On Steane-enlargement of quantum codes from Cartesian product point sets
In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018. https://doi.org/10.1109/TIT.2017.2755682 ). We gi...
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| creator | Christensen, René Bødker Geil, Olav |
| description | In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018.
https://doi.org/10.1109/TIT.2017.2755682
). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound. |
| doi_str_mv | 10.1007/s11128-020-02691-9 |
| format | Article |
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https://doi.org/10.1109/TIT.2017.2755682
). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.</description><identifier>ISSN: 1570-0755</identifier><identifier>EISSN: 1573-1332</identifier><identifier>DOI: 10.1007/s11128-020-02691-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Binary system ; Cartesian coordinates ; Codes ; Data Structures and Information Theory ; Enlargement ; Error analysis ; Error correcting codes ; Error correction ; Expansion ; Mathematical Physics ; Parameters ; Physics ; Physics and Astronomy ; Quantum Computing ; Quantum Information Technology ; Quantum Physics ; Spintronics</subject><ispartof>Quantum information processing, 2020-07, Vol.19 (7), Article 192</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-6d60059851eb43b22c5ae1154b5dcbc12b57c0d0dca58d67999f8cbdce89a9c73</citedby><cites>FETCH-LOGICAL-c319t-6d60059851eb43b22c5ae1154b5dcbc12b57c0d0dca58d67999f8cbdce89a9c73</cites><orcidid>0000-0002-9209-3739 ; 0000-0002-9666-3399</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11128-020-02691-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11128-020-02691-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Christensen, René Bødker</creatorcontrib><creatorcontrib>Geil, Olav</creatorcontrib><title>On Steane-enlargement of quantum codes from Cartesian product point sets</title><title>Quantum information processing</title><addtitle>Quantum Inf Process</addtitle><description>In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018.
https://doi.org/10.1109/TIT.2017.2755682
). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.</description><subject>Algorithms</subject><subject>Binary system</subject><subject>Cartesian coordinates</subject><subject>Codes</subject><subject>Data Structures and Information Theory</subject><subject>Enlargement</subject><subject>Error analysis</subject><subject>Error correcting codes</subject><subject>Error correction</subject><subject>Expansion</subject><subject>Mathematical Physics</subject><subject>Parameters</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Computing</subject><subject>Quantum Information Technology</subject><subject>Quantum Physics</subject><subject>Spintronics</subject><issn>1570-0755</issn><issn>1573-1332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKt_wFPAczST3exujlLUCoUe1HPIJrOlpZttk-zBf2_aFbx5GGZg3nszfITcA38EzuunCACiYVzwXJUCpi7IDGRdMCgKcXme86qW8prcxLjjXEDVVDOyXHv6kdB4ZOj3JmywR5_o0NHjaHwae2oHh5F2YejpwoSEcWs8PYTBjTbRw7DN6ogp3pKrzuwj3v32Ofl6fflcLNlq_fa-eF4xW4BKrHIV51I1ErAti1YIKw0CyLKVzrYWRCtryx131sjGVbVSqmts6yw2yihbF3PyMOXmF44jxqR3wxh8PqlFmZO5FKXKKjGpbBhiDNjpQ9j2Jnxr4PpETE_EdCamz8T0yVRMppjFfoPhL_of1w81Y26O</recordid><startdate>20200701</startdate><enddate>20200701</enddate><creator>Christensen, René Bødker</creator><creator>Geil, Olav</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9209-3739</orcidid><orcidid>https://orcid.org/0000-0002-9666-3399</orcidid></search><sort><creationdate>20200701</creationdate><title>On Steane-enlargement of quantum codes from Cartesian product point sets</title><author>Christensen, René Bødker ; Geil, Olav</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-6d60059851eb43b22c5ae1154b5dcbc12b57c0d0dca58d67999f8cbdce89a9c73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algorithms</topic><topic>Binary system</topic><topic>Cartesian coordinates</topic><topic>Codes</topic><topic>Data Structures and Information Theory</topic><topic>Enlargement</topic><topic>Error analysis</topic><topic>Error correcting codes</topic><topic>Error correction</topic><topic>Expansion</topic><topic>Mathematical Physics</topic><topic>Parameters</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Computing</topic><topic>Quantum Information Technology</topic><topic>Quantum Physics</topic><topic>Spintronics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Christensen, René Bødker</creatorcontrib><creatorcontrib>Geil, Olav</creatorcontrib><collection>CrossRef</collection><jtitle>Quantum information processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Christensen, René Bødker</au><au>Geil, Olav</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Steane-enlargement of quantum codes from Cartesian product point sets</atitle><jtitle>Quantum information processing</jtitle><stitle>Quantum Inf Process</stitle><date>2020-07-01</date><risdate>2020</risdate><volume>19</volume><issue>7</issue><artnum>192</artnum><issn>1570-0755</issn><eissn>1573-1332</eissn><abstract>In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018.
https://doi.org/10.1109/TIT.2017.2755682
). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11128-020-02691-9</doi><orcidid>https://orcid.org/0000-0002-9209-3739</orcidid><orcidid>https://orcid.org/0000-0002-9666-3399</orcidid></addata></record> |
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| subjects | Algorithms Binary system Cartesian coordinates Codes Data Structures and Information Theory Enlargement Error analysis Error correcting codes Error correction Expansion Mathematical Physics Parameters Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum Physics Spintronics |
| title | On Steane-enlargement of quantum codes from Cartesian product point sets |
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