Self-Correcting Quantum Memories Beyond the Percolation Threshold

Understand

We analyze several high dimensional generalizations of the toric code at nonzero temperature.

• We find that in 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.