Most research into brain function and AI employs models that are at the lowest level atomic (i.e., basic chemistry). In ignoring quantum mechanical effects, we are like physicists who approximate a function with a Taylor's series and then truncate the series' higher-order terms. They shouldn't be significant but there's that nagging thought that sometimes they are.
In the book "Tending Adam's Garden : Evolving the Cognitive Immune Self" Irun Cohen discusses (among other things) how evolutionary processes may set up shop in any available ecological niche, regardless of how inefficient or convoluted the process may be. More nagging thoughts.
Degrees of freedom involving quantum mechanical operations are available; there's no reason they wouldn't be used. And as others have stated here, evidence is accumulating that they are used in biological systems. Hard evidence that the brain uses such processes would be revolutionary.
Many models of atomic and electromagnetic theory lie strewn by the roadside as science moves forward: ">Maxwell's molecular-vortex model of electromagnetism ( http://victorian.lang.nagoya-u.ac.jp/victorianweb/science/ma... ) and William Thomson's (Lord Kelvin) vortex model of the atom come to mind. I hope we're not as far off the correct path with current theories of intelligence and the mind.