Continuous error correction for Ising anyons

Adrian Hutter and James R. Wootton
Phys. Rev. A 93, 042327 – Published 18 April 2016

Abstract

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 pc>0 such that for all error rates p<pc the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.

  • Figure
  • Received 1 September 2015
  • Revised 18 February 2016

DOI:https://doi.org/10.1103/PhysRevA.93.042327

©2016 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Adrian Hutter and James R. Wootton

  • Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

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Issue

Vol. 93, Iss. 4 — April 2016

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