Linear-time general decoding algorithm for the surface code

TL;DR

This paper introduces a fast, efficient decoding algorithm for the surface code that accounts for complex noise features, outperforming traditional methods across various realistic noise models.

Contribution

The authors develop a novel tensor-network-based decoder capable of handling general noise, including coherences and correlations, improving decoding performance over existing algorithms.

Findings

Outperforms conventional matching algorithms on multiple noise models

Handles non-Pauli and spatially correlated noise effectively

Uses tensor-network methods for approximate logical channel calculation

Abstract

A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including coherences and correlations. We demonstrate that the decoder significantly outperforms the conventional matching algorithm on a variety of noise models, including non-Pauli noise and spatially correlated noise. The algorithm is based on an approximate calculation of the logical channel using a tensor-network description of the noisy state.