A quantum algorithm for approximating the influences of boolean functions and its applications
文献类型：期刊论文
| 作者 | Li, Hongwei1,2,3,4; Yang, Li1,3 |
| 刊名 | Quantum information processing
 |
| 出版日期 | 2015-06-01 |
| 卷号 | 14期号:6页码:1787-1797 |
| 关键词 | The bernstein-vazirani algorithm Quantum algorithm Influence of boolean function |
| ISSN号 | 1570-0755 |
| DOI | 10.1007/s11128-015-0954-8 |
| 通讯作者 | Yang, li(yangli@iie.ac.cn) |
| 英文摘要 | We investigate the influences of variables on a boolean function f based on the quantum bernstein-vazirani algorithm. a previous paper (floess et al. in math struct comput sci 23:386, 2013) has proved that if an n-variable boolean function f (x(1) ,..., x(n)) does not depend on an input variable x(i), using the bernstein-vazirani circuit for f will always output y that has a 0 in the ith position. we generalize this result and show that, after running this algorithm once, the probability of getting a 1 in each position i is equal to the dependence degree of f on the variable x(i), i.e., the influence of x(i) on f. based on this, we give an approximation algorithm to evaluate the influence of any variable on a boolean function. next, as an application, we use it to study the boolean functions with juntas and construct probabilistic quantum algorithms to learn certain boolean functions. compared with the deterministic algorithms given by floess et al., our probabilistic algorithms are faster. |
| WOS研究方向 | Physics |
| WOS类目 | Physics, Multidisciplinary ; Physics, Mathematical |
| 语种 | 英语 |
| WOS记录号 | WOS:000355264700004 |
| 出版者 | SPRINGER |
| URI标识 | http://www.irgrid.ac.cn/handle/1471x/2376591 |
| 专题 | 中国科学院大学 |
| 通讯作者 | Yang, Li |
| 作者单位 | 1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China 2.Henan Inst Educ, Sch Math & Stat, Zhengzhou 450046, Henan, Peoples R China 3.Chinese Acad Sci, Data Assurance & Commun Secur Res Ctr, Beijing 100093, Peoples R China 4.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Hongwei,Yang, Li. A quantum algorithm for approximating the influences of boolean functions and its applications[J]. Quantum information processing,2015,14(6):1787-1797. |
| APA | Li, Hongwei,&Yang, Li.(2015).A quantum algorithm for approximating the influences of boolean functions and its applications.Quantum information processing,14(6),1787-1797. |
| MLA | Li, Hongwei,et al."A quantum algorithm for approximating the influences of boolean functions and its applications".Quantum information processing 14.6(2015):1787-1797. |
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来源：中国科学院大学
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