Quantum-versus-classical query complexity for Fourier sampling

Determine whether any classical algorithm with membership access can match quantum Fourier sampling query-for-query for the delay-PUF Fourier-audit task.

Background

The study compares ideal Fourier sampling with a Kushilevitz–Mansour classical baseline under matched membership access, but the experiments do not establish equality of their query complexities. The authors emphasize that coherent oracle calls and classical model evaluations are different physical resources.

The unresolved issue is therefore broader than the finite experimental comparison: the paper does not prove that all classical algorithms can match Fourier sampling on a query-for-query basis for the considered delay-PUF auditing problem.

References

We do not prove that every classical algorithm matches Fourier sampling query for query, nor that every quantum feature map is classically competitive.

— Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models  (2610.02636 - Friedewald et al., 2 Oct 2026) in Section 5, paragraph 'What it does not say'