Likewise, you don't ever explore the entire state space when you perform quantum computation. As it happens, most states are inaccessible. As shown by Poulin et

Likewise, you don't ever explore the entire state space when you perform quantum computation. As it happens, most states are inaccessible. As shown by Poulin et al. in Physical Review Letters, 106, 170501 (2011), you can only ever explore a very small fraction of quantum states in polynomial time. Edit: tezthenerd has said pretty much the same thing below. I just included the reference in case you'd like a formal proof.