Southwest Quantum Information and Technology

Fault-tolerant quantum memory for systems of non-Abelian anyons

Presenting Author: Guillaume Dauphinais, Université de Sherbrooke
Contributing Author(s): David Poulin

The study of error correction for systems giving rise to excitations described by non-abelian anyons has recently been undertaken, but is more complicated than in the abelian case due to the existence of multiple fusion channels. Error correction algorithms for specific anyonic models have been numerically shown to posses a threshold [1-3]. These results were all obtained using one-shot error correction; once the noise has affected the system, the correction algorithm is performed perfectly, in a noiseless environment. Continuous error correction for a system of Ising anyons have been analytically shown to possess a threshold [4]. However, none of these studies have considered the case where measurements are faulty. In the present work, a generalization of a fault-tolerant scheme introduced in [5] for the toric code is presented. This algorithm is extended to systems giving rise to non-abelian anyonic excitations, and uses the idea of cellular automaton and renormalization. A noise model including measurement errors is studied, and a threshold of about 0.1% is numerically found for a system giving rise to Ising anyons, while analytical work showing the existence of a threshold for systems giving rise to a larger class of non-abelian anyons is under way. [1] C. Brell et al., PRX 4, 031058 (2014) [2] J. Wootton et al., PRX 4, 011051 (2014) [3] S. Burton et al., arXiv:1506.03815 (2015) [4] A. Hutter et al., arXiv:1508.04033v1 (2015) [5] J. Harrington, Ph. D. thesis, Caltech (2004)

(Session 5 : Thursday from 5:00 - 7:00 pm)