&gt;This is why if we can ever build a quantum computer, it would be exponentially more powerful than a classic computer.<p>The truth is a little more complicated than that. If we could precisely inspect the quantum state of a system, then quantum computers trivially give us an exponential speed up. However, once we measure the result of the computation, we collapse the state down to a pure state[0], and all future measurements of the system will give us the same result. This means that we would need to repeat the computation an exponential number of times to get the full result with a bounded probability of error.<p>As it turns out, there are some tricks we can do with interference to improve efficiency, and for some problems achieve an exponential speed up.<p>[0] Or rather, according to the many worlds interpenetration, we become entangled with the system; however this is one of those cases where the Copenhagen interpretation is actually easier to use.