Continuous error correction for Ising anyons

TL;DR

This paper demonstrates the feasibility of continuous error correction for Ising anyons in topological quantum computing, showing that a finite error rate can be managed to ensure scalable, reliable quantum operations.

Contribution

It provides the first analysis proving that continuous error correction for non-Abelian anyons, specifically Ising anyons, is feasible and establishes a threshold error rate for scalable quantum computation.

Findings

Finite error rate can be corrected continuously for Ising anyons.

Existence of a threshold error rate $p_c>0$ for reliable quantum computation.

Logical error probability can be exponentially suppressed below the threshold.

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 provide the first study of this problem and prove its feasibility, 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.