灵活的固定相位量子搜索算法  

Flexibly Fixed Phase Quantum Search Algorithm

作　　者：肖红[1] 刘新彤 李盼池[1] XIAO Hong;LIU Xintong;LI Panchi(School of Computer and Information Technology,Northeast Petroleum University,Daqing 163318,Heilongjiang,China)

机构地区：[1]东北石油大学计算机与信息技术学院,黑龙江大庆163318

出　　处：《北京工业大学学报》2023年第6期630-638,共9页Journal of Beijing University of Technology

基　　金：黑龙江省自然科学基金资助项目(LH2022F006)。

摘　　要：为解决Grover算法的普适性不够理想的问题,提出一种灵活的量子搜索算法.首先,通过设计包含任意数目基态的量子均衡叠加态,实现任意大小无序数据库的构建;其次,通过求解算法的迭代方程,导出旋转相位与成功概率及搜索步数之间的定量关系,其中旋转相位可取(0,π]内的任意值;再次,通过迭代步数与成功概率的统计分析,确定当标记态数未知时旋转相位的最佳取值,并设计搜索方案;最后,考察不同旋转相位及不同标记态数下,成功概率及迭代步数的数值结果.理论分析表明该算法可以实现经典算法的二次加速.To address the problem that the universality of Grover's algorithm is not ideal,a flexible quantum search algorithm was proposed in this paper.The flexibility of the proposed algorithm was manifested in three aspects.First,by designing quantum equilibrium superposition states containing any number of basis states,the construction method of unordered database of any size was given.Second,by solving the iterative equation of the algorithm,the quantitative relationship between the rotation phase and the success probability and the number of search steps was derived,where the rotation phase could take any value within(0,π].Third,through the statistical analysis of iteration steps and success probability,the optimal value of rotation phase was determined when the number of marked states was unknown,and the search scheme was designed.Finally,the numerical results of the probability of success and the number of iteration steps under different rotation phases and different numbers of marked states were investigated.The theoretical analysis shows that the proposed algorithm leads to a square-root speedup over the corresponding classical algorithm.

关 键 词：量子计算 量子算法 量子搜索 相位匹配 量子叠加态 量子线路设计 

分 类 号：TP8[自动化与计算机技术—检测技术与自动化装置]