Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning

TL;DR

This paper introduces a machine learning-based decoder for heavy hexagonal quantum error-correcting codes, significantly improving decoding thresholds and efficiency over traditional methods by leveraging gauge equivalence and novel classification techniques.

Contribution

The work presents the first ML-based decoder for heavy hexagonal codes, enhancing decoding thresholds and introducing gauge equivalence for error class reduction.

Findings

ML decoder achieves ~5x higher threshold than MWPM

Gauge equivalence reduces error classes by a factor of four

Rank-based classification method is faster than linear search

Abstract

Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold, for various noise models. We show that the proposed ML based decoding method achieves $\sim5 \times$ higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors, and thus a further improvement of $\sim 14\%$ in the threshold over the basic ML decoder. Lastly, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.