I only have had entry-level introductions into QM, but had no trouble understanding this. It that may be because I do have a background in computational dynamics, but I'm no expert in either field.

If I understood correctly, what the article is trying to explain is that the software/hardware architecture optimized for neural net processing is equally suited for many-body simulation of quantum equations. The architecture allows to broadcast the intermediate results among all individual particle simulators, which is untractable in other architectures: Monte-Carlo simulations lose accuracy and coupled cluster simulations can only solve stable lattice configurations.

Personally, I like the observation they made that the fitness constraint for their training is determined by physics: whichever solution yields the lowest total-system energy wins.