{"id":314075,"date":"2018-11-06T17:09:00","date_gmt":"2018-11-07T01:09:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=314075"},"modified":"2018-11-06T17:09:00","modified_gmt":"2018-11-07T01:09:00","slug":"graphs-quadratic-forms-quantum-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/graphs-quadratic-forms-quantum-codes\/","title":{"rendered":"Graphs, Quadratic Forms, and Quantum Codes"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings 2002 IEEE International Symposium on Information Theory (ISIT 2002), Lausanne, Switzerland, June\/July 2002, p. 45","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"45","msr_page_range_start":"45","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings 2002 IEEE International Symposium on Information Theory (ISIT 2002), Lausanne, Switzerland, June\/July 2002, p. 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