Demonstrating non-Abelian statistics of Majorana fermions using twist defects

Abstract

We study the twist defects in the toric code model introduced by Bombin\n[Phys. Rev. Lett. 105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner\ntransformation, we show explicitly the twist defects carry unpaired Majorana\nzero modes. We also draw the same conclusion using two alternative approaches\nof a perturbation theory and a projective construction. We propose a quantum\nnon-demolition measurement scheme of the parity of Majorana modes. Such a\nscheme provides an alternative avenue to demonstrate the non-Abelian statistics\nof Majorana fermions with measurement-based braidings.\n