Separate Within-Trajectory Association from Shared Optimization Drift

Determine whether within-trajectory associations between the residual term-space composition coordinate and finite-step optimization behavior can be separated from shared optimization drift in the time-controlled sensitivity analyses of variational quantum optimization trajectories.

Background

The paper examines whether the residual term-space composition coordinate C contains information about finite-step behavior beyond standard first-order geometry. A post hoc sensitivity analysis considers the realized first-order residual and a step-normalized directional-curvature proxy, with normalized optimization-step index added as a control for shared trajectory drift.

The time-controlled specifications have limited estimability: only a minority of experimental cells provide sufficient data for stable estimation. Consequently, the analysis cannot determine whether apparent associations involving C reflect genuine within-trajectory relationships or merely common optimization-time trends. The authors explicitly leave this separation unresolved.

References

In the post hoc sensitivity analysis, the time-controlled specification was designated in advance as primary for interpretation but was estimable in only a minority of cells, so the separation of within-trajectory association from shared optimization drift remains unresolved.

— From Trainability Diagnostics to Optimization Claims: Boundaries and Controls in Variational Quantum Optimization  (2609.21243 - Kang, 18 Sep 2026) in Section 7, Discussion, paragraph “Scope and limitations”