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Self correction requires Energy Barrier for Abelian quantum doubles

Kómár, Anna and Landon-Cardinal, Olivier and Temme, Kristan (2016) Self correction requires Energy Barrier for Abelian quantum doubles. Physical Review A, 93 . Art. No. 052337. ISSN 1050-2947. doi:10.1103/PhysRevA.93.052337.

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We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Zd. We have made the concept of the energy barrier therein mathematically well-defined, it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.

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Additional Information:©2016 American Physical Society. Received 22 February 2016. We thank B. Brown and J. Preskill for helpful discussions and for valuable comments on an early version of the draft. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NFS Grants No. PHY-1125565 and No. PHY-0803371) with support of the Gordon and Betty Moore Foundation (Grant No. GBMF-12500028). O.L.C. is partially supported by Fonds de Recherche Quebec-Nature et Technologies and the Natural Sciences and Engineering Research Council of Canada (NSERC).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
National Science FoundationPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Fonds de Recherche QuebecNature et TechnologiesUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Record Number:CaltechAUTHORS:20160622-143120606
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68601
Deposited By: Jacquelyn O'Sullivan
Deposited On:22 Jun 2016 22:25
Last Modified:11 Nov 2021 04:02

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