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Quantum error correction (QEC) is indispensable for suppressing noise in near-term and future quantum processors. Most neural decoders proposed for the surface code exploit predominantly local syndrome neighborhoods, which limits their ability to capture lattice-wide correlations. To overcome this limitation, we develop a two-stage learning-based decoding framework that leverages transformer self-attention to provide a global receptive field. In the first stage, a low-level decoder (LLD) based on a feedforward neural network predicts physical corrections from measured syndromes. In the second stage, a high-level decoder (HLD) performs logical-level verification by classifying the logical equivalence class and checking logical consistency; the HLD is instantiated using either a convolutional network or a transformer encoder. Monte Carlo experiments under depolarizing noise demonstrate clear threshold gains: for code distance d = 3, 5 and 7, the threshold improves from 0.03339 ± 0.00072 (LLD only) to 0.04110 ± 0.00085 with a CNN-based HLD, and further to 0.05350 ± 0.00112 when the HLD is implemented with a transformer; comparable improvements are observed for larger code distances. These results indicate that explicit logical-level discrimination mitigates decoding failures caused by degeneracy, and that global attention better captures long-range topological structure than convolutional baselines.
Wang et al. (Fri,) studied this question.