Relevant question. Don't know enough yet, but I did get excited at the idea of some proposition.

I feel like learning that the sun is a star at 31. Wait everyone knows ??

This method allows for more refined quantum-classical hybridation, for example in an HPC context.

Furthermore, it is unclear now if the linear response in equation (16) is optimal. One could introduce more complex noise models, or non-linear response models.

This is quite interesting for highly non-convex structures like in PQCs training, where shot-noise, non-convexities and potentially flat landscapes are an obstacle to training.

We show that a simple hyperparameters fine-tuning in BFGS updates helps exploring noisy landscapes, pathological in parametric quantum circuits. The method allows for skipping points where second order information is insufficient in the Hessian approximation.