I don't know. But I don't think we can say that matter is just some dead and inert substance any more :P. That said, I like that Massimo has decided to shun reductionism.
My guess is that if someone could simulate a brain at the QM level (what a gedanken experiment!) it would end up after a few minutes with a smear of probabilities covering just about every possibility, or the simulation would simply not produce sensible results because it would not model some non-material input - much as a simulation of a radio would be pretty boring if it didn't include the information coming from radio waves. The difference is that we know about radio waves, but as yet we don't know about the coupling with the non-material - though there are obvious candidates.
You should beware of "stochastic reductionism" - i.e. thinking that the purely random contribution of standard QM makes much difference.
Of course, my guess is that matter is linked with a non-material realm - particularly if the matter in question is the human brain - and that the current scientific view is just an approximation.