There's a sorta-fringe theory of consciousness called Orchestrated Objective Reduction, which hypothesizes consciousness as residing at the quantum level, and functioning via microtubule structures in the brain working as miniature quantum isolation chambers.
I think it's pretty out to lunch, but I imagine any proven model/theory of consciousness working at the same level as quantum mechanics, insofar as it can be proven via experiment but isn't something our brains are capable of grasping outside of doing the math.