Learning to Regularize Variational Quantum Dynamics under Distribution Shift

Variational quantum imaginary-time evolution (VarQITE) uses the quantum geometric tensor (QGT) to convert imaginary-time evolution into parameter-space updates, but solving the resulting QGT linear systems is sensitive to ill-conditioning, estimation error, and changes in problem geometry. We study whether regularization itself can be transferred across such changes. A single absolute Tikhonov value and a single spectrum-scaled Tikhonov value are selected on source validation and then frozen for every confirmatory target; the family-wise validation optima, which span more than six orders of magnitude, are used only as a diagnostic of heterogeneity. We introduce guarded learned regularization, in which a source-trained controller maps task-local QGT/force descriptors to either scalar damping or mode-wise spectral filtering, while a deterministic resolved-subspace verifier can revert an inadmissible proposal to a trusted QNG–LM reference. Across seven frozen non-floor confirmatory regimes under the predeclared full-source/leave-one-family training protocols, SpectralGuard attains the lowest descriptive method-level worst-case relative regret, 20.9%, without target-side hyperparameter selection. Under strong synthetic estimator perturbations, however, ScalarGuard is more stable and the spectral verifier falls back to the reference on most updates, exposing a clear expressivity–robustness boundary rather than uniform spectral superiority. The QEC branch should be read as transfer across stabilizer-derived Hamiltonian families, not as a decoding or fault-tolerance result. Overall, the evidence supports transferable regularization with explicit numerical verification, while also identifying the regimes in which learned spectral adaptation ceases to be the dominant deployed action.