So far as we know, it isn't possible to solve NP-complete problems quickly using any means. Even quantum computers, which are fundamentally more powerful than t

So far as we know, it isn't possible to solve NP-complete problems quickly using any means. Even quantum computers, which are fundamentally more powerful than the computers we have now, are not known to be able to solve NP-complete problems in polynomial time (i.e., efficiently). So it seems unlikely that simulating the brain is out in NP; it's probably no worse than BQP (what quantum computers can do).