Sebastian Stengele, Ángela Capel, Li Gao, Ángelo Lucia, David Pérez-Garcı́a, Antonio Pérez, Cambyse Rouzé, Simone Warzel
Abstract We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions. We prove that conditions of Dobrushin–Shlosman-type on the quantum Gibbs state imply a modified logarithmic Sobolev inequality with a constant that is uniform in the system’s size. This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the CSS quantum setting. The results in particular imply the rapid thermalization at any positive temperature of the toric code in 2D and the star part of the toric code in 3D, implying a rapid loss of stored quantum information for these models.