Machine Learning-Based Surface Code Decoding for Logical Circuits with Transversal Gates

Recent advancements brought the execution of error-corrected logical algorithms within reach, enabling the practical exploration of quantum algorithms. However, access to an efficient classical decoding algorithm is an essential prerequisite for achieving fault-tolerant quantum computation. While various decoding schemes have been extensively studied for error-correcting quantum memory, these schemes do not readily adapt to logical circuit decoding. In this work, we introduce a machine learning-based surface code decoder designed for logical circuits. Our approach allows the decoder to learn the noise model directly from training data, providing a key advantage over conventional methods that typically require prior knowledge of the noise model. Furthermore, we demonstrate that our model effectively decodes correlated errors arising from entangling logical gates, where the widely-used minimum-weight perfect matching algorithm fails and other graph-based decoders encounter substantial difficulties.