Self-correction phase transition in the dissipative toric code

TL;DR

This paper demonstrates that a dissipative toric code can exhibit a self-correcting phase transition, maintaining topological order and error correction capabilities even without a finite threshold, through a Lindblad master equation approach.

Contribution

It introduces a time-continuous cellular automaton decoder modeled by a Lindblad equation, revealing a thermodynamical phase where self-correction persists without a finite threshold.

Findings

Steady state is topologically ordered in certain regimes

Self-correction occurs without a finite error threshold

Phase diagram shows competition between error correction and classical field updates

Abstract

We analyze a time-continuous version of a cellular automaton decoder for the toric code in the form of a Lindblad master equation. In this setting, a self-correcting quantum memory becomes a thermodynamical phase of the steady state, which manifests itself through the steady state being topologically ordered. We compute the steady state phase diagram, finding a competition between the error correction rate and the update rate for the classical field of the cellular automaton. Strikingly, we find that self-correction of errors is possible even in situations where conventional quantum error correction does not have a finite threshold.