Efficient Decoding of Surface Code Syndromes for Error Correction in Quantum Computing

TL;DR

This paper introduces a two-level machine learning-based decoding scheme for surface code error correction in quantum computing, significantly improving thresholds over traditional MWPM methods.

Contribution

It proposes a novel two-level ML decoding approach that enhances error correction thresholds and reduces training data requirements compared to existing methods.

Findings

Achieves ~10x higher pseudo-threshold than MWPM.

Achieves ~2x higher threshold than MWPM.

Maintains performance with low train-test ratios.

Abstract

Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low and high) ML-based decoding scheme, where the first level corrects errors on physical qubits and the second one corrects any existing logical errors, for different noise models. Our results show that our proposed decoding method achieves $\sim10 \times$ and $\sim2 \times$ higher values of pseudo-threshold and threshold respectively, than for MWPM. We show that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance. Finally, data generation for training the ML decoder requires significant overhead hence lower volume of training data is desirable. We have shown that our decoder maintains a good performance with the train-test-ratio as low as $40:60$.