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

Errors in surface code have typically been decoded using the popular Blossom decoder which uses Minimum Weight Perfect Matching (MWPM) algorithm. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. In this work, we propose a two-level (low and high) ML-based decoding scheme, where the low-level decoder corrects errors on physical qubits and the high-level decoder corrects any logical errors introduced by faulty detection of the low-level decoder, for symmetric and asymmetric noise models. Our results show that our proposed decoder achieves ∼10× and ∼2× higher values of pseudo-threshold (physical error probability beyond which logical error probability exceeds physical error probability) and threshold (physical error probability beyond which increasing the distance of the code leads to higher logical error probability) respectively than for MWPM. We show that usage of more sophisticated ML models with higher training/testing time does 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.