# Vortex Majorana braiding in a finite time

## TL;DR

This paper proposes a finite-time vortex braiding method in Fe-based superconductors that mimics Majorana exchange without physical swapping, offering robustness against parameter variations and speed, advancing quantum computing prospects.

## Contribution

It introduces a non-adiabatic, finite-time vortex braiding scheme called the Majorana carousel, which is analytically shown to be robust and applicable to Y-junctions.

## Key findings

- Finite-time vortex braiding is feasible without physical exchange.
- The method is robust against material and speed variations.
- Analytical proof confirms the robustness of the approach.

## Abstract

Abrikosov vortices in Fe-based superconductors are a promising platform for hosting Majorana zero modes. Their adiabatic exchange is a key ingredient for Majorana-based quantum computing. However, the adiabatic braiding process can not be realized in state-of-the-art experiments. We propose to replace the infinitely slow, long-path braiding by only slightly moving vortices in a special geometry without actually physically exchanging the Majoranas, like a Majorana carousel. Although the resulting finite-time gate is not topologically protected, it is robust against variations in material specific parameters and in the braiding-speed. We prove this analytically. Our results carry over to Y-junctions of Majorana wires.