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Comparison of memory thresholds for planar qudit geometries

Marks, Jacob and Jochym-O’Connor, Tomas and Gheorghiu, Vlad (2017) Comparison of memory thresholds for planar qudit geometries. New Journal of Physics, 19 (11). Art. No. 113022. ISSN 1367-2630. doi:10.1088/1367-2630/aa939a.

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We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of 5.6% compared to the 8.0% obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around 11.9%. All the analysis is performed using QTop, a new open-source software for simulating and visualizing topological quantum error correcting codes.

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Additional Information:© 2017 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 20 February 2017; Accepted 16 October 2017; Accepted Manuscript online 16 October 2017; Published 15 November 2017. The authors thank Michele Mosca for fruitful discussions and comments regarding the manuscript, and the IQC technical staff for providing access to the Heavylift computing clusters at the IQC. We also thank Earl Campbell and Benjamin Brown for useful comments. JM acknowledges support from a Yale Richter Fellowship and Undergraduate Research Award from the University of Waterloo. TJO acknowledges support from NSERC through the Vanier CGS as well from the Burke Institute through the Sherman Fairchild Fellowship. VG acknowledges support from NSERC and CIFAR. IQC is supported in part by the Government of Canada and the Province of Ontario.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
University of WaterlooUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Government of CanadaUNSPECIFIED
Province of OntarioUNSPECIFIED
Subject Keywords:quantum, error correction, color codes, qudit, fault-tolerant
Issue or Number:11
Record Number:CaltechAUTHORS:20171130-105953500
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Official Citation:Jacob Marks et al 2017 New J. Phys. 19 113022
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83599
Deposited By: Tony Diaz
Deposited On:30 Nov 2017 19:08
Last Modified:12 Jul 2022 19:44

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