Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912916560674816 |
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| author | Kung, Ching-Feng Kuo, Kao-Yueh Lai, Ching-Yi |
| author_facet | Kung, Ching-Feng Kuo, Kao-Yueh Lai, Ching-Yi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_21118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction Kung, Ching-Feng Kuo, Kao-Yueh Lai, Ching-Yi Quantum Physics Information Theory 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. |
| title | Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2412.21118 |