Fast classical algorithms beyond the stoquastic setting

Develop fast classical sampling and counting algorithms for general quantum spin systems beyond the stoquastic setting.

Background

The framework in the paper relies on the nonnegative representations available for stoquastic systems. General quantum spin systems beyond the stoquastic class are not covered by the results, and the authors explicitly identify the development of fast classical algorithms in that broader setting as an unresolved problem.

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. Finally, it would be of significant interest to obtain fast classical algorithms for general quantum spin systems beyond the stoquastic setting.

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

However, the field breaks the diagonal structure on which Proposition~\ref{prop:sampling} rests, so that no classical sampler is known for the density itself or for spectral functionals beyond fixed-order moments, while the hardware routes of Sec.~\ref{sec:quantum} remain available.

— Learning structural balance of graphs from quantum spectral features  (2609.11736 - Scali et al., 10 Sep 2026) in Section 4, Subsection “Classical samplability at zero field”