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Topological Quantum Computing

Lattice Model for Fermionic Toric Code

arXiv
Authors: Zheng-Cheng Gu, Zhenghan Wang, Xiao-Gang Wen

Year

2013

Paper ID

32503

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

Abstract

The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact soluble string-net models. However, the most important topologically ordered phases of matter are arguably the fermionic fractional quantum Hall states. Topological phases of matter for fermion systems are strictly richer than their bosonic counterparts because locality has different meanings for the two kinds of systems. In this paper, we describe a simple fermionic version of the toric code model to illustrate many salient features of fermionic exactly soluble models and fermionic topologically ordered states.

Why This Paper Matters

  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2013 reference point for readers tracking recent quantum research.
  • The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1309.7032 [2] arXiv https://arxiv.org/abs/1309.7032 [3] Publisher https://arxiv.org/abs/1309.7032

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