Quantum and non-perturbative corrections to Krylov spread complexity

Determine whether quantum or non-perturbative corrections modify the conclusion that semiclassical Krylov spread complexity of the thermofield-double state exhibits approximately quadratic rather than linear growth.

Background

The paper finds that operator Krylov complexity reproduces the late-time linear growth associated with the two-sided BTZ interior, whereas the Krylov spread complexity of the thermofield-double state, computed from the semiclassical AdS3 partition function, remains approximately quadratic over the accessible time range. The authors explicitly leave unresolved whether quantum or non-perturbative effects could change this qualitative distinction.

References

Whether quantum or non-perturbative corrections modify this conclusion remains an important open question.

— Krylov complexity and the growth of the black hole interior in 3D gravity  (2608.19373 - Bhattacharyya et al., 19 Aug 2026) in Section 5, Conclusions and outlook

Establishing the strict asymptotic behavior and the effects of quantum and non-perturbative corrections, including eventual saturation, remains an important open problem. It would also be interesting to determine whether a linear regime analogous to that of the bulk volume can emerge at later times.

— Krylov complexity and the growth of the black hole interior in 3D gravity  (2608.19373 - Bhattacharyya et al., 19 Aug 2026) in Section 5, Future directions, item “Long-time behavior of Krylov spread complexity”

A gravitational identification of this saddle is not known.

— The ETH matrix model for DSSYK: non-perturbative corrections and intersection theory  (2608.23298 - Alfinito et al., 24 Aug 2026) in Section 10, Comments on relation to other non-perturbative results, paragraph “Comparison with recent DSSYK non-perturbative results”