Determine the asymptotic behavior of the annealing advantage

Determine whether the excitation-matched quantum-annealing concentration advantage Δβ_ann saturates or slowly decays as the system size increases, using systems larger than the currently studied range.

Background

The paper defines Δβ_ann as the difference between the effective shell-concentration parameter inferred from neutral-atom quantum annealing and that obtained from an excitation-matched, spatially uncorrelated Bernoulli baseline. This residual is intended to isolate concentration attributable to quantum-generated correlations rather than to differences in excitation density.

The measured advantage is positive across the studied system sizes, but its apparent decrease is driven primarily by the smallest-size group, which also exhibits the strongest finite-size effects. The remaining groups, covering N = 60–125 sites, show no resolvable size dependence, so the available data do not establish the large-system trend.

References

Second, the asymptotic behavior of Δβ_ann remains open at the present sizes. As shown in Sec.~\ref{sec:experiment}, its apparent decrease is driven by the small group, which also exhibits the strongest finite-size effects in Appendix~\ref{app:degeneracy}. The remaining three groups show no resolvable size dependence over N=60--125. Whether the advantage saturates or slowly decays therefore remains open and requires larger systems.

— Shots-to-Approximate-Solution Scaling in Neutral-Atom Quantum Optimization  (2608.12858 - Jung et al., 13 Aug 2026) in Section 4.3, subsection “Finite-size limitations”