Certify SYK-like parameters during gradient descent

Develop a method to certify that candidate coupling parameters encountered during gradient descent correspond to Hamiltonians that are SYK-like in the sense required for the available quasi-polynomial thermal-expectation algorithms to succeed.

Background

The sample-efficient learning method relies on an optimization problem whose direct implementation is not known to be computationally efficient. A possible strategy is to use quasi-polynomial algorithms for estimating thermal expectations while running gradient descent over disorder parameters. However, those algorithms require the candidate Hamiltonian to satisfy SYK-like conditions, and the paper identifies the lack of a certification procedure along the optimization path as an unresolved barrier to obtaining a time-efficient algorithm at all constant temperatures.