Utilizing the non-Abelian braiding properties of Majorana zero modes for quantum algorithms — an outstanding problem in the field of topological quantum computing — requires a platform that can be both scaled to large quantum registers and controlled in real time and space.

Here, we analyze the realization of topological quantum Z- and X-gates in two platforms based on two-dimensional magnet-superconductor hybrid (MSH) structures, from initialization all the way to read-out of the final many-body state. We demonstrate the time- and spatially-resolved spectroscopic signatures of these braiding processes by computing the non-equilibrium local density of states. This quantity is proportional to the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments, allowing us to directly image Majorana world lines.

Using these gates, we are able to perform the first successful simulation of the Bernstein-Vazirani algorithm in two-dimensional MSH structures, for which we introduce an optimized braiding protocol and a scalable architecture for its implementation with an arbitrary number of qubits.