Non-Abelian operation on chiral Majorana fermions by quantum dots

Abstract

The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid junction btween a quantum anomalous Hall insulator and an s-wave superconductor. Here we show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, the resulting resonant exchange of chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any operation in the braid group can be achieved by this scheme. We further propose electrical transport experiments to observe the braiding of four chiral Majorana fermions and demonstrate the non-Abelian braiding statistics in four-terminal devices of the hybrid junctions. Both a conductance peak due to the braiding and the braiding-order dependent conductance are predicted. These findings pave a way to perform any braiding operation of chiral Majorana fermions by electrically controllable quantum dots.