Pseudocodeword-based Decoding of Quantum Color Codes

TL;DR

This paper extends pseudocodeword-based decoding techniques to quantum color codes, introducing a low-complexity, two-stage decoder that improves decoding performance over previous methods.

Contribution

It generalizes pseudocodeword-based decoding to quantum color codes, offering a local, efficient, and more effective decoding approach.

Findings

Improved decoding performance for quantum color codes.

Low-complexity, local decoding operations.

Effective generalization of previous pseudocodeword-based decoders.

Abstract

In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based analysis, we have also introduced a two-stage decoder based on pseudocodewords for quantum cycle codes that leads to improved decoding performance. In this paper, we consider quantum (stabilizer) color codes and propose a two-stage decoder that is a generalization of the pseudocodeword-based decoder for quantum cycle codes. Our decoder has only local or error-weight-dependent operations of low computational complexity and better decoding performance compared with previous decoding approaches for these types of codes.