Quantum algorithm based on the ε-random linear disequations for the continuous hidden shift problem

作     者：Bae, Eunok Lee, Soojoon 

作者机构：Kyung Hee Univ Dept Math Seoul 02447 South Korea Kyung Hee Univ Res Inst Basic Sci Seoul 02447 South Korea 

出 版 物：《QUANTUM INFORMATION PROCESSING》 (量子信息处理)

年 卷 期：2021年第20卷第10期

页      面：347-347页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：National Research Foundation of Korea - Ministry of Science and ICT (MSIT) [NRF-2019R1A2C1006337, NRF-2020M3E4A1079678] National Research Foundation of Korea - MSIT [NRF-2019K1A3A1A12071493] MSIT, under the Information Technology Research Center support program [IITP-2021-2018-0-01402] Quantum Information Science and Technologies program of the National Research Foundation of Korea - MSIT [NRF-2020M3H3A1105796] 

主　　题：Quantum algorithm Continuous hidden shift problem epsilon-Random linear disequations 

摘      要：There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we define the continuous hidden shift problem on R-n with a continuous oracle function as an extension of the hidden shift problem, and also define the epsilon-random linear disequations which is a generalization of the random linear disequations. By employing the newly defined concepts, we show that there exists a quantum computational algorithm which solves this problem in time polynomial in n.