Quantum Mechanics as a physical theory that describes behavior of particles, structure of atoms, etc. does not have much to say about behavior of larger molecules, let alone cells such as neurons, or their interactions.

But at the core of the modern QM lies a mathematical theory that, unfortunately, only rarely is seen as something that is independent from the QM's concrete physical aspects. That theory is a kind of probability theory that is different from the one that we all know and love (or hate). It is exactly that difference that makes QM unreachable for our intuition. But as a mathematical framework it can be expected to be useful in describing behavior of some other systems that have nothing to do with Quantum Mechanics and which could possibly include mechanisms of consciousness.