Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code

TL;DR

This paper demonstrates that despite the general intractability of simulating anyonic quantum systems, a specific structured class allows classical simulation of Fibonacci anyon error correction, achieving thresholds comparable to other models.

Contribution

The authors develop a classical simulation method for Fibonacci anyon error correction protocols, revealing a lower bound on the error threshold around 0.125 errors per edge.

Findings

Successfully simulated a 128x128 lattice system.

Estimated a lower bound error threshold of approximately 0.125.

Showed the structured class of processes enables classical simulation.

Abstract

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128x128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for abelian and (non-universal) nonabelian anyon models.