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

arXiv: https://arxiv.org/abs/2610.02636 · HTML: https://mlsanity.com/paper/2610.02636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [2.5D Root of Trust: Secure System-Level Integration of Untrusted Chiplets](https://mlsanity.com/paper/2009.02412/) (2020)

## Abstract (arXiv)

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× 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.