One of the things i would really, really like to see some day is a working quantum computer. Quantum mechanics is deep magic that nobody really understands, but we have learnt a lot about how to use it during the last century–including its application to some kinds of computation. As you surely know, the most outstanding quantum algorithm is Shor’s prime factorization, which allows factoring a number N with a time complexity . That means that we go from exponential to polynomial time when going from classical to quantum *for this particular problem* (and related ones: the Wikipedia article on QC gives a pretty good survey; see also David Deutsch’s introductory lectures). I’m stressing the last point because there’s a widespread misconception that quantum computers will be able to solve NP-complete problems in polynomial time. Not so. On the contrary, experts are almost sure by now that this won’t be the case (note, by the way, that factoring is *not* NP-complete).

The most recent examples of such bogus claims are the reports on D-wave’ demos of their ‘quantum computer’, which are surrounded by piles of hype. So please, before taking them at face value, see Scott Aaronson’s The Orion Quantum Computer Anti-Hype FAQ (more here here here). Scott Aaronson is an expert in the field and the author of a PhD thesis under the title Limits on Efficient Computation in the Physical World (for a less technical introduction to quantum computing, see his nice Quantum Computing Since Democritus lectures). For an executive summary, here’s the first entry in the FAQ:

- Q: Thanks to D-Wave Systems — a startup company that’s been in the news lately for its soon-to-be-unveiled “Orion” quantum computer — is humanity now on the verge of being able to solve NP-complete problems in polynomial time?
- A: No. We’re also not on the verge of being able to build perpetual-motion machines or travel faster than light.

The old rule applies: no silver bullet. But, of course, their limitations notwithstanding, quantum computers would (will?) be an interesting challenge for us programmers, and we do not have to wait for the hardware to play with them: see this Brief survey of quantum programming languages, or a more in-depth description of how an imperative quantum programming language looks like, although, if you ask me, functional quantum languages like QML are nicer. Simon Gay has also put together a comprehensive Bibliography of Quantum Programming Languages.

Finally, if you’d rather write some code, there’s André van Tonder’s Scheme simulator (which will work with any R5RS scheme), and a QML simulator written in Haskell. Haskellers will also enjoy Jerzy Karczmarczuk’s Structure and Interpretation of Quantum Mechanics: a functional framework.

Happy quantum hacking!

February 18, 2007 at 5:52 pm

[...] an another note, Programming Musings has done a survey of programming languages for quantum computing. Interest in quantum computing has gone up dramatically since a Candian company called D-Wave [...]

February 18, 2007 at 6:17 pm

“(note, by the way, that factoring is

notNP-complete).”Is that actually known? Factoring would be trivially NP-complete, for instance, if P=NP.February 19, 2007 at 5:50 am

we don’t know that. factoring is probably not in P, and is also not NP-complete. it is obviously in NP.

If we could somehow prove that factoring was NP-hard (and hence NP-complete), it would imply NP=coNP and that is suspected false.

February 20, 2007 at 7:38 am

Interestingly, dwave has a blog here at WordPress.com:

http://dwave.wordpress.com/