Graph Neural Network Decoders for Surface Code Quantum Error Correction

N. Meters, D. Petrov, K. Yamamoto

We design a message-passing graph neural network decoder for the rotated surface code that operates in O(n) time per syndrome measurement round. The decoder is trained on synthetic noise models and generalizes to hardware-calibrated noise without fine-tuning. At code distances 5 through 21, it achieves logical error rates within a factor of 1.3 of minimum-weight perfect matching while running 50x faster, enabling real-time decoding at the repetition rates required by near-term superconducting quantum processors.