The correlated matching decoder for the 4.8.8 color code

TL;DR

This paper introduces a correlated matching decoder for the 4.8.8 color code that leverages lattice correlations to improve decoding thresholds, outperforming previous decoders and matching the best performance at low error rates.

Contribution

It presents a novel correlated decoder for the color code, derived from surface code decoding techniques, enhancing threshold performance over existing methods.

Findings

Higher thresholds than restricted and unified decoders.

Thresholds of 10.38% (bit-flip, code capacity) and 3.13% (phenomenological noise).

Surface code thresholds of 16.62% and 3.52% for depolarizing noise.

Abstract

Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the restricted decoder (Kubica and Delfosse, 2023), suffer from limited decoding performance. Inspired by the global decoding insight of the unified decoder (Benhemou et al., 2023), this paper introduces a correlated decoder for the 4.8.8 color code, which improves upon the conventional restricted decoder by leveraging correlations between restricted lattices, and is derived by mapping the correlated matching decoder for the surface code onto the color code lattice. Analytical and numerical results show that the correlated decoder achieves higher thresholds than the restricted and unified decoders, while matching the performance of the unified decoder at very low physical error rates. Under the code capacity and phenomenological noise models, the estimated thresholds for the color code against bit-flip error are 10.38% and 3.13%, respectively. Furthermore, by applying the surface-color code mapping, the thresholds of 16.62% and 3.52% are obtained for the surface code against depolarizing noise.