Deterministic algorithms for the hidden subgroup problem
The hidden subgroup problem (HSP) plays a crucial role in the field of quantum computing, since several celebrated quantum algorithms including Shor's algorithm have a uniform description in the framework of HSP. The problem is as follows: for a finite group G and a finite set X, given a functi...
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| Veröffentlicht in: | Information and computation Jg. 289; S. 104975 |
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| Abstract | The hidden subgroup problem (HSP) plays a crucial role in the field of quantum computing, since several celebrated quantum algorithms including Shor's algorithm have a uniform description in the framework of HSP. The problem is as follows: for a finite group G and a finite set X, given a function f:G→X and the promise that for any g1,g2∈G,f(g1)=f(g2) iff g1H=g2H for a subgroup H≤G, the goal of the decision version is to determine whether H is trivial, and the goal of the search version is to find H. Nayak (2021) asked whether there exist deterministic algorithms with O(|G||H|) query complexity for HSP. We answer this problem for Abelian groups, which also extends the main results of Ye et al. (2021), since here the algorithms do not rely on any prior knowledge of H. |
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| AbstractList | The hidden subgroup problem (HSP) plays a crucial role in the field of quantum computing, since several celebrated quantum algorithms including Shor's algorithm have a uniform description in the framework of HSP. The problem is as follows: for a finite group G and a finite set X, given a function f:G→X and the promise that for any g1,g2∈G,f(g1)=f(g2) iff g1H=g2H for a subgroup H≤G, the goal of the decision version is to determine whether H is trivial, and the goal of the search version is to find H. Nayak (2021) asked whether there exist deterministic algorithms with O(|G||H|) query complexity for HSP. We answer this problem for Abelian groups, which also extends the main results of Ye et al. (2021), since here the algorithms do not rely on any prior knowledge of H. |
| ArticleNumber | 104975 |
| Author | Li, Lvzhou Ye, Zekun |
| Author_xml | – sequence: 1 givenname: Zekun surname: Ye fullname: Ye, Zekun email: yezekun@mail2.sysu.edu.cn organization: Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China – sequence: 2 givenname: Lvzhou surname: Li fullname: Li, Lvzhou email: lilvzh@mail.sysu.edu.cn organization: Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China |
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| Keywords | Hidden subgroup problem Quantum computing Query complexity Deterministic algorithm |
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