Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models

Owen Friedewald, Ali Shiri Sichani, Chi-Ren Shyu

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.…