Description
In this talk, we will review and compare two methods to efficiently prepare the Gibbs state of the 2D toric code at any positive temperature. We will first show that the Davies generator associated to the 2D toric code satisfies a modified logarithmic Sobolev inequality at any positive temperature, and hence mixes rapidly towards the Gibbs state. This allows for efficient Gibbs sampling via dissipation. Secondly, we will show that the 2D toric code can be mapped with a circuit of polynomial depth to two decoupled Ising chains, and thus can be efficiently sampled by sampling the Ising chains and conjugating with the circuit. Both methods are extended to larger families of CSS codes.
