Self-Correcting Quantum Memories Beyond the Percolation Threshold

TL;DR

This paper explores high-dimensional quantum codes, showing a temperature range where quantum memory remains stable despite defect percolation, supported by analytic and numerical evidence.

Contribution

It demonstrates the existence of a temperature window where self-correcting quantum memories operate beyond the percolation threshold in high dimensions.

Findings

Distinct separation between critical and percolation temperatures in high dimensions.

Existence of a temperature regime where quantum memory is self-correcting despite defect percolation.

Observation of hysteretic behavior near the critical temperature.

Abstract

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. 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.