Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons 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 $${10^{-4}}$$ 10 - 4 and $${10^{-3}}$$ 10 - 3 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-017-2923-9
Publisher site
See Article on Publisher Site

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 $${10^{-4}}$$ 10 - 4 and $${10^{-3}}$$ 10 - 3 .

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Jul 10, 2017

References

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