{"title":"在更高的字母上的拓扑颜色代码","authors":"P. Sarvepalli","doi":"10.1109/CIG.2010.5592860","DOIUrl":null,"url":null,"abstract":"Color codes are a class of topological codes that have come into prominence in the recent years. Like the surface codes the codespace defined by them can be associated to the degenerate ground state of a local Hamiltonian. In addition they can be designed to have an extended set of transversal encoded gates (compared to surface codes) increasing their appeal for fault tolerant quantum computation. In this paper we generalize the color codes to arbitrary prime power alphabet. We show that in the 2D case there exist color codes for which the nonbinary Clifford group can be implemented transversally.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"292 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Topological color codes over higher alphabet\",\"authors\":\"P. Sarvepalli\",\"doi\":\"10.1109/CIG.2010.5592860\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Color codes are a class of topological codes that have come into prominence in the recent years. Like the surface codes the codespace defined by them can be associated to the degenerate ground state of a local Hamiltonian. In addition they can be designed to have an extended set of transversal encoded gates (compared to surface codes) increasing their appeal for fault tolerant quantum computation. In this paper we generalize the color codes to arbitrary prime power alphabet. We show that in the 2D case there exist color codes for which the nonbinary Clifford group can be implemented transversally.\",\"PeriodicalId\":354925,\"journal\":{\"name\":\"2010 IEEE Information Theory Workshop\",\"volume\":\"292 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE Information Theory Workshop\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CIG.2010.5592860\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE Information Theory Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CIG.2010.5592860","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Color codes are a class of topological codes that have come into prominence in the recent years. Like the surface codes the codespace defined by them can be associated to the degenerate ground state of a local Hamiltonian. In addition they can be designed to have an extended set of transversal encoded gates (compared to surface codes) increasing their appeal for fault tolerant quantum computation. In this paper we generalize the color codes to arbitrary prime power alphabet. We show that in the 2D case there exist color codes for which the nonbinary Clifford group can be implemented transversally.
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