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.
Highlights
Recent experiments on low-dimensional superconducting structures have revealed localized electronic states at the Fermi level
We substantially simplify the direct approach of physically braiding vortex Majoranas and show how braiding is realized in finite time
We showed that Majorana braiding with superconducting vortices can be achieved robustly and in finite time by only slightly moving the vortices
Summary
Recent experiments on low-dimensional superconducting structures have revealed localized electronic states at the Fermi level. There, Abrikosov vortices carry spatially localized peaks in the density of states at zero bias voltage [10,11,12,13,14,15,16,17,18,19] We substantially simplify the direct approach of physically braiding vortex Majoranas and show how braiding is realized in finite time To this end, vortex Majoranas are spatially arranged such that changing the position of one of them on a short, well-defined path is equivalent to ordinary braiding. Other distances r j can be used as well, in particular for different material systems
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