden number from the topological system. Finally, I will extend this to low-energy Majorana edge modes in 2D MSH systems and show how they, in combination with magnetic vortices, can be employed as a quantum memory for topological quantum computing.<p></p>