Rapid thermalization of lattice CSS codes

Calderbank-Shor-Steane (CSS) codes, such as the toric code, are a widely studied class of quantum error-correcting codes. Understanding the thermalization time of these systems is important not only for error correction but also for applications like Gibbs sampling.

We show that CSS codes on a lattice satisfy a modified logarithmic Sobolev inequality and thus thermalize rapidly in any dimension at sufficiently high temperatures. For a special subclass, including the toric code, this rapid thermalization even holds at all positive temperatures. The central idea underlying our approach is to exploit the structure of CSS codes to decompose a quantity into two simpler, (almost) classical components, allowing us to apply tools from classical statistical mechanics to analyze the thermalization. In the last part I will show how this method generalizes to 2D Abelian quantum double models.

This is joint work with Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Antonio Pérez-Hernández, Cambyse Rouzé and Simone Warzel.