Implementation of Topological Quantum Gates and Algorithms in Magnet-Superconductor Hybrid Structures

The implementation of topological quantum gates and algorithms using Majorana zero modes (MZMs) is a major outstanding problem in the field of topological quantum computing. In this talk, I will demonstrate the non-equilibrium realization of σ_z and σ_x quantum gates as well as the Bernstein-Vazirani quantum algorithm by theoretically showing how Majorana zero modes can be manipulated at the nanoscale in real time in magnet-superconductor hybrid (MSH) structures.

I will show how the spatial braiding of MZMs in time can be visualized in MSH systems via the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments. Moreover, I will demonstrate how quantum algorithms and gates can be initialized both in the even and odd-parity sector, and how the successful realization of a quantum algorithm can be read out by fusing the MZMs and measuring the time-dependent charge density.