Systematicity of the high steady-state loss under combined training strategies

Determine whether the relatively rapid initial reduction in trajectory-density loss followed by a comparatively high steady-state loss, observed when combining chirped excitation with randomized initial conditions in the full-trajectory quantum neural network framework, is systematic across a broader range of Hamiltonian structures and system parameters.

Background

The paper compares sinusoidal and Gaussian chirped excitation, randomized initial quantum states, and combinations of these strategies for learning unknown Hamiltonians with a quantum neural network. For the combined chirp and randomized-initialization strategy, the authors observe fast early decreases in trajectory-density loss but comparatively high steady-state losses. They report this behavior for only three Hamiltonians, so the observation may reflect the particular Hamiltonians or parameter choices examined rather than a general property of the training strategy.

The unresolved issue is whether this convergence pattern persists across a substantially broader collection of Hamiltonian structures and system parameters. Establishing its systematicity would clarify when combining the two strategies is beneficial and whether rapid initial convergence is associated with inferior final reconstruction accuracy.