发表机构
University of Missouri（密苏里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出三门量子审计协议，通过结构、算法与实现三层分析，证明量子傅里叶采样在延迟PUF安全模型中无端到端优势，其几何差异可源于经典病态条件。
AI 中文摘要
量子傅里叶采样可能有助于审计基于延迟的物理不可克隆函数（PUF）的谱可学习性。我们探究这一前景在访问匹配、强经典比较器以及预言机合成条件下是否依然成立。三个门结构构成了评估框架。结构方面：在可达挑战长度下，低阶并非小支撑集；对于n=14的4-XOR问题，阶数≤d_f(0.1)的字符覆盖了全部2^n个字符的91%，且中位数90%质量集合跨越了谱的三分之一。算法方面：构建相位预言机逻辑上蕴含经典成员访问，使得Kushilevitz-Mansour成为正确的基线；在45个任务中，它穷尽了每个有限域，且没有任何4-XOR理想采样案例在2^n次调用内达到90%的质量。量子核诊断看似更有利，在N=512个挑战时几何差异升至2.151，但它与经典Gram矩阵K_C的1/√(λ_min(K_C))相关系数为0.991，且4-XOR标签复杂度比率未超过保平衡置换零模型（p=0.930）。因此，迹归一化几何差异可仅通过经典病态条件增长，而无需任务标签对齐。实现方面：基于量子傅里叶变换的定点相位预言机经模拟器验证，可实现18.9%的路由深度缩减，但在静态后端快照上，最小认证精度对应的估计持续时间为映射量子比特中位退相干时间T_2的1.18至1.55倍，且未进行硬件执行。我们发现在评估范围内没有端到端优势，尽管理想采样在阈值化任务上确实使用更少的相干调用。贡献在于三门量子审计协议：一种可复现的程序，用于区分理想查询优势与可实现的安全收益。这不是关于已部署硅片的声明，也不是不可能性结果。
英文摘要
Quantum Fourier sampling may help audit the spectral learnability of delay-based physical unclonable functions (PUFs). We ask whether that promise survives access matching, a strong classical comparator, and oracle synthesis. Three gates structure the evaluation. Structure: low degree is not small support at reachable challenge lengths; for 4-XOR at $n=14$, degree $\le d_f(0.1)$ admits $91\%$ of all $2^n$ characters and the median $90\%$-mass set spans a third of the spectrum. Algorithmics: constructing the phase oracle logically implies classical membership access, making Kushilevitz--Mansour the correct baseline; across 45 tasks it exhausts each finite domain, and no 4-XOR ideal-sampling case reaches $90\%$ mass within $2^n$ calls. A quantum-kernel diagnostic appears more favorable, with geometric difference rising to $2.151$ at $N=512$ challenges, but it correlates $0.991$ with $1/\sqrt{λ_{\min}(K_C)}$ for the classical Gram matrix $K_C$, and the 4-XOR label-complexity ratio does not exceed a balance-preserving permutation null ($p=0.930$). Trace-normalized geometric difference can therefore grow through classical ill-conditioning alone, without task-label alignment. Implementation: a simulator-validated fixed-point phase oracle based on the quantum Fourier transform admits an $18.9\%$ routed-depth reduction, yet the least certified precisions have estimated durations of $1.18$--$1.55\times$ the median dephasing time $T_2$ of the mapped qubits on a static backend snapshot, without hardware execution. We find no end-to-end advantage in the evaluated regime, although ideal sampling does use fewer coherent calls on the thresholded task. The contribution is the Three-Gate Quantum Audit Protocol: a reproducible procedure separating an ideal query advantage from a realizable security benefit. This is not a claim about deployed silicon and not an impossibility result.
CommentsAccepted for presentation as a long oral at the NeurIPS 2026 SaTQuML Workshop, December 12-13, 2026, Atlanta, GA. arXiv version includes minor formatting revisions to meet submission requirements
