Anyons are a special kind of excitations which are allowed in two dimensional systems, along with fermions and bosons.
It was proposed by Kitaev, that braiding of non-abelian anyons may allow a realization of quantum computing gates which is immune to noise.
The robustness of topological computing relies to a large extent on the stability of the topological phase to perturbations.
The insensitivity of the model to a localized noise source is a built-in feature of these phases. However, an issue of great importance is much harder to prove: a slight deformation of the
Hamiltonian describing the phase by perturbations which are locally tiny but are spread over through the entire system.
Such will always arise if the realization of the Hamiltonian in a particular system is not quite perfect.
General statements regarding such perturbations are often hard.
The subject of the talk will be a proof of such stability.
