Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological...

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Autores principales:	Courtney G. Brell, Simon Burton, Guillaume Dauphinais, Steven T. Flammia, David Poulin
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2014
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/9e21cc7dad97447296e18ecc06c206b9
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spelling	oai:doaj.org-article:9e21cc7dad97447296e18ecc06c206b92021-12-02T11:17:36ZThermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems10.1103/PhysRevX.4.0310582160-3308https://doaj.org/article/9e21cc7dad97447296e18ecc06c206b92014-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.4.031058http://doi.org/10.1103/PhysRevX.4.031058https://doaj.org/toc/2160-3308We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range from 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.Courtney G. BrellSimon BurtonGuillaume DauphinaisSteven T. FlammiaDavid PoulinAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 4, Iss 3, p 031058 (2014)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Courtney G. Brell Simon Burton Guillaume Dauphinais Steven T. Flammia David Poulin Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
description	We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range from 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.
format	article
author	Courtney G. Brell Simon Burton Guillaume Dauphinais Steven T. Flammia David Poulin
author_facet	Courtney G. Brell Simon Burton Guillaume Dauphinais Steven T. Flammia David Poulin
author_sort	Courtney G. Brell
title	Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
title_short	Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
title_full	Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
title_fullStr	Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
title_full_unstemmed	Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems
title_sort	thermalization, error correction, and memory lifetime for ising anyon systems
publisher	American Physical Society
publishDate	2014
url	https://doaj.org/article/9e21cc7dad97447296e18ecc06c206b9
work_keys_str_mv	AT courtneygbrell thermalizationerrorcorrectionandmemorylifetimeforisinganyonsystems AT simonburton thermalizationerrorcorrectionandmemorylifetimeforisinganyonsystems AT guillaumedauphinais thermalizationerrorcorrectionandmemorylifetimeforisinganyonsystems AT steventflammia thermalizationerrorcorrectionandmemorylifetimeforisinganyonsystems AT davidpoulin thermalizationerrorcorrectionandmemorylifetimeforisinganyonsystems
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Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems

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