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It is certainly true that quantum mechanics influences how neurons operate, insofar as we are talking about electrons, ions and small-scale reactions. However, this is a bit of a cop out, as all Chemistry and Physics build on quantum effects, and it is somewhat of a semantic argument as to whether a particular process is "biochemistry" or "quantum mechanics".
There is no (good) theory suggesting anything like our minds really operate as abstract quantum wavefunctions held in place by brain meat or anything similar.
However, **some traditionally quantum effects are important to how we perceive the world**. The `vibration theory of olfaction` suggests that smell works based on the vibrational modes of molecules -- a fundamentally quantum entity, particularly in detection via promoting electrons' energy levels -- although the theory is not uniformly agreed upon (the competing theory is a docking theory, where smell is defined based purely on binary Yes/No activations based on how a molecule locks into a detector protein).
Overall I'd say biology has no cares about our perception of "Quantum". **Evolution stumbles across whatever best gives an advantage and many biological processes use legitimately quantum effects (eg. photosynthesis), but we don't have a clear cut case for anything especially quantum happening inside your skull.**
There's nothing here!