Protecting topological order by dynamical localization

TL;DR

This paper demonstrates that disorder-induced dynamical localization can preserve topological order in a 2D toric code model during time evolution, enhancing its robustness as a quantum memory.

Contribution

It introduces the concept that dynamical localization can protect topological order during non-equilibrium evolution, a novel approach to quantum memory stability.

Findings

Dynamical localization makes time evolution a local unitary transformation.

Topological order remains robust after a quantum quench due to localization.

Wilson loop and entanglement entropy confirm the preservation of topological order.

Abstract

As a prototype model of topological quantum memory, two-dimensional toric code is genuinely immune to generic local static perturbations, but fragile at finite temperature and also after non-equilibrium time evolution at zero temperature. We show that dynamical localization induced by disorder makes the time evolution a local unitary transformation at all times, which keeps topological order robust after a quantum quench. We verify this conclusion by investigating the Wilson loop expectation value and topological entanglement entropy. Our results suggest that the two dimensional topological quantum memory can be dynamically robust at zero temperature.