Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

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 $10^{-3}$.

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Measurement-Only Topological Quantum Computation
• Majorana qubit decoherence by quasiparticle poisoning
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• A short introduction to Fibonacci anyon models
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Decoherence of Majorana qubits by noisy gates
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Can long-range interactions stabilize quantum memory at nonzero temperature?

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