Extend real-time thermal-observable algorithms to system-size-dependent times

Determine whether the classical algorithm based on the quantum cavity method for evaluating real-time dynamics in disordered mean-field systems can be extended to times that grow with the system size, including times of the order of the scrambling time.

Background

The paper develops a rigorous quantum cavity method and uses it to construct polynomial-time classical algorithms for estimating local thermal expectations of the SYK model at arbitrary fixed constant temperatures. The discussion considers whether related diagrammatic and cavity-based techniques can handle real-time observables rather than only thermal, imaginary-time quantities.

A prior non-rigorous result is cited as having evaluated real-time dynamics with high accuracy, but only without rigorous control over times increasing with the number of Majorana fermions. Extending the method to system-size-dependent time scales, such as the scrambling time, is explicitly left unresolved; rigorous control could also support algorithms for out-of-time-order correlators.

References

It is open if this technique can extend to times that grow with the system size (e.g., the scrambling time).

— Polynomial-time classical algorithms for mean-field models up to the glass transition  (2610.06807 - Schmidhuber et al., 5 Oct 2026) in Section 1, subsection “Discussion,” bullet “Real-time dynamics”