Localization of Toric Code Defects

Understand

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.