发表机构
Magic State Labs（Magic State Labs）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出健全性规则筛选解码量子干涉测量（DQI）的候选问题，证明其优势上限，并通过AI搜索发现两个新应用，实验显示DQI在较大实例上超越经典求解器。
AI 中文摘要
解码量子干涉测量（DQI）利用经典纠错来解决优化问题，但很难判断哪些问题能为其带来量子优势。我们开发了健全性规则，通过代码参数、解码保证和经典基线来筛选候选问题。对于统计满足约束的标准目标，我们证明在最坏情况下的汉明解码中，DQI的保证最多能超过Prange完成的$(\sqrt{2}-1)/2$。最优多项式交集（OPI）渐近地达到这一差距上限，因此在此设置下，任何候选问题的差距都不能超过OPI的差距。我们还推导了实值目标的性能定律：目标既决定了解决方案的质量，也决定了解码器必须纠正哪些错误。由这些规则引导的AI代理搜索发现了两个候选应用。McEliece型公钥上的交替最大一致性测试了秘密解码器对DQI的价值，与仅看到公开实例的经典求解器相比。乘法多项式交集是一个由离散对数构建的背包型问题，将余弦目标与用于符号错误的公开解码器配对。对于这两个问题，我们都证明了解码保证和与Prange重启的有限长度比较，并且在我们测试的较大实例上，DQI的预期质量超过了我们的经典求解器在固定预算内达到的质量。
英文摘要
Decoded quantum interferometry (DQI) uses classical error correction to solve optimization problems, but it is hard to tell which problems could give it a quantum advantage. We develop soundness rules that screen candidate problems by their code parameters, decoding guarantees and classical baselines. For the standard objective of counting satisfied constraints, we prove that under worst-case Hamming decoding DQI's guarantee can exceed Prange completion by at most $(\sqrt{2}-1)/2$. Optimal polynomial intersection (OPI) attains this margin cap asymptotically, so no candidate in this setting can exceed OPI's margin. We also derive a performance law for real-valued objectives: the objective fixes both the solution quality and which errors the decoder must correct. An AI-agent search guided by these rules found two candidate applications. Alternant max-agreement on McEliece-type public keys tests what a secret decoder is worth to DQI against classical solvers that see only the public instance. Multiplicative polynomial intersection, a knapsack-type problem built from discrete logarithms, pairs a cosine objective with a public decoder for signed errors. For both we prove decoding guarantees and finite-length comparisons with Prange restarts, and on the larger instances we tested, DQI's expected quality exceeds what our classical solvers reach within fixed budgets.
