[reikonomusha]

There are many, many experiments done simulating molecules, from hydrogen dimers to water. Just one example of many:

https://arxiv.org/pdf/1803.10238.pdf

[erichocean]

That paper is about using a classical computer to simulate a quantum computing algorithm.

I'm pretty sure OP is talking about an actual, physical, exists-in-reality usage of a quantum computer to do anything meaningful, not theory. There's lot of theory.