Continuous error correction for Ising anyons
Adrian Hutter, James R. Wootton · Physical Review A · 2016
Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture truly scalable, even rare errors need to be corrected. Error correction for non-Abelian anyons is complicated by the fact that it needs to be performed on a continuous basis, and further errors may occur while we are correcting existing ones. Here, we prove the feasibility of this task, establishing non-Abelian anyons as a viable platform for scalable quantum computation. We thereby focus on Ising anyons as the most prominent example of non-Abelian anyons and show that for these a finite error rate can indeed be corrected continuously. There is a threshold error rate ${p}_{c}>0$ such that for all error rates $p<{p}_{c}$ the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.