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Cellular-automaton decoders with provable thresholds for topological codes

Kubica, Aleksander and Preskill, John (2019) Cellular-automaton decoders with provable thresholds for topological codes. Physical Review Letters, 123 (2). Art. No. 020501. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20190201-155942835

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Abstract

We propose a new cellular automaton (CA), the sweep rule, which generalizes Toom’s rule to any locally Euclidean lattice. We use the sweep rule to design a local decoder for the toric code in d ≥ 3 dimensions, the sweep decoder, and rigorously establish a lower bound on its performance. We also numerically estimate the sweep decoder threshold for the three-dimensional toric code on the cubic and body-centered cubic lattices for phenomenological phase-flip noise. Our results lead to new CA decoders with provable error-correction thresholds for other topological quantum codes including the color code.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.123.020501DOIArticle
https://arxiv.org/abs/1809.10145arXivDiscussion Paper
Additional Information:© 2019 American Physical Society. Received 26 October 2018; published 8 July 2019. A. K. thanks Nicolas Delfosse for invaluable feedback throughout the project and Ben Brown and Mike Vasmer for stimulating discussions. A. K. acknowledges funding provided by the Simons Foundation through the “It from Qubit” Collaboration. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. J. P. acknowledges support from ARO, DOE, IARPA, NSF, and the Simons Foundation. The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Intelligence Advanced Research Projects Activity (IARPA) UNSPECIFIED
NSFUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20190201-155942835
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190201-155942835
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92603
Collection:CaltechAUTHORS
Deposited By: Bonnie Leung
Deposited On:04 Feb 2019 17:42
Last Modified:25 Jul 2019 15:02

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