Optimal inverse-temperature bounds

Determine optimal bounds on the inverse temperature under which the sampling and counting algorithms for stoquastic spin systems apply.

Background

The paper develops fast classical sampling and counting algorithms for general stoquastic spin systems, ferromagnetic Heisenberg models, and antiferromagnetic Heisenberg models on bipartite graphs in a high-temperature regime. The applicability of these algorithms is established only under explicit upper bounds on the inverse temperature, and the authors identify obtaining optimal such bounds as an unresolved question.

References

Several natural questions remain open. First, it would be interesting to obtain optimal bounds on the inverse temperature for which our algorithms apply.

— Fast Algorithms for Stoquastic Spin Systems  (2608.19489 - Mann, 19 Aug 2026) in Section Conclusion & Outlook

However, several key challenges remain open, such as efficient sampling of the Gaussian decompositions, optimized locality dependence, and the tightness of the strong-coupling result in Theorem~\ref{thm:hubbard-strong}.

— Convex-Gaussianity of fermionic Gibbs states in perturbation theory  (2609.09608 - Bu et al., 9 Sep 2026) in Section 4, Conclusion