Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Dancing the quantum dream," by Paul Parsons. New Scientist, 24 January 2004, pages 30-34.

This article discusses intriguing research that could prove to be the basis for quantum computers. No one has yet figured out how to build a quantum computer, but the research being done today demonstrates just how powerful such devices would be and has begun to lay the theoretical foundations for their development. In 1989, physicist Edward Witten made a crucial connection between the ground-breaking knot theory work of Vaughan Jones and the quantum world. Witten showed that the paths quantum particles take weave together into a braid that is amenable to analysis by the techniques Jones developed. This kind of braiding affects the quantum states of the particles, and those quantum states are exactly what encode the results of computations done in a quantum computer. But there is a catch: As Parsons puts it in the article, "braiding doesn't affect the observable properties of most particles, which means you can't tell anything about the braid---and thus the computation---from examining them." A possible way around this difficulty is to make use of a new type of particle called a "nonabelian anyon". Theoretical researchers who work in this area, such as Fields Medalist Michael Freedman, are convinced that nonabelian anyons must exist, but they have not yet been found. Some physicists are now on the hunt to find them.

--- Allyn Jackson