Parafermion stabilizer codes

TL;DR

This paper introduces parafermion stabilizer codes, generalizing Majorana-based models, offering new error correction methods for quantum information with potential topological and parity-based protections.

Contribution

It defines parafermion stabilizer codes, provides explicit examples, and establishes a mapping from qudit codes, enhancing quantum error correction strategies.

Findings

Several smallest parafermion stabilizer codes are identified.

A locality-preserving embedding from qudit to parafermion operators is demonstrated.

A 2D parafermion construction combines topological and parity protections.

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.