Bounded light cone and robust topological order out of equilibrium

TL;DR

This paper demonstrates that bounded light cones can preserve topological order during unitary evolution, enabling potential stability of quantum memories out of equilibrium at zero temperature.

Contribution

It introduces the concept that bounded light cones can make topological order dynamically robust, extending stability beyond equilibrium conditions.

Findings

Bounded light cones preserve topological order during evolution.

Topological order can be maintained through suitable perturbations.

Quantum memories may be stable out of equilibrium at zero temperature.

Abstract

The ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories, which are unfortunately not stable away from equilibrium even at zero temperature. This plague precludes practical robust self-correction since stability at zero temperature is a prerequisite for finite-temperature robustness. In this work, we show that the emergence of a bounded light cone renders the unitary time evolution a quasi-adiabatic continuation that preserves topological order, with the initial ground space retaining its macroscopic distance at all times as a quantum code. We also show how bounded light cones can emerge through suitable perturbations in Kitaev's toric code and honeycomb model. Our results suggest that topological orders and self-correcting quantum memories can be dynamically robust at zero temperature.