General tensor network decoding of 2D Pauli codes

TL;DR

This paper introduces a general tensor network decoder for 2D quantum codes, achieving near-optimal decoding performance across various codes and noise models with efficient approximation methods.

Contribution

The paper presents a novel tensor network decoder for 2D stabiliser and subsystem codes, with an efficient contraction scheme and implementation, advancing quantum error correction decoding techniques.

Findings

Achieves state-of-the-art thresholds for multiple 2D codes

Demonstrates near-optimal decoding performance under various noise models

Provides an efficient contraction scheme for arbitrary 2D tensor networks

Abstract

In this work we develop a general tensor network decoder for 2D codes. Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. For a code consisting of $n$ qubits our decoder has a runtime of $O(n\log n+n\chi^3)$, where $\chi$ is an approximation parameter. We numerically demonstrate the power of this decoder by studying four classes of codes under three noise models, namely regular surface codes, irregular surface codes, subsystem surface codes and colour codes, under bit-flip, phase-flip and depolarising noise. We show that the thresholds yielded by our decoder are state-of-the-art, and numerically consistent with optimal thresholds where available, suggesting that the tensor network decoder well approximates optimal decoding in all these cases. Novel to our decoder is an efficient and effective approximate contraction scheme for arbitrary 2D tensor networks, which may be of independent interest. We have also released an implementation of this algorithm as a stand-alone Julia package: SweepContractor.jl.