But I’d like a decent reference on quantum computation focusing on the question implied by the post: can you get something for nothing here, and if so, how and in what sense?

I seem to remember there was a good Scientific American article a few years ago, as well.

Dan, that’s such a good question that I scooted over to the Stanford bookstore to try to find a book that might be a good place to start. Unfortunately, I didn’t find any unambiguously good candidates for you: they were heavy on analogies and hand-waving, and light on the details. For example, I think that the book by Aczel on Entanglement would not be to your liking.

There are probably two reasonable places to start:

1. Wikipedia has a pretty good page on quantum mechanics, and another page on just the basics.

2. Daniel’s suggestion above is actually a pretty good one: try reading the third volume of the Feynman lectures. Feynman doesn’t spend much time on entanglement, but he does an excellent job on the two-slit experiment. There is math, but I bet that you could just skim over it on the first reading. (It’s mostly just algebra—even if it looks more abstract than you saw in high school—and the first year of calculus.)

If I were going to write a book on quantum mechanics for the layman, I think that I’d describe one experiment per chapter, anticipate the result using “classical” intuition, and then describe the actual result. The apparent paradox would then be a vehicle for explaining what seems to be so odd about the universe. (For example, after a discussion of the two-slit experiment and a Bell-inequality experiment, I’d discuss the quantum eraser.) After ten or so chapters, you could probably gain a pretty good understanding of the subject in a general way. I’d forget the history completely; there are enough books on that subject already. Maybe there’s a book available that’s like this, but I didn’t see it at the bookstore.

I have a hard time finding anything between newspaper articles and popular science books (comprehensible, but only because they skip all the awkward bits, and make up with analogies and hand-waving), and the papers explaining the details (too much specialised math for the likes of me).

I can tell you exactly how transistors work, at the electron/semiconductor physics level. But there’s a mysterious “then a miracle occurs” step two in my understanding going from that to an actual chip doing calculations.

Really? That’s when it gets easy. At that point, it’s boolean logic all the way up.

Take the average humanities PhD as an example. Have that worthy read the Nature paper. Then read all of the references. Then read of the references’ references. Stop only when you get to something you’ve read before. What’s the average nesting distance?

But then it goes on to imply that they also know which state it was in (in this case, the “don’t run the algorithm” state.) And if you’ve measured to determine the particle’s path (in the two slit problem), then it no longer interferes with itself. So there’s something different going on here. I assume it’s explained in the Nature article (or in the references or the references of the references, since high profile physics articles are now constrained to being 3 pages long, which is much too short to actually explain any work starting from basics.), but that’s behind a subscription wall.

This in addition to the general weirdness of quantum computing. Of course, regular computing is pretty weird, too—I can tell you exactly how transistors work, at the electron/semiconductor physics level. But there’s a mysterious “then a miracle occurs” step two in my understanding going from that to an actual chip doing calculations. I have a similar problem transitioning in my mind from well understand prinsiples of quantum mechanics to performing calculations with them.

Just one more in the ever expanding list of fascinating things I don’t have time to learn.

It doesn’t really; it explains things away rather than explaining them, by postulating a monstrous coincidence with respect to an utterly mysterious probability measure. It’s not really much of an advance on the theory that God wills it so.