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Quasiparticle Localisation via Frequent Measurements

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.