量子计算可解锁隐藏修复特征,让系统先修后拒,避免误杀可行方案。
Repair Before Veto, When Repair Is Hidden: Quantum-Accessible Features for Repair-Augmented Constraint Learning

- 先修复后拒绝:若修复计划能恢复可行性则接受,否则给出结构化拒绝理由。
- 量子算法在六组素数上错误拒率低于1.1%,远超经典模型的随机水平。
- 适合研究量子优势在约束学习中的机制,或设计抗误判决策系统的人。
硬约束决策系统通常直接否决不可行候选。但若系统具备行动能力,且已知一种低成本修复能使不可行候选变为可行且有价值,则直接拒绝实为虚假否决。本文提出Q-RACL(量子修复增强约束学习),构建先修复后否决框架:定义修复-可行推理为关键链路,即从观测候选与上下文判断哪类修复可恢复可行性。构造基于离散对数难题(DLP)隐藏的修复家族,其中修复类别是潜变量指数 a = log_g(x) 的平移区间规则,而学习者仅观察到 x = g^a mod p。标准DLP假设下,高效经典策略无法访问该坐标,但量子代理可通过Shor/Fourier结构获取。在六组素数、十组种子下,经典策略近似随机表现,错误拒率高;而量子DLP策略保持错误拒率<1.1%,所有配对种子全胜,条件量子非独立性(QNI_cond)达0.9777至0.9972。经典DLog预言机可匹配其性能,证明量子优势源于特征访问而非分类器容量。因此,量子智能在此类问题中并非通用升级,而是填补修复-否决闭环所缺失的关键特征。
原文摘要 · Abstract (English)
Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.
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