Fault-tolerant error correction for a universal non-Abelian topological quantum computer at finite temperature

TL;DR

This paper demonstrates that a 2D Fibonacci anyon-based quantum memory can be fault-tolerant at finite temperature using cellular automaton decoders, supporting the feasibility of universal non-Abelian topological quantum computing.

Contribution

It provides the first numerical evidence that a 2D non-Abelian topological code with Fibonacci anyons can achieve fault tolerance at finite temperature.

Findings

Code exhibits fault-tolerant behavior in simulations

Threshold behavior likely present for error correction

Supports feasibility of universal non-Abelian topological quantum computing

Abstract

We study fault-tolerant error correction in a quantum memory constructed as a two-dimensional model of Fibonacci anyons on a torus, in the presence of thermal noise represented by pair-creation processes and measurement errors. The correction procedure is based on the cellular automaton decoders originating in the works of G\'acs and Harrington. Through numerical simulations, we observe that this code behaves fault-tolerantly and that threshold behavior is likely present. Hence, we provide strong evidence for the existence of a fault-tolerant universal non-Abelian topological quantum computer.