Quaternionic quantum walks

被引：0
作者：
Konno N. [1 ]
机构：
[1] Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama
来源：
Quantum Studies: Mathematics and Foundations | 2015年 / 2卷 / 1期
基金：
日本学术振兴会;
关键词：
Quantum walks; Quaternionic quantum walk; Stationary measure;
D O I：
10.1007/s40509-015-0035-9
中图分类号：
学科分类号：
摘要：
The discrete-time quantum walk (QW) has been extensively and intensively investigated in the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is quaternion. We call this model quaternionic quantum walk (QQW) and present some properties. This paper is the first step for the study on QQWs. © 2015, Chapman University.
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收藏
页码：63 / 76
页数：13
相关论文
共 14 条
  • [1] Kempe J., Quantum random walks - an introductory overview, Contemporary Physics, 44, pp. 307-327, (2003)
  • [2] Kendon V., Decoherence in quantum walks - a review, Math. Struct. in Comp. Sci., 17, pp. 1169-1220, (2007)
  • [3] Venegas-Andraca S.E., Quantum Walks for Computer Scientists, (2008)
  • [4] Venegas-Andraca S.E., Quantum walks: a comprehensive review, Quantum Inf. Process., 11, pp. 1015-1106, (2012)
  • [5] Konno N., Quantum Walks, Lecture Notes in Mathematics, 1954, pp. 309-452, (2008)
  • [6] Cantero M.J., Grunbaum F.A., Moral L., Velazquez L., The CGMV method for quantum walks, Quantum Inf. Process., 11, pp. 1149-1192, (2012)
  • [7] Manouchehri K., Wang J., Physical Implementation of Quantum Walks, (2013)
  • [8] Portugal R., Quantum Walks and Search Algorithms, (2013)
  • [9] Zhang F., Quaternions and matrices of quaternions, Linear Algebra Appl., 251, pp. 21-57, (1997)
  • [10] Ambainis A., Bach E., Nayak A., Vishwanath A., Watrous J., One-dimensional quantum walks, Proceedings of the 33Rd Annual ACM Symposium on Theory of Computing, pp. 37-49, (2001)
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