Learning to Correct Quantum Errors

Abstract Fault-tolerant quantum computers must continually decode noisy parity-check data, known as the syndrome, to determine whether an encoded logical qubit has been corrupted. The standard decoder, minimum-weight perfect matching (MWPM), assumes independent, graph-like errors and is sub-optimal under realistic circuit-level noise. We present a compact residual 3D convolutional neural network (0.5–0.6 million parameters) that reads the space-time syndrome of a rotated surface code as a volumetric image. Trained on Stim simulations at code distances d = 3 and d = 5 and evaluated on 3.6 million held-out shots, a three-seed ensemble outperforms correlated MWPM, the strongest baseline we test, at all 18 noise settings, with 6–46% fewer logical errors (paired McNemar p-value below 0.03 in every setting). On real Google Sycamore data (d = 3, five rounds), the network is pre-trained on the device's fitted error model and fine-tuned on half of the shots. It achieves a logical error rate of 13.03%, compared with 13.57% for correlated MWPM on the same held-out shots, and outperforms it on all eight cross-validation folds, although it does not match belief-matching or tensor-network decoders. Its outputs are well calibrated (ROC AUC = 0.998): discarding the 10% least-confident shots reduces errors tenfold. An ablation study identifies space-time locality as the essential inductive bias. All models train in 49 minutes on two freely available GPUs, and the data and code are publicly available.