Indeed, once I realized quantum mechanics took exponential computing power, I considered this inelegant until I concluded the many-worlds interpretation means it's being put to good use after all. Is that a case of ending up at the right belief for the wrong reason? On the one hand you could say SI doesn't bat an eyelid at exponentially inefficient computation. On the other hand you could say it does, when you take into account the need to specify spacetime coordinates of the observer as well as underlying laws; in a sense, that discourages too much inefficiency of the wrong sort.

Having said that, I'm inclined to think continuum arithmetic isn't the 'wrong sort' of inefficiency in this sense. But see my reply to Daniel - how do you bite this bullet without making the 'arbitrary choice of basis' limitation much worse?