Rafael I. Nepomechie, Francesco Ravanini, David Raveh
{"title":"自旋$s$迪克态及其制备方法","authors":"Rafael I. Nepomechie, Francesco Ravanini, David Raveh","doi":"10.1002/qute.202400057","DOIUrl":null,"url":null,"abstract":"<p>The notion of <span></span><math>\n <semantics>\n <mrow>\n <mi>s</mi>\n <mi>u</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$su(2)$</annotation>\n </semantics></math> spin-<span></span><math>\n <semantics>\n <mi>s</mi>\n <annotation>$s$</annotation>\n </semantics></math> Dicke states is introduced, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of <span></span><math>\n <semantics>\n <mrow>\n <mi>s</mi>\n <mi>u</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mi>s</mi>\n <mo>+</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$su(2s+1)$</annotation>\n </semantics></math> qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as <span></span><math>\n <semantics>\n <mrow>\n <mi>s</mi>\n <mi>k</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mi>s</mi>\n <mi>n</mi>\n <mo>−</mo>\n <mi>k</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$sk(2sn-k)$</annotation>\n </semantics></math>, where <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> is the number of qudits and <span></span><math>\n <semantics>\n <mi>k</mi>\n <annotation>$k$</annotation>\n </semantics></math> is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits.</p>","PeriodicalId":72073,"journal":{"name":"Advanced quantum technologies","volume":"7 12","pages":""},"PeriodicalIF":4.4000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qute.202400057","citationCount":"0","resultStr":"{\"title\":\"Spin-\\n \\n s\\n $s$\\n Dicke States and Their Preparation\",\"authors\":\"Rafael I. Nepomechie, Francesco Ravanini, David Raveh\",\"doi\":\"10.1002/qute.202400057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The notion of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>s</mi>\\n <mi>u</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$su(2)$</annotation>\\n </semantics></math> spin-<span></span><math>\\n <semantics>\\n <mi>s</mi>\\n <annotation>$s$</annotation>\\n </semantics></math> Dicke states is introduced, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>s</mi>\\n <mi>u</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mi>s</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$su(2s+1)$</annotation>\\n </semantics></math> qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>s</mi>\\n <mi>k</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mi>s</mi>\\n <mi>n</mi>\\n <mo>−</mo>\\n <mi>k</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$sk(2sn-k)$</annotation>\\n </semantics></math>, where <span></span><math>\\n <semantics>\\n <mi>n</mi>\\n <annotation>$n$</annotation>\\n </semantics></math> is the number of qudits and <span></span><math>\\n <semantics>\\n <mi>k</mi>\\n <annotation>$k$</annotation>\\n </semantics></math> is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits.</p>\",\"PeriodicalId\":72073,\"journal\":{\"name\":\"Advanced quantum technologies\",\"volume\":\"7 12\",\"pages\":\"\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qute.202400057\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced quantum technologies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/qute.202400057\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced quantum technologies","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qute.202400057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
The notion of spin- Dicke states is introduced, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits.
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