Error correction for non-Abelian topological quantum computation

Abstract

The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals forAbelian anyons, forwhich decoding algorithms have been tailor-made formany topological errorcorrecting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general.We also choose a specific anyonmodel and errormodel to probe the probleminmore detail. The anyonmodel is the charge submodel of D(S3). This sharesmany properties with important models such as the Fibonaccianyons, making our method more generally applicable. The error model is a straight forward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.