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. doi:10.1103/PhysRevLett.123.020501. https://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.
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| 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: | Institute for Quantum Information and Matter | ||||||||||||||||
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| Issue or Number: | 2 | ||||||||||||||||
| DOI: | 10.1103/PhysRevLett.123.020501 | ||||||||||||||||
| Record Number: | CaltechAUTHORS:20190201-155942835 | ||||||||||||||||
| Persistent URL: | https://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: | 16 Nov 2021 03:51 |
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