Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

TL;DR

This paper introduces a fault-tolerant error correction scheme for non-Abelian anyons in topological quantum systems, capable of handling thermal and measurement errors, and establishes a fault-tolerance threshold through analytical and numerical methods.

Contribution

It presents a novel local cellular automaton-based error correction scheme applicable to both abelian and non-abelian anyons, including measurement errors, with proven fault-tolerance thresholds.

Findings

Fault-tolerance threshold between 10^{-4} and 10^{-3} for Ising anyons.

Analytical proof of fault-tolerance threshold for certain non-Abelian anyon models.

Numerical simulations support the effectiveness of the correction scheme.

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 G\'acs [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 $10^{-3}$.