Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models
Abstract
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 ≤ df(0.1) admits 91% of all 2n 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 2n 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/√(λmin(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 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 T2 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.
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BibTeX
@misc{friedewald2026where,
title = {{Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models}},
author = {Owen Friedewald and Ali Shiri Sichani and Chi-Ren Shyu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02636},
eprint = {2610.02636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02636},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models
AU - Owen Friedewald
AU - Ali Shiri Sichani
AU - Chi-Ren Shyu
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02636
UR - https://arxiv.org/abs/2610.02636
AB - 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 ≤ 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/√(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.
ER -