{"ID":23551636,"CreatedAt":"2026-09-18T04:14:56.806955139Z","UpdatedAt":"2026-09-18T04:14:56.806955139Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20537","arxiv_id":"2609.20537","title":"Coherent error threshold for quantum LDPC codes","abstract":"A key appeal of quantum low-density parity check (qLDPC) codes is their ability to suppress stochastic Pauli noise below nonzero thresholds. Coherent errors are fundamentally different: they produce superpositions of error patterns whose amplitudes can interfere even after syndrome measurement. Rigorous understanding of coherent errors remains limited. Here we show that general qLDPC codes admit a nonzero code capacity threshold against local coherent noise and more generally local channel noise. For any family of qLDPC codes with distance $d=Ω(\\log n)$, we show that there is a constant noise strength below which the logical recovery error in diamond distance decays exponentially with the code distance. The result is established for optimal recovery as well as the minimum-weight decoder. The key technical ingredient is what we call a \\emph{cluster resummation}: rather than bounding superposed error configurations one by one, we isolate a large connected error cluster in the channel expansion and exactly resum all errors disconnected from it before taking norms. Standard cluster counting then yields exponential suppression. This work resolves a longstanding challenge in fault tolerance theory, providing general robustness guarantees for qLDPC codes against coherent noise and laying a rigorous foundation for future studies of fault-tolerant quantum technologies.","short_abstract":"A key appeal of quantum low-density parity check (qLDPC) codes is their ability to suppress stochastic Pauli noise below nonzero thresholds. Coherent errors are fundamentally different: they produce superpositions of error patterns whose amplitudes can interfere even after syndrome measurement. Rigorous understanding o...","url_abs":"https://arxiv.org/abs/2609.20537","url_pdf":"https://arxiv.org/pdf/2609.20537v1","authors":"[\"Zhengyi Han\",\"Yuanchen Zhao\",\"Yijia Xu\",\"Yixu Wang\",\"Zi-Wen Liu\"]","published":"2026-09-17T15:08:53Z","proceeding":"quant-ph","tasks":"[\"quant-ph\"]","methods":"[]","has_code":false}