Quantum computing technology is progressing rapidly, but we are not quite there yet. There are several paths through which physicists hope to realize fully-fledged quantum computers. One of them is topological quantum computing which relies on exotic quasi-particles which live in 2 dimensions, so-called anyons.
All fundamental particles are either fermions (example: electrons) or bosons (example: photons). If you take two photons and swap them, nothing changes. If you swap two electrons, though, quantum mechanics mandates an tiny change, which is responsible for the fact that electrons in atoms occupy different orbitals — remember your high-school chemistry? If you swap two electrons twice, though, you’re back where you started.
If you swap two anyons, more significant effects might occur. In topological quantum theory, the technical term for swapping is braiding, as exchanging two anyon’s positions is the equivalent as keeping one fixed and moving the other in a circle around the first one.
The existence of quasi-particles with such exotic behavior has been largely theoretical until recently: A group of physicists at the University of Purdue, 200km south of Chicago, have published a paper in which they describe how they were, for the first time, able to directly observe the effects of braiding. The anyons they realized have the property that swapping them three times gives a situation which is identical to the one you started with. Yup, definitely weird.
That sounds like good news…
… but: Anyons come in two fundamental types, abelian and non-abelian. The ones for which braiding was realized in the Purdue experiments were of the abelian type, but for quantum computing you need non-abelian anyons. The effect of braiding non-abelian anyons can be more profound than the simple phase change that abelian anyons experience upon braiding.