Conditions for efficient thermalization of the Khovanov Hodge Laplacian

Characterize necessary and sufficient conditions under which the Hodge Laplacian of Khovanov homology admits efficient thermalization procedures that prepare low-temperature Gibbs states with inverse-polynomial overlap with the ground space.

Background

The proposed quantum algorithm relies on pre-thermalization: preparing a Gibbs state of the Hodge Laplacian at sufficiently low temperature before projecting onto the kernel. Complexity-theoretic barriers suggest thermalization cannot be efficient for all instances, but typical-case behavior appears favorable. A rigorous characterization of when efficient thermalization is possible would determine the algorithm’s scope of efficiency.