From "Scientists Find a Fast Way to Describe Quantum Systems" (2024) https://www.quantamagazine.org/scientists-find-a-fast-way-to... :

So that’s what the team behind the new paper ended up doing: They ported an optimization tool from mathematics into their field of quantum learning. First they reformulated the problem of calculating a system’s Hamiltonian into a family of polynomial equations. Now the goal was to prove that they could solve these equations reasonably quickly — which seemed like an equally hard goal. “In general, if I have an arbitrary polynomial system, I cannot hope to solve it efficiently,” Bakshi said. Even simple polynomial systems are just too hard.

But theoretical computer scientists are good at finding workarounds in such situations, by using what’s called a relaxation technique. This approach converts problems that are hard to optimize — they have too many solutions that appear right but aren’t valid everywhere — into simpler ones with a unique global solution. By approximating difficult problems via simpler ones, the relaxation technique helps find solutions closer to the true solution.

The relaxation technique is well known in the field of approximation algorithms, but it had never been tried in quantum learning.