Near-quadratic runtime for structure learning

Reduce the processing runtime of the stationarity-test structure-learning algorithm for 2-local quantum systems to \(\widetilde{O}(n^2)\) while preserving sample-optimality.

Background

The paper’s structure-learning algorithm identifies the interaction graph and coefficients of lattice Hamiltonians from Gibbs-state samples with near-optimal sample complexity. Its processing time is instead bounded by a higher polynomial in the system size, arising in part from the naive neighborhood-guessing procedure.

The authors ask whether convex-optimization techniques could replace neighborhood guessing and achieve the quadratic-time scaling known for related classical graphical-model problems, without sacrificing the algorithm’s sample-optimality.

References

Next, can we decrease the processing runtime of the structure learning algorithm for 2-local systems to $\Tilde{O}(n2)$, while maintaining sample-optimality, as in ?

— The stationarity test: a framework for learning quantum many-body systems from their thermal states  (2610.01074 - Bergamaschi, 1 Oct 2026) in Section 1, subsection “Discussion and related work,” paragraph “Open questions”