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arXiv · 1409.4724

Parafermion stabilizer codes

Utkan Güngördü·Rabindra Nepal·Alexey A. Kovalev
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Abstract

We define and study parafermion stabilizer codes which can be viewed as generalizations of Kitaev's one dimensional model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against low-weight 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 which 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.

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Utkan Güngördü, Rabindra Nepal, Alexey A. Kovalev. 2014-10-29. Parafermion stabilizer codes. https://doi.org/10.1103/physreva.90.042326

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