And here's where the catch can kill you: as the size of your system increases, the gap between the lowest two energy states decreases *exponentially*. This means that you have to make the system exponentially colder, *and* that you have to change it exponentially slower. Thus, adiabatic computers are not expected to be able to solve NP-complete problems in linear time, as there is still a cost in time (and cooling effort) which grows exponentially with the size of your problem. Nonetheless, it's likely that you can get a quadratic speed-up equivalent to Grover's search algorithm by building such a computer.
This, by-the-way, is why many quantum computing people believe that D-wave is ultimately going to fail -- probably not with this particular computer, but with scaling it up to the point where it's actually useful. But hey, maybe we're wrong and they've figured it all out; we can certainly hope that's the case.
