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Communications in Mathematical Physics

, Volume 355, Issue 2, pp 519–560 | Cite as

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

  • Guillaume DauphinaisEmail author
  • David Poulin
Article

Abstract

While topological quantum computation is intrinsically fault-tolerant at zero temperature, it loses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting non-cyclic anyons against thermal and measurement errors. The correction procedure builds on the work of Gács (J Comput Syst Sci 32:15–78, 1986. doi: 10.1145/800061.808730) and Harrington (Analysis of quantum error-correcting codes: symplectic lattice codes and toric code, 2004) and operates as a local cellular automaton. In contrast to previously studied schemes, our scheme is valid for both abelian and non-abelian anyons and accounts for measurement errors. We analytically prove the existence of a fault-tolerant threshold for a certain class of non-Abelian anyon models, and numerically simulate the procedure for the specific example of Ising anyons. The result of our simulations are consistent with a threshold between \({10^{-4}}\) and \({10^{-3}}\).

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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institut quantique & Département de physiqueUniversité de SherbrookeSherbrookeCanada

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