删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

基于Hadamard算子的二维离散量子行走的概率测度估计

本站小编 Free考研考试/2021-12-27

基于Hadamard算子的二维离散量子行走的概率测度估计 韩琦, 陈芷禾, 殷世德, 陆自强西北师范大学数学与统计学院, 兰州 730070 Estimation of Probability Measure for 2-D Discrete Quantum Walk Based on Hadamard Operator HAN Qi, CHEN Zhihe, YIN Shide, LU ZiqiangSchool of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
摘要
图/表
参考文献
相关文章(1)
点击分布统计
下载分布统计
-->

全文: PDF(400 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)
摘要二维离散时间量子行走是直线上的量子行走的推广.通过演化算子的作用,行走者能够按照一定规律进行移动.在本文中,我们将Hadamard算子作为控制行走者方向的硬币算子,通过与控制行走者位置的条件转移算子结合,构成完整的演化算子.通过傅里叶变换,将行走者所处的时域空间转换成频域空间后,用傅里叶积分的平稳相位法得到了行走者在t步后处于位置(x,y)的振幅以及此时的概率估计.
服务
加入引用管理器
E-mail Alert
RSS
收稿日期: 2018-11-01
PACS:O211.9
O413.1
基金资助:国家自然科学基金地区科学基金资助项目(11861057).

引用本文:
韩琦, 陈芷禾, 殷世德, 陆自强. 基于Hadamard算子的二维离散量子行走的概率测度估计[J]. 应用数学学报, 2020, 43(1): 49-61. HAN Qi, CHEN Zhihe, YIN Shide, LU Ziqiang. Estimation of Probability Measure for 2-D Discrete Quantum Walk Based on Hadamard Operator. Acta Mathematicae Applicatae Sinica, 2020, 43(1): 49-61.
链接本文:
http://123.57.41.99/jweb_yysxxb/CN/ http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I1/49


[1] Nielsen M A, Chuang I L. Quantum computation and quantum information. Cambridge:Cambridge University Press, 2000
[2] Aharonov Y, Davidovich L, Zagury N. Quantum random walks. Physical Review A, 1993, 48(2):1687-1690
[3] Farhi E, Gutmann S. An Analog Analogue of a Digital Quantum Computation. Physical Review A, 1998, 57(4):2403-2406
[4] Venegas-Andraca S E. Quantum walk:a comprehensive review. Quantum Information Processing, 2012, 11:1015-1106
[5] Inui N, Konno N, Segawa E. One-dimensional three-state quantum walk. Physical Review E, 2005, 72:056112
[6] Machida T. Limit distribution for a time-inhomogeneous 2-state quantum walk. Journal of Computational and Theoretical Nanoscience, 2013, 10:1571-1578
[7] Endo T, Konno N. The stationary measure of a space-inhomogeneous quantum walk on the line. Yokohama Mathematical Journal, 2014, 60:33-47
[8] Wang C, Liu X, Wang W. The stationary measure of a space-inhomogeneous three-state quantum walk on the line. Quantum Information Processing, 2015, 14:867-880
[9] Kawai H, Komatsu T, Konno N. Stationary measures of three-state quantum walks on the one-dimensional lattice. Yokohama Mathematical Journal, 2017, 63:59-74
[10] Konno N. The uniform measure for discrete-time quantum walks in one dimension. Quantum Information Processing, 2014, 13:1103-1125
[11] 韩琦, 郭婷, 殷世德, 陈芷禾. 直线上空间非齐次三态量子游荡的平稳测度. 数学物理学报, 2019, 39(1):133-142(Han Q, Guo T, Yin S, Chen Z. The Stationary Measure of a Space-inhomogeneous Three-state Quantum Walk on the Line. Acta Mathematica Scientia, Series A, 2019, 39(1):133-142)
[12] Inui N, Konishi Y, Konno N. Localization of two-dimensional quantum walks. Physical Review A, 2004, 69:052323
[13] Watabe K, Kobayashi N, Katori M, Konno N. Limit distributions of two-dimensional quantum walks. Physical Review A, 2008, 77:062331
[14] Márquez-Martín I, Molfetta G, Pérez A. Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time. Physical Review A, 2017, 95:042112
[15] Ariano G, Mosco N, Perinotti P, Tosini A. Discrete Time Dirac Quantum Walk in 3+1 Dimensions. Entropy, 2016, 18:228
[16] Goyal S, Roux F, Forbes A, Konrad T. Implementation of multidimensional quantum walks using linear optics and classical light. Physical Review A, 2015, 92:040302
[17] Bender C, Orszag S. Advanced Mathematical Methods for Scientists and Engineers. New York:Springer-Verlag, 1978
[18] Nayak A, Vishwanath A. Quantum walk on the line. arXiv:quant-ph/0010117v1, 2000
[19] Brun T, Carteret H, Ambainis A. Quantum walks driven by many coins. Physical Review A, 2003, 67(5):1-17
[20] 韩琦, 殷世德, 陈芷禾. 量子计算中旋转算子的相关性质. 山东大学学报(理学版), 2019, 54(2):121-126(Han Q, Yin S, Chen Z. Properties of rotation operators in Quantum Computation. Journal of Shandong University (Science Edition), 2019, 54(2):121-126)

[1]王祜民. 产生可控宏观形状和位置分形山的谱综合方法[J]. 应用数学学报(英文版), 1997, 20(3): 0-0.



PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14710
相关话题/空间 概率 控制 统计 数学