  Topological quantum memories in two dimensions are not thermally stable,
since once a quasiparticle excitation is created, it will delocalise at no
energy cost. This places an upper bound on the lifetime of quantum information
stored in them. We address this issue for a topological subsystem code
introduced in [Bravyi S. et al., Quant.Inf.Comp.13(11):0963]. By frequently
measuring the gauge operators of the code, a technique known as Operator
Quantum Zeno Effect [Li Y. et al, preprint arXiv:1305.2464], the dynamics
responsible for quasiparticle motion is suppressed, and can eventually be
"frozen" in the large frequency limit. A feature of this method is that the
density operator of the code does not commute with the measurement operators,
so the density matrix will be randomised after a few measurements. However the
logical operators commute with the measurement operators and are thus
protected.
