Learning to decode logical circuits.

Abstract

As quantum hardware advances toward enabling error-corrected quantum circuits in the near future, the absence of an efficient polynomial-time decoding algorithm for logical circuits presents a critical bottleneck. While quantum memory decoding has been well studied, inevitable correlated errors introduced by transversal entangling logical gates prevent the straightforward generalization of quantum memory decoders. Here we introduce a data-centric, modular decoder framework, the Multi-Core Circuit Decoder (MCCD), which consists of decoder modules corresponding to each logical operation supported by the quantum hardware. The MCCD handles both single-qubit and entangling gates within a unified framework. We train MCCD using mirror-symmetric random Clifford circuits, demonstrating its ability to effectively learn correlated decoding patterns. Through extensive testing on circuits substantially deeper than those used in training, we show that MCCD maintains high logical accuracy while exhibiting competitive polynomial decoding time across increasing circuit depths and code distances. When compared with conventional decoders such as minimum weight perfect matching (MWPM), most likely error (MLE) and belief propagation with ordered statistics post-processing (BP-OSD), MCCD achieves competitive accuracy with substantially better time efficiency, particularly for circuits with entangling gates. Our approach provides a noise-model-agnostic solution to the decoding challenge in deep logical quantum circuits.