Extension to low temperatures and unbounded-degree graphs

Extend the sampling and counting algorithms for stoquastic spin systems to the low-temperature setting and to graphs of unbounded degree.

Background

The results are restricted to high-temperature systems represented on bounded-degree graphs. The authors explicitly identify extending these results both to low temperatures and to graphs of unbounded degree as an open direction, noting that analogous extensions have been achieved for classical models.

References

Several natural questions remain open. First, it would be interesting to obtain optimal bounds on the inverse temperature for which our algorithms apply. Second, it would be interesting to extend our results to the low-temperature setting and to graphs of unbounded degree, both of which have been achieved for classical models.

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