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Learning to decode logical circuits
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DOI：10.1038/s43588-025-00897-4.png)
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Abstract
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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. This study reports a machine learning decoder that efficiently corrects errors in quantum logical circuits with entangling gates. The Multi-Core Circuit Decoder achieves competitive accuracy while running much faster than conventional methods.
Keywords:
Quantum error correction
Logical quantum circuits
Machine learning decoder
Multi-Core Circuit Decoder
Entangling gates
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