  We analyze the effect of typical, unknown perturbations on the 2D toric code
when acting as a quantum memory, incorporating the effects of error correction
on read-out. By transforming the system into a 1D transverse Ising model
undergoing an instantaneous quench, and making extensive use of Lieb-Robinson
bounds, we prove that for a large class of perturbations, the survival time of
stored information grows at least logarithmically with the system size. A
uniform magnetic field saturates this scaling behavior. We show that
randomizing the stabilizer strengths gives a polynomial survival time with a
degree that depends on the strength of the perturbation.
