R.R. Tucci comments
Hey! Only 2 sentences devoted to a 100 page paper. Proust you are not. What I would like to hear from the audience are opinions on how far and in what sense does this paper advance the programme of topological quantum computing. And how close are Kitaev and Freedman to finding a physical realization of their ideas
So I will spend more than 2 sentences.
The model Kitaev considers is a model with two qubit interactions on a two dimensional honeycomb lattice. These two qubit interactions are all Ising interactions along different directions. Interestingly, Duan, Demler, and Lukin have shown how to implement these interactions in this geometry using an optical lattice. So, in some sense, this represents a very nice model with Abelian anyons which could be realized in a laboratory. What is even nicer is that Kitaev can actually exactly solve the Hamiltonian associated with this model. Unfortunately for quantum computing enthusiests, this model does not support universal quantum computation. So, to answer the question, I would say that this model is exciting because it might be physically realizable, but the fact that it is not universal means that we will need something a little or a lot more in order to move towards topological quantum computing.