Description
Anderson localization emerges in quantum systems when
randomised parameters cause the exponential suppression of
motion. In this talk we will consider the localization
phenomenon in the toric code, demonstrating its ability to
sustain quantum information in a fault tolerant way. We show
that an external magnetic field induces quantum walks of
anyons, causing logical information to be destroyed in a
time linear with the system size when even a single pair of
anyons is present. However, by taking into account the
disorder inherent in any physical realisation of the code,
it is found that localization allows the memory to be stable
in the presence of a finite anyon density. Enhancements to
this effect are also considered using random lattices.
