← 研踪 PaperTrailarXiv:2611.06818 · v1
Linear-time erasure recovery for quantum expander codes
首次提交 2026-11-05 01:31
版本更新 2026-11-05 01:31
雷达观测 2026-11-05 12:12
摘要
Erasures are used to model faults at a subset of known locations in various platforms used to construct fault-tolerant quantum computers. Beyond the utility in erasure recovery, efficient decoders for erasures are useful to both understand error decoders and as a subroutine for error decoding. Classical expander codes, which belong to the family of low-density parity-check (LDPC) codes, can be equipped with the Peeling decoder which works in linear time. Our main result is the algorithm Small-Set-Peeling, a quantum generalization of the classical Peeling decoder for erasures, that applies to quantum expander codes (Tillich, Zémor, IEEE T-IT 2013; Leverrier, Tillich, Zémor, FOCS 2015). This decoder can correct up to $D-1$ erasures, where $D$ is the (design) distance of the code and, importantly, is the first decoder that is guaranteed to do so in linear time. Combining with the erasure-conversion algorithm Small-Set-Find (Krishna, Livni-Navon, Wootters, SODA 2024), our result also implies the existence of a novel graph-local linear-time decoder for Pauli errors.
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v1 · 2026-11-05 01:31 · 最新观测版本
Linear-time erasure recovery for quantum expander codes
Erasures are used to model faults at a subset of known locations in various platforms used to construct fault-tolerant quantum computers. Beyond the utility in erasure recovery, efficient decoders for erasures are useful to both understand error decoders and as a subroutine for error decoding. Classical expander codes, which belong to the family of low-density parity-check (LDPC) codes, can be equipped with the Peeling decoder which works in linear time. Our main result is the algorithm Small-Set-Peeling, a quantum generalization of the classical Peeling decoder for erasures, that applies to quantum expander codes (Tillich, Zémor, IEEE T-IT 2013; Leverrier, Tillich, Zémor, FOCS 2015). This decoder can correct up to $D-1$ erasures, where $D$ is the (design) distance of the code and, importantly, is the first decoder that is guaranteed to do so in linear time. Combining with the erasure-conversion algorithm Small-Set-Find (Krishna, Livni-Navon, Wootters, SODA 2024), our result also implies the existence of a novel graph-local linear-time decoder for Pauli errors.
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