Establish learning guarantees for other thermal generators

Establish whether the Hamiltonian-learning guarantees proved for the Gaussian-filtered, shifted-Metropolis detailed-balanced Lindbladian with single-site Pauli jumps continue to hold for other thermal generators.

Background

The analysis throughout the paper uses a particular detailed-balanced Lindbladian construction with Gaussian-filtered Hamiltonian evolution and single-site Pauli jump operators. The construction is selected because its explicit frequency-domain structure supports the metastability, approximate detailed-balance, and learning estimates.

The paper notes that other quantum thermalization generators, including quantum Glauber and Metropolis constructions, are natural alternatives, but their compatibility with the same learning guarantees is not established.

References

Establishing the same learning guarantees for other thermal generators remains open.

— Efficient learning of quantum interactions from thermal metastable states  (2610.01538 - Wang et al., 1 Oct 2026) in Appendix A, subsection “Thermal dynamics and detailed balance”

While we believe the approximate detailed balance condition can continue to play a role --- and that the presented protocol can very well work --- it is not clear how to derive this condition beyond Lindbladian stationary states.

— Efficient learning of quantum interactions from thermal metastable states  (2610.01538 - Wang et al., 1 Oct 2026) in Section 1, Discussion, paragraph “Beyond detailed-balanced Lindbladians”