This seems a little redundant, given my recent 6 month break from blogging, but I’m gone on holidays for three weeks starting in about 36 hours, first for two weeks in New Zealand, and then for one more week’s back in Brisbane, which will mostly be spent attending the Ideas Festival. Should be fun, but I won’t be blogging during that time.

# Month: March 2006

## Junk DNA and the design of living things

This is a plug for a free public lecture (with free drinks and nibblies after) about junk DNA and the role it plays in biology, by Professor John Mattick of the University of Queensland. It’s to be held 6:30 pm, Monday March 13 in the Judith Wright Center, Fortitude Valley, Brisbane.

(The lecture is the first of a monthly series to be known as BrisScience. My partner, Jen Dodd, is running the series.)

The topic of the talk is really interesting. One of the biggest problem in modern biology is how we go from DNA to fully fledged living beings. It’s pretty well understood how we go from DNA to the proteins which form the building blocks for living beings. But that’s a far cry from a full understanding: knowing how to put together a steel girder doesn’t imply that you can build the Eiffel tower or the Empire State building. Figuring out the link between DNA and the large-scale structure (the architectural design, if you like) seems to be very poorly understood.

The speaker, John Mattick, has some really interesting (and controversial) ideas about how this happens. He thinks the so-called junk DNA in the human genome (pieces of the DNA which don’t code for proteins) carries the information about the design. As an outsider it’s hard for me to judge how successful the ideas are, but they’re certainly getting some attention: his work was named by *Science* magazine in its list of the ten most significant breakthroughs of 2004, and he had an article about it in *Scientific American* a couple of years back.

## Quantum computation as geometry

It’s probably surprising if you don’t already know it, but in the standard “quantum circuit” model quantum computers are actually quite similar to ordinary computers. A quantum computation is built up out of quantum gates that perform quantum logic operations on quantum bits. All of this proceeds pretty much by analogy with classical computers, where gates perform logical operations on bits. There are some technical differences, but the broad picture is pretty similar.

Mark Dowling, Mile Gu, Andrew Doherty and I have recently developed a rather different *geometric* approach to quantum computation. (Here’s the link to the abstract, and here’s the link to the full text at *Science*. Jonathan Oppenheim has also written a nice perspective piece (sorry, I don’t have the full text).)

Our result is pretty simple: we show that finding the best (read smallest) quantum circuit to solve a particular problem is equivalent to finding the shortest paths between two points in a particular curved geometry. Intuitively, this problem is like an orienteer or hiker trying to find the shortest path between two points in a hilly landscape, although the space we are working in is harder to visualize. There’s some technical caveats to the result, but that’s the general gist.

What use is this? At the moment it’s difficult to say – unfortunately, we don’t yet have any killer applications of the result. But our result does mean that problems in quantum computation can be viewed in terms of equivalent problems in the field known as Riemannian geometry. This opens up the possibility of using some of the deep ideas of Riemannian geometry to solve problems in quantum computing. And who knows: maybe ideas from quantum computing will have a useful stimulating effect, injecting new ideas into the study of geometry!