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Quantum error correction via codes over GF(4)

Calderbank, A. Robert and Rains, Eric M. and Shor, P. W. and Sloane, Neil J. A. (1998) Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory, 44 (4). pp. 1369-1387. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:20170925-160358492

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Abstract

The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/18.681315DOIArticle
http://ieeexplore.ieee.org/document/681315PublisherArticle
https://arxiv.org/abs/quant-ph/9608006arXivDiscussion Paper
Additional Information:© 1998 IEEE. Manuscript received July 15, 1996; revised December 4, 1997. The work of E. M. Rains was performed while he was with the Institute for Defense Analyses, Princeton, NJ USA. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Ulm, Germany, 1997. The authors wish to thank Aaron Gulliver for finding the quasicyclic codes mentioned in Section V, and our colleague Ronald H. Hardin for his contributions to our search for interesting nonadditive codes. We also thank Patrick Solé for drawing our attention to the work of B. Runge and G. Höhn.
Subject Keywords:Codes, additive; codes, quantum; codes, quaternary; codes, self-orthogonal, geometry, orthogonal; geometry, symplectic; group, Clifford
Record Number:CaltechAUTHORS:20170925-160358492
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170925-160358492
Official Citation:A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, "Quantum error correction via codes over GF(4)," in IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1369-1387, Jul 1998. doi: 10.1109/18.681315 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=681315&isnumber=14976
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81821
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 23:12
Last Modified:25 Sep 2017 23:12

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