Abstract

Quantum Fourier sampling (QFS) appears to offer a direct route to auditing 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, and report where it stops short. Three gates structure the evaluation. **Structure:** low degree is not small support at reachable challenge lengths; for 4-XOR at _n_ = 14, degree _ df_ (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 KushilevitzMansour 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 _/_ ~~~~ __ min( _KC_ ) for the classical Gram matrix _KC_ , 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 (QFT) admits an 18 _._ 9% routed-depth reduction, yet the least certified precisions have estimated durations of 1 _._ 181 _._ 55 __ 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.