The aim of a quantum memory is to protect an encoded quantum state against errors for long periods of time. Quantum double models are a class of 2D quantum memories proposed by Kitaev, in which the protection from noise is due to the topological properties of the ground state degeneracy.
Heuristic arguments have long pointed to a weakness of these models against thermal noise processes. In this talk I will present a rigorous estimate on the lifetime of these memories under a noise process modeled by Davies generators which confirms these findings. This estimate is obtained by proving that the spectral gap of the generator is lower bounded by a positive constant uniformly in the system size.