Critical non-equilibrium phases from noisy topological memories

TL;DR

This paper uncovers a non-equilibrium critical phase in the surface code under noisy measurements, characterized by unique information decay properties and partial logical information retention, analyzed through loop model mappings.

Contribution

It introduces the concept of a non-equilibrium critical phase in topological memories and relates it to loop models, providing new insights into information decay and decoding capabilities.

Findings

Extended critical phase with sub-exponential CMI decay

Partial logical information can be recovered globally but not locally

Analytic relation between CMI decay and loop model length scale

Abstract

We demonstrate the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information (CMI), in the surface code subject to heralded random Pauli measurement channels. By mapping the resulting mixed state to the ensemble of completely packed loops on a square lattice, we relate the extended phase to the Goldstone phase of the loop model. In particular, CMI is controlled by the characteristic length scale of loops, and we use analytic results of the latter to establish polylogarithmic decay of CMI in the critical phase. We find that the critical phase retains partial logical information that can be recovered by a global decoder, but not by any quasi-local decoder. To demonstrate this, we introduce a diagnostic called punctured coherent information which provides a necessary condition for quasi-local decoding.