Well, since Quantum Field Theories were really effiecient in describing the other 3 interactions, people hope it can be used for gravitation as well, that's why graviton is hoped to exist.
Postulating the existence of such a particle will also give Newton's 1/r law in the classical limit(just like GR), which is a good thing, but... There are problems with incorporating gravitons to the Standard Model of praticle physics, so this is kind of one frontier of theoretical(and mathematical) physics...