Incoherent dynamics in the toric code subject to disorder

TL;DR

This paper investigates how different types of disorder affect the stability and behavior of anyons in the toric code, revealing new codes and unexpected effects on error thresholds and anyon dynamics.

Contribution

It introduces a new class of random lattice codes that outperform standard codes under biased noise and analyzes the incoherent and coherent effects of disorder on anyon motion.

Findings

Random lattice codes approach optimal error thresholds.

Disorder can increase the lifetime of encoded states unexpectedly.

Disorder suppresses coherent anyon transport.

Abstract

We numerically study the effects of two forms of quenched disorder on the anyons of the toric code. Firstly, a new class of codes based on random lattices of stabilizer operators is presented, and shown to be superior to the standard square lattice toric code for certain forms of biased noise. It is further argued that these codes are close to optimal, in that they tightly reach the upper bound of error thresholds beyond which no correctable CSS codes can exist. Additionally, we study the classical motion of anyons in toric codes with randomly distributed onsite potentials. In the presence of repulsive long-range interaction between the anyons, a surprising increase with disorder strength of the lifetime of encoded states is reported and explained by an entirely incoherent mechanism. Finally, the coherent transport of the anyons in the presence of both forms of disorder is investigated, and a significant suppression of the anyon motion is found.