High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping
Original manuscript July 29, 2009
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2013
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| Online Access: | http://hdl.handle.net/1721.1/80828 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1811069810190057472 |
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| author | Shor, Peter W. Smith, Graeme Smolin, John A. Zeng, Bei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Shor, Peter W. Smith, Graeme Smolin, John A. Zeng, Bei |
| author_sort | Shor, Peter W. |
| collection | MIT |
| description | Original manuscript July 29, 2009 |
| first_indexed | 2024-09-23T08:16:30Z |
| format | Article |
| id | mit-1721.1/80828 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:16:30Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/808282022-09-30T08:47:11Z High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping Shor, Peter W. Smith, Graeme Smolin, John A. Zeng, Bei Massachusetts Institute of Technology. Department of Mathematics Shor, Peter W. Original manuscript July 29, 2009 We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n ≥ 8 except n=2r-1. We generalize this construction to employ classical codes over GF(3) with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, conceptually simple (though potentially computationally expensive) encoding and decoding circuits are available. 2013-09-20T15:00:58Z 2013-09-20T15:00:58Z 2011-10 2011-05 Article http://purl.org/eprint/type/JournalArticle 0018-9448 1557-9654 http://hdl.handle.net/1721.1/80828 Shor, Peter W., Graeme Smith, John A. Smolin, and Bei Zeng. “High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping.” IEEE Transactions on Information Theory 57, no. 10 (October 2011): 7180-7188. https://orcid.org/0000-0003-4626-5648 en_US http://dx.doi.org/10.1109/tit.2011.2165149 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Shor, Peter W. Smith, Graeme Smolin, John A. Zeng, Bei High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title | High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title_full | High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title_fullStr | High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title_full_unstemmed | High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title_short | High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping |
| title_sort | high performance single error correcting quantum codes for amplitude damping |
| url | http://hdl.handle.net/1721.1/80828 https://orcid.org/0000-0003-4626-5648 |
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