Robustness of Topological Order in the Toric Code with Open Boundaries

TL;DR

This paper investigates how topological order in the toric code with open boundaries responds to perturbations, revealing that boundary conditions significantly influence robustness, with some configurations maintaining order better than others.

Contribution

It classifies boundary conditions into condensing and non-condensing types and analyzes their impact on the robustness of topological order under perturbations.

Findings

Non-condensing boundaries enhance robustness of topological order.

Condensing boundaries lead to rapid loss of topological order with perturbations.

Quantum phase diagrams of equivalent Ising models explain robustness differences.

Abstract

We analyze the robustness of topological order in the toric code in an open boundary setting in the presence of perturbations. The boundary conditions are introduced on a cylinder, and are classified into condensing and non-condensing classes depending on the behavior of the excitations at the boundary under perturbation. For the non-condensing class, we see that the topological order is more robust when compared to the case of periodic boundary conditions while in the condensing case topological order is lost as soon as the perturbation is turned on. In most cases, the robustness can be understood by the quantum phase diagram of a equivalent Ising model.