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.