Report on 1907.06497v2

Abstract

This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors.That "Holy Grail" of topological quantum information processing has not yet been reached in the laboratory, but there now exists a variety of platforms in which one can search for the Majorana braiding statistics.After an introduction to the basic concepts of braiding we discuss how one might be able to braid immobile Majorana zeromodes, bound to the end points of a nanowire, by performing the exchange in parameter space, rather than in real space.We explain how Coulomb interaction can be used to both control and read out the braiding operation, even though Majorana zero-modes are charge neutral.We ask whether the fusion rule might provide for an easier pathway towards the demonstration of non-Abelian statistics.In the final part we discuss an approach to braiding in real space, rather than parameter space, using vortices injected into a chiral Majorana edge mode as "flying qubits".

Authors 1

1. C. W. J. Beenakker corresponding Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Universiteit Leiden , P.O. Box 9506 , 2300 RA Leiden , The Netherlands

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands