The only thing that computers can do that humans can't is to work without getting bored.
It's always interesting to compare computers and humans, especially computer scientist seem to do that :) But since it seems that plants use some kind of quantum coherence just to do photosynthesis (see http://en.wikipedia.org/wiki/Photosynthesis#Quantum_mechanical_effects), I would not be surprised that our human brain also uses some clever (quantum?) tricks to achieve what it does, tricks which might not be simulated by a regular computer, no matter how fast it runs. But didn't Gödel "proved" that already somehow with its incompleteness theory? Nah I'm just mixing up things here ;) Okay, enough of that, I'm getting seriously off topic here, and I don't know at all what quantum coherence is, it just sounds cool ;-) Cheers, Peter