Optimal adaptation of surface-code decoders to local noise

TL;DR

This paper introduces a tensor-network-based method to optimize surface-code decoders by identifying key local noise parameters, significantly improving quantum error correction performance.

Contribution

It presents a simple, systematic approach to determine the most impactful noise features for decoder adaptation in surface codes.

Findings

Decoding performance improves by focusing on a few critical noise parameters.

The method effectively identifies important noise features like coherence and bias.

Adapting to key parameters yields near-optimal error correction with minimal complexity.

Abstract

Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit) noise, we present a simple method to determine the maximum extent to which adapting a surface-code decoder to a noise feature can lead to a performance improvement. Our method is based on a tensor-network decoding algorithm, which uses the syndrome information as well as a process matrix description of the noise to compute a near-optimal correction. By selectively mischaracterizing the noise model input to the decoder and measuring the resulting loss in fidelity of the logical qubit, we can determine the relative importance of individual noise parameters for decoding. We apply this method to several physically relevant uncorrelated noise models with features such as coherence, spatial inhomogeneity and bias. While noise generally requires many parameters to describe completely, we find that to achieve near optimal decoding it appears only necessary adapt the decoder to a small number of critical parameters.