Structure learning from thermal metastable samples

Determine whether the structure of a quantum Hamiltonian can be learned from samples of thermal metastable states, in analogy with classical structure-learning results, while retaining the framework and guarantees for lattice Hamiltonians.

Background

The paper develops a stationarity-test framework that learns the interaction structure of lattice Hamiltonians from exact Gibbs-state samples and learns Hamiltonian coefficients from thermal metastable-state samples. It does not combine these two capabilities: the metastable-state result assumes that the interaction set is known, whereas the structure-learning result assumes access to exact Gibbs states.

The unresolved direction is therefore to infer both the interaction graph and its coefficients when the available input consists only of metastable samples. The authors note that this problem appears compatible with their stationarity-test framework but explicitly leave it untreated.

References

Can a quantum local Markov property similarly be turned into a learning algorithm for metastable states?

— Efficient learning of quantum interactions from thermal metastable states  (2610.01538 - Wang et al., 1 Oct 2026) in Section 1, Discussion, paragraph “Connection to Markov properties”

First, a natural question is whether one can achieve ``the best of both worlds'' and learn Hamiltonian structure from metastable samples, akin to the classical work of . While this task should fit within the framework of this paper, we do not attempt it here for conciseness.

— The stationarity test: a framework for learning quantum many-body systems from their thermal states  (2610.01074 - Bergamaschi, 1 Oct 2026) in Section 1, subsection “Discussion and related work,” paragraph “Open questions”