Hamiltonian structure learning without known interaction terms

Determine whether a k-local Hamiltonian H acting on n qubits can be learned from access to its real-time evolution unitaries e^{-iHt} without any prior knowledge of which interaction terms E_a may be present (i.e., recover both the interaction structure and the corresponding coefficients).

Background

Prior work on Hamiltonian learning typically assumes the interaction terms E_a are known and only the interaction strengths λ_a are unknown. This restricts applicability because the structure must be specified in advance, and existing techniques rely on that knowledge to design measurements or decoupling schemes.

The authors frame this as the structure learning problem for Hamiltonians, analogous to structure learning in graphical models, and highlight that prior techniques cannot handle even a single unspecified long-range interaction.