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Machine-Learning based Decoding of Surface Code Syndromes in Quantum Error Correction

: 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, although how an ML decoder will behave in a more realistic asymmetric noise model has not been studied. In this article we (i) establish a methodology to formulate the surface code decoding problem as an ML classiﬁcation problem, and (ii) propose a two-level (low and high) ML-based decoding scheme, where the ﬁrst (low) level corrects errors on physical qubits and the second (high) level corrects any existing logical errors, for various noise models. Our results show that our proposed decoding method achieves ∼ 10 × and ∼ 2 × higher values of pseudo-threshold and threshold respectively, than for those with MWPM. We also empirically establish that usage of more sophisticated ML models with higher training/testing time, do not provide signiﬁcant improvement in the decoder performance.