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arXiv · 1607.02159

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

Guillaume Dauphinais·David Poulin
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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 [Gacs 1986] and Harrington [Harrington 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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Guillaume Dauphinais, David Poulin. 2017-07-11. Fault-Tolerant Quantum Error Correction for non-Abelian Anyons. https://doi.org/10.1007/s00220-017-2923-9

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