I read this article by Rivka Galchen on quantum computing. Much of the article was about an eccentric scientist in his fifties named David Deutch. I’m sure the guy is brilliant but I wasn’t particularly interested in his not particularly interesting life story (apparently he’s thin and lives in Oxford). There was a brief description of quantum computing itself, which reminds me of the discussion we had a couple years ago under the heading, The laws of conditional probability are false (and the update here).
I don’t have anything new to say here; I’d just never heard of quantum computing before and it seemed relevant to our discussion. The uncertainty inherent in quantum computing seems closely related to Jouni’s idea of fully Bayesian computing, that uncertainty should be inherent in the computational structure rather than tacked on at the end.
P.S. No, I’m not working on July 4th! This post is two months old, we just have a long waiting list of blog entries.
You might be interested in Scott Aaronson's blog, which is about the power of quantum computers (among other things).
http://www.scottaaronson.com/blog
He responded to Galchen's article (which gets a lot wrong) here:
http://www.scottaaronson.com/blog/?p=613
Scott Aaronson wrote a long piece on this article, especially about the treatment of quantum computing.
I stumbled across your post via a google alert. I am a sometime quantum information theorist and am one of a small band of researchers who believe that the best way to understand quantum theory is as a generalization of probability theory. This view has had some notable advocates, particularly von Neumann who did a lot to work out the mathematical details. The view is by no means essential, but it is a question of whether it is a more elegant and fruitful way of thinking about quantum theory than more conventional approaches, and I personally believe that it is.
Regarding applications to fields other than quantum physics, which you mentioned in earlier posts, there is no reason to believe that the specific structures used in physics should be more generally applicable. However, the basic idea that we should not assume that there is always a joint probability distribution for every observable quantity may well be sound. What is needed is a generalization of probability theory based on this basic idea that includes classical and quantum theory as special cases, but does not assume anything that is specific to experiments in quantum physics. Fortunately, such generalized theories already exist. They were developed beginning in the 1950s as an outgrowth of work on quantum logic and the axiomatization of quantum theory. Interest in them has been revived recently as a way of understanding the structure of the information processing capabilities of quantum theory.
For an introduction to the formalism, you could try my paper http://arxiv.org/abs/quant-ph/0611295 Feel free to contact me if you want any further references. I would be very interested if it turns out that these sort of models have applications outside of physics.