A fast fault-tolerant decoder for qubit and qudit surface codes

TL;DR

This paper introduces a fast, fault-tolerant decoder for surface codes that works efficiently for qubits and qudits of any dimension, achieving high error thresholds under realistic noise conditions.

Contribution

It generalizes the Bravyi-Haah decoder to qudits and demonstrates its effectiveness with high error thresholds in noisy environments.

Findings

Achieves a threshold error rate of over 8% with high qudit dimensions.

Supports efficient decoding for both qubits and qudits of any dimension.

Enhances fault-tolerance in quantum error correction for surface codes.

Abstract

The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111, 200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are subject to generalized uncorrelated bit-flip noise (and the higher dimensional equivalent). We show that, with appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more than 8% can be achieved.