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

2026-10-01

AI Summary

This project evaluates the practical advantages of quantum Fourier sampling within security models for delay-based physical unclonable functions (PUFs). It proposes a reproducible three-gate quantum auditing protocol that integrates a Kushilevitz–Mansour baseline, quantum kernel diagnostics, and a fixed-point phase oracle simulator to rigorously validate the learnability and hardware feasibility of quantum sampling across structural, algorithmic, and implementation dimensions, thereby effectively distinguishing idealized query advantages from genuine security gains. The study reveals no end-to-end quantum advantage within the evaluated scope. Furthermore, it exposes geometric discrepancy artifacts induced by classical pathological conditions alongside critical hardware latency bottlenecks.

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 $\le d_f(0.1)$ 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.

Problem

• Quantum Fourier Sampling
• Delay-PUF
• Spectral Learnability
• Security Audit
• Physical Unclonable Functions

Innovation

• Three-Gate Audit Protocol
• Delay-PUF
• Quantum Fourier Sampling
• Phase Oracle
• Kushilevitz-Mansour