Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code

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 ar...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Authors: Burton, Simon, Brell, Courtney G, Flammia, Steven T
Format: Article
Language:English
Subjects:
Computer simulation
Error analysis
Error correction
Error correction & detection
Lower bounds
Mathematical models
Quantum computing
Quantum phenomena
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1506.03815