Learning without strictly bounded interaction range

Determine whether a k-local Hamiltonian with potentially long-range interactions (e.g., beyond strictly bounded range) can be learned from access to e^{-iHt}, rather than assuming a hard cutoff on interaction range.

Background

Much of the literature assumes Hamiltonians have bounded-range interactions (strict locality with a hard cutoff), but many physical models exhibit algebraic decay (e.g., power-law interactions).

The authors cite a central open question from prior work concerning what structural assumptions are truly necessary for Hamiltonian learning and contrast with classical settings where bounded local norms suffice.