Implementation of Topological Quantum Gates in Magnet-Superconductor Hybrid Structures

TL;DR

This paper demonstrates the implementation of topologically protected quantum gates using Majorana zero modes in magnet-superconductor hybrids, utilizing advanced spin control and visualization techniques to advance topological quantum computing.

Contribution

It introduces a braiding protocol for Majorana modes in 2D hybrid structures and visualizes the process via local density of states calculations.

Findings

Successful implementation of topological quantum gates.

Visualization of braiding process in space and time.

Use of electron-spin-resonance for control.

Abstract

The creation of topological quantum gates using Majorana zero modes -- an outstanding problem in the field of topological quantum computing -- relies on our ability to control the braiding process of these particles in time and space. Here, we demonstrate the successful implementation of topologically protected $\sqrt{\sigma_z}$-, $\sigma_z$- and $\sigma_x$-quantum gates using Majorana zero modes in two-dimensional magnet-superconductor hybrid structures. We propose a braiding protocol that makes use of recent advances in the ability to control the spin of individual atoms using electron-spin-resonance techniques. We visualize the braiding process in time and space by computing the non-equilibrium local density of states, which is proportional to the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments.