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.
Do you think it's a good idea that all the teams working on quantum computing have put their money on the surface code? What are your thoughts? Do you believe that we are putting all our eggs in one basket?
I'm not an expert on this, but I think the surface code is so popular because it's 2-dimensionally local and has great parameters and speed of error correction. But people certainly work on other codes too, and if someone invents something that's unequivocally better than the surface code---or better for what the experimentalists are building now---I guarantee you they'll take notice! They don't always care about finer points of complexity theory, but this they do care about.
