The Simulation of Non-Abelian Statistics of Majorana Fermions in Ising Chain with Z2 Symmetry

TL;DR

This paper numerically demonstrates the non-Abelian statistics of Majorana fermions in a Z2 symmetric Ising chain, highlighting its potential for topological quantum computing.

Contribution

It provides numerical verification of non-Abelian statistics of Majorana fermions in a spin model with Z2 symmetry, connecting Majorana chains to quantum computing applications.

Findings

Numerical evidence of non-Abelian statistics in the Ising model.

Verification of Majorana fermions' properties in both representations.

Ground states form a platform for topological quantum computation.

Abstract

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions on the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana-representation and spin-representation are presented. The degenerate ground states of a symmetry protected spin chain therefore previde a promising platform for topological quantum computation.