Weighted Range-Constrained Ising-Model Decoder for Quantum Error Correction - Guo, Xinyi; Awano, Hiromitsu; Sato, Takashi (2025 62nd ACM/IEEE Design Automation Conference (DAC), 2025)
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.