Weighted Range-Constrained Ising-Model Decoder for Quantum Error Correction

Ising model-based Quantum Error Correction decoders reduce topological complexity compared to classical decoders. However, the SOTA Ising decoder has a higher time complexity than union-find (UF) and a lower threshold than minimum-weight perfect-matching (MWPM). We propose the Weighted Range-Constrained Ising Model-Based (WRIM) decoder. WRIM uses a polygonal region to enclose flipped syndromes, ensuring the coverage of all potential error chains while optimizing coupling and external field coefficients. WRIM reduces the variable count by $97.8 x$, achieves microsecondlevel decoding, and has a worst-case time complexity of $O(n)$, outperforming UF. WRIM exhibits threshold behavior up to 10.7$\mathbf{1 1. 0 \%}$, surpassing the MWPM’s highest reported threshold.