An interesting question at the talk Sunday was, suppose you build a quantum computer, how do you really know that these crazy quantum laws are governing the computer? What I love about this question is that you can turn it around and ask the same question about classical computers! At heart we believe that if we put together a bunch of transistors to form a large computation, each of these components is behaving itself and there is nothing new going on as the computer gets larger and larger. But for quantum computers there is a form of skepticism which says that once your computer large enough, the description of quantum theory will fail in some way (See for example, Scott Aaronson’s “Are Quantum States Exponentially Long Vectors?”, quant-ph/0507242, for a nice discussion along these lines.) But wait, why shouldn’t we ask the question of whether classical evolution continues to hold for a computer as it gets bigger and bigger. Of course, we have never seen such a phenomenon as far as I know. But if I were really crazy, I would claim that the computer just isn’t big enough yet. And if I were even crazier I would suggest that once a classical computer gets to a certain size its method of computation changes drastically and allows for a totally different notion of computational complexity. And if I were flipping mad, I would suggest that we do have an example of such a system, and this system is our brain. Luckily I’m only crazy, not flipping mad, but still this line of reasoning is fun to pursue.
The Quantum Pontiffs