  Comprehensive no-go theorems show that information encoded over local
two-dimensional topologically ordered systems cannot support macroscopic energy
barriers, and hence will not maintain stable quantum information at finite
temperatures for macroscopic timescales. However, it is still well motivated to
study low-dimensional quantum memories due to their experimental amenability.
Here we introduce a grid of defect lines to Kitaev's quantum double model where
different anyonic excitations carry different masses. This setting produces a
complex energy landscape which entropically suppresses the diffusion of
excitations that cause logical errors. We show numerically that entropically
suppressed errors give rise to super-exponential inverse temperature scaling
and polynomial system size scaling for small system sizes over a
low-temperature regime. Curiously, these entropic effects are not present below
a certain low temperature. We show that we can vary the system to modify this
bound and potentially extend the described effects to zero temperature.
