{"title":"对称群上的量子傅里叶变换","authors":"Y. Kawano, Hiroshi Sekigawa","doi":"10.1145/2465506.2465940","DOIUrl":null,"url":null,"abstract":"This paper proposes an <i>O</i>(<i>n</i><sup>4</sup>) quantum Fourier transform (QFT) algorithm over symmetric group <i>S<sub>n</sub></i>, the fastest QFT algorithm of its kind. We propose a fast Fourier transform algorithm over symmetric group <i>S<sub>n</sub></i>, which consists of <i>O</i>(<i>n</i><sup>3</sup>) multiplications of unitary matrices, and then transform it into a quantum circuit form. The QFT algorithm can be applied to constructing the standard algorithm of the hidden subgroup problem.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Quantum fourier transform over symmetric groups\",\"authors\":\"Y. Kawano, Hiroshi Sekigawa\",\"doi\":\"10.1145/2465506.2465940\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes an <i>O</i>(<i>n</i><sup>4</sup>) quantum Fourier transform (QFT) algorithm over symmetric group <i>S<sub>n</sub></i>, the fastest QFT algorithm of its kind. We propose a fast Fourier transform algorithm over symmetric group <i>S<sub>n</sub></i>, which consists of <i>O</i>(<i>n</i><sup>3</sup>) multiplications of unitary matrices, and then transform it into a quantum circuit form. The QFT algorithm can be applied to constructing the standard algorithm of the hidden subgroup problem.\",\"PeriodicalId\":243282,\"journal\":{\"name\":\"International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2465506.2465940\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2465506.2465940","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper proposes an O(n4) quantum Fourier transform (QFT) algorithm over symmetric group Sn, the fastest QFT algorithm of its kind. We propose a fast Fourier transform algorithm over symmetric group Sn, which consists of O(n3) multiplications of unitary matrices, and then transform it into a quantum circuit form. The QFT algorithm can be applied to constructing the standard algorithm of the hidden subgroup problem.
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