Active error correction for Abelian and non-Abelian anyons

TL;DR

This paper introduces a class of decoding algorithms applicable to error correction in both Abelian and non-Abelian anyon models, providing threshold proofs and analyzing active correction methods under noisy conditions.

Contribution

It extends decoding algorithms to non-Abelian anyons and proves finite noise thresholds for Abelian models, advancing quantum error correction techniques.

Findings

Finite noise threshold for Abelian models with these decoders

Threshold proof for single shot non-Abelian error correction

Detailed analysis of active error correction for non-Abelian anyons

Abstract

We consider a class of decoding algorithms that are applicable to error correction for both Abelian and non-Abelian anyons. This class includes multiple algorithms that have recently attracted attention, including the Bravyi-Haah RG decoder. They are applied to both the problem of single shot error correction (with perfect syndrome measurements) and that of active error correction (with noisy syndrome measurements). For Abelian models we provide a threshold proof in both cases, showing that there is a finite noise threshold under which errors can be arbitrarily suppressed when any decoder in this class is used. For non-Abelian models such a proof is found for the single shot case. The means by which decoding may be performed for active error correction of non-Abelian anyons is studied in detail. Differences with the Abelian case are discussed.