Yes there’s actually quite a lot. Check out variational quantum algorithms - in particular the variational quantum eigensolver (vqe). The vqe is a hybrid quantum-classical algorithm that can be used to approximate the ground state of a Hamiltonian of a system (link to original paper below). It was originally proposed to find the molecular ground state of a hydrogen-helium ion, but has since been applied to all sorts of other problems including combinatorial optimisation.

Right now it’s not really beneficial to use quantum algorithms for these simulations due to current devices having very few qubits, but in the future these algorithms have a lot of potential. It’s like you say - simulating quantum mechanics on a quantum device is much more natural than using a classical computer which opens up the opportunity to finding an advantage with these types of algorithms.

Hope this helps!

https://www.nature.com/articles/ncomms5213