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-Constra...

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Bibliographic Details
Published in:2025 62nd ACM/IEEE Design Automation Conference (DAC) pp. 1 - 7
Main Authors: Guo, Xinyi, Awano, Hiromitsu, Sato, Takashi
Format: Conference Proceeding
Language:English
Published: IEEE 22.06.2025
Subjects:
Complexity theory
Couplings
Decoding
Error analysis
Error correction
Error correction codes
fast decoding method
Ising model
Limiting
Quantum annealing
Quantum error correction
Qubit
surface code
Time complexity
variable reduction
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Summary: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.
DOI:10.1109/DAC63849.2025.11133309