Localization of Toric Code Defects

TL;DR

This paper investigates passive error correction in the toric code, showing that Anderson localization of defects can protect against logical errors caused by coherent dynamics, potentially enabling self-correcting quantum memory.

Contribution

It introduces the idea that Anderson localization of defects can serve as a passive error correction mechanism in the toric code.

Findings

Coherent dynamics induce logical errors in the toric code.

Anderson localization can prevent defect propagation.

Numerical results suggest self-correcting memory is possible with localized defects.

Abstract

We explore the possibility of passive error correction in the toric code model. We first show that even coherent dynamics, stemming from spin interactions or the coupling to an external magnetic field, lead to logical errors. We then argue that Anderson localization of the defects, arising from unavoidable fluctuations of the coupling constants, provides a remedy. This protection is demonstrated using general analytical arguments that are complemented with numerical results which demonstrate that self-correcting memory can in principle be achieved in the limit of a nonzero density of identical defects.