Duration: 34:58

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While topological quantum computation is intrinsically fault-tolerant at zero temperature, it looses 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 and Harrington and operates as a local cellular automaton. In contrast to previously studied schemes, ours is valid for both abelian and non-abelian anyons and accounts for measurement errors. We prove the existence of a fault-tolerant threshold and numerically simulate the procedure for Ising anyons. Our simulations are consistent with a threshold between 0.0001 and 0.001.