Self-Correcting Quantum Memories Beyond the Percolation Threshold
Matthew B. Hastings, Grant Watson, Roger G. Melko · Physical Review Letters · 2014
We analyze several high dimensional generalizations of the toric code at a nonzero temperature. We find that in a large enough dimension, there can be a distinct separation between the critical temperature ${T}_{c}$, given by thermodynamic singularities, and the percolation temperature ${T}_{p}$, given by the percolation of defects. We argue that the regime ${T}_{p}<T<{T}_{c}$ is a range of temperatures where a self-correcting quantum memory can operate despite having percolating defects. We present analytic arguments and numerical evidence in support of this scenario, including a mean-field treatment and Monte Carlo simulations. Near ${T}_{c}$, simulations observe a large hysteretic behavior, which may have applications by allowing the self-correcting phase to survive in a ``superheated'' regime.