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We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept of tube algebras, we construct a set of measurements and of quantum gates whichmap arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting errorsyndrome in terms of doubled Fibonacci anyons.
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