Protecting topological phases against local perturbations

Topological quantum error correcting codes, such as the Toric code, are ideal candidates for protecting a logical quantum bit against local noise. How are we to get the best performance from these codes when an unknown local perturbation is applied? I propose to discuss a subset of my recent results (arXiv:1208.4924 and Phys. Rev. Lett. 107, 270502 (2011)) as to how knowledge, or lack thereof, about the error affects the error correcting threshold, and how thresholds can be improved by introducing randomness to the system. These studies are directed at trying to understand how quantum information can be encoded and passively protected in order to maximise the span of time between successive rounds of error correction, and what properties are required of a topological system to induce a survival time that grows sufficiently rapidly with system size.