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arXiv · 2412.21118

Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction

Ching-Feng Kung·Kao-Yueh Kuo·Ching-Yi Lai
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Abstract

Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief propagation (BP) statistics to identify and remove highly reliable qubits, substantially reducing the effective problem size. Additionally, we identify a degeneracy condition that allows high-order OSD to be simplified to order-0 OSD. By integrating these techniques, we present an ADOSD algorithm that significantly improves OSD efficiency. Our BP+RSR+ADOSD framework extends naturally to circuit-level noise and can handle large-scale codes with more than $10^4$ error variables. Through extensive simulations, we demonstrate improved performance over MWPM and Localized Statistics Decoding for a variety of CSS and non-CSS codes under the code-capacity noise model, and for rotated surface codes under realistic circuit-level noise. At low physical error rates, RSR reduces the effective problem size to as little as 1\% (e.g., for $ε=0.001$ in surface-code DEM), enabling higher-order OSD with drastically reduced computational complexity. These results highlight the practical efficiency and broad applicability of the BP+ADOSD framework for both theoretical and realistic quantum error correction scenarios.

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Ching-Feng Kung, Kao-Yueh Kuo, Ching-Yi Lai. 2026-02-21. Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction. https://arxiv.org/abs/2412.21118

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