Demonstrating non-Abelian statistics of Majorana fermions using twist defects

TL;DR

This paper demonstrates that twist defects in the toric code model host unpaired Majorana zero modes and proposes a measurement scheme to verify their non-Abelian statistics, advancing quantum computation research.

Contribution

It explicitly shows twist defects carry Majorana zero modes using multiple methods and introduces a measurement scheme for their non-Abelian braiding properties.

Findings

Twist defects host unpaired Majorana zero modes.

A quantum non-demolition measurement scheme is proposed.

The approach offers a new way to demonstrate non-Abelian statistics.

Abstract

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