Efficient near-optimal decoding of the surface code through ensembling

TL;DR

This paper presents harmonization, an ensembling approach that combines multiple noisy decoders to significantly improve the accuracy of surface code decoding, approaching maximum-likelihood performance with manageable computational costs.

Contribution

The paper introduces harmonization, a novel ensembling method for surface code decoders that enhances accuracy and provides confidence measures for layered decoding schemes.

Findings

Harmonized ensembles outperform individual decoders in logical error rates.

Layered decoding using consensus as confidence achieves near maximum-likelihood accuracy.

Harmonization enables highly accurate real-time decoding with limited computational overhead.

Abstract

We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual counterparts on repetition and surface code benchmarks, approaching maximum-likelihood accuracy at large ensemble sizes. We can use the degree of consensus among the ensemble as a confidence measure for a layered decoding scheme, in which a small ensemble flags high-risk cases to be checked by a larger, more accurate ensemble. This layered scheme can realize the accuracy improvements of large ensembles with a relatively small constant factor of computational overhead. We conclude that harmonization provides a viable path towards highly accurate real-time decoding.