With the development of quantum hardware bringing the error-corrected quantum
circuits to the near future, the lack of an efficient polynomial-time decoding
algorithms for logical circuits presents a critical bottleneck. While quantum
memory decoding has been well-studied, inevitable correlated errors introduced
by entangling logical gates prevent the straightforward generalization of
quantum memory decoders. We introduce a data-centric modular decoder framework,
Multi-Core Circuit Decoder (MCCD), consisting 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 significantly 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 like 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 represents a noise-model agnostic solution to the decoding challenge
for deep logical quantum circuits.

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