Parafermion stabilizer codes

Authors

Utkan Güngördü, University of Nebraska-LincolnFollow
Rabindra Nepal, University of Nebraska-LincolnFollow
Alexey Kovalev, University of Nebraska - LncolnFollow

Date of this Version

2014

Citation

Phys. Rev. A 90, 042326 (2014); DOI: 10.1103/PhysRevA.90.042326

Comments

©2014 American Physical Society. Used by permission.

Abstract

We define and study parafermion stabilizer codes, which can be viewed as generalizations of Kitaev’s onedimensional (1D) model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against lowweight errors acting on a small subset of parafermion modes in analogy to qudit stabilizer codes. Examples of several smallest parafermion stabilizer codes are given. A locality-preserving embedding of qudit operators into parafermion operators is established that allows one to map known qudit stabilizer codes to parafermion codes. We also present a local 2D parafermion construction that combines topological protection of Kitaev’s toric code with additional protection relying on parity conservation.