Determine large-system and cross-problem persistence of the regime structure

Determine whether the strength–imbalance regime structure identified for small-system MaxCut instances persists at substantially larger system sizes and for other classes of problem Hamiltonians.

Background

The results are based on exact noiseless simulations of small MaxCut instances, with the largest reported system size being n=16. Within the studied range, the coarse organization of gradient response and near-optimal solution regions appears robust across selected depths, schedules, graph families, and weighted versus unweighted cost Hamiltonians.

The authors explicitly leave unresolved whether these observations continue to hold at substantially larger sizes or generalize beyond MaxCut. Resolving this issue is necessary to distinguish features that are universal aspects of QAOA trainability from those that depend on the particular optimization problem.

References

In particular, it is unclear how trainability, optimization performance, and solution quality evolve as the number of encoded variables grows well beyond the regimes explored in this work.

— Loan Portfolio Optimization with Variational Quantum Algorithms  (2609.30195 - Bhargava et al., 24 Sep 2026) in Section Outlook

The present numerical study is restricted to small-system MaxCut instances and does not establish whether the same regime structure persists at substantially larger sizes or for other classes of problem Hamiltonians.

— Dynamical regimes of QAOA gradient response  (2609.01280 - Shakibaei et al., 1 Sep 2026) in Discussion