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.