The Simulation of Non-Abelian Statistics of Majorana Fermions in Ising   Chain with Z2 Symmetry
  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. 
Xiao-Ming Zhao, Jing Yu, Jing He, Qiu-Bo Cheng, Ying Liang, and   Su-Peng Kou
cond-mat.mes-hall cond-mat.other