Improved single-shot decoding of higher dimensional hypergraph product codes

TL;DR

This paper demonstrates that joint decoding of data and syndrome errors in higher dimensional hypergraph product codes significantly improves single-shot thresholds, surpassing previous results and reducing qubit overhead.

Contribution

The study introduces an improved single-shot decoding method for higher dimensional hypergraph product codes, achieving higher thresholds than prior approaches.

Findings

Single-shot threshold for 3D toric code exceeds 7.1%.

Single-shot threshold for 4D toric code exceeds 4.3%.

Balanced product and 4D hypergraph codes reduce qubit overhead.

Abstract

In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes. For the 3D toric code and a phenomenological noise model, our results are consistent with a sustainable threshold of 7.1% for $Z$ errors, compared to the threshold of 2.90% previously found using a two-stage decoder~[Quintavalle et al., 2021]. For the 4D toric code, for which both $X$ and $Z$ error correction is single-shot, our results are consistent with a sustainable single-shot threshold of 4.3% which is even higher than the threshold of 2.93% for the 2D toric code for the same noise model but using $L$ rounds of stabiliser measurement. We also explore the performance of balanced product and 4D hypergraph product codes which we show lead to a reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%.