1 |
Aharonov Y , Davidovich L , Zagury N . Quantum random walks. Physical Review A, 1993, 48 (2): 1687- 1690
doi: 10.1103/PhysRevA.48.1687
|
2 |
Shenvi N , Kempe J , Whaley K B . Quantum random-walk search algorithm. Physical Review A, 2003, 67 (5): 052307
doi: 10.1103/PhysRevA.67.052307
|
3 |
Ambainis A . Quantum walk algorithm for element distinctness. SIAM Journal on Computing, 2007, 37 (1): 210- 239
doi: 10.1137/S0097539705447311
|
4 |
Farhi E , Gutmann S . Quantum computation and decision trees. Physical Review A, 1998, 58 (2): 915- 928
doi: 10.1103/PhysRevA.58.915
|
5 |
Watrous J . Quantum simulations of classical random walks and undirected graph connectivity. Journal of Computer System Sciences, 2001, 62 (2): 376- 391
doi: 10.1006/jcss.2000.1732
|
6 |
Andraca V, Elías S. Quantum Walks for Computer Scientists. USA, Vermont: Morgan & Claypool, 2008
|
7 |
Venegasandraca S E . Quantum walks: a comprehensive review. Quantum Information Processing, 2012, 11 (5): 1015- 1106
|
8 |
Higuchi Y , Konno N , Sato I , et al. Periodicity of the discrete-time quantum walk on a finite graph. Interdisciplinary Information Sciences, 2017, 23, 75- 86
doi: 10.4036/iis.2017.A.10
|
9 |
Krovi H , Brun T A . Hitting time for quantum walks on the hypercube. Physical Review A, 2006, 73 (3): 501- 507
|
10 |
Konno N , Namiki T , Soshi T . Symmetry of distribution for the one-dimensional hadamard walk. Interdisciplinary Information Sciences, 2002, 10 (1): 11- 22
|
11 |
Konno N . A new type of limit theorems for the one-dimensional quantum random walk. Journal of The Mathematical Society of Japan, 2005, 57 (4): 1179- 1195
|
12 |
韩琦, 陈芷禾, 殷世德, 等. 基于hadamard算子的二维离散量子行走的概率测度估计. 应用数学学报, 2020, 43 (1): 49- 61
|
|
Han Q , Chen Z H , Yin S D , et al. Estimation of probability measure for 2-D discrete quantum walk based on hadamard operator. Acta Mathematicae Applicatae Sinica, 2020, 43 (1): 49- 61
|
13 |
Linden N , Sharam J . Inhomogeneous quantum walks. Physical Review A, 2009, 80 (5): 052327
doi: 10.1103/PhysRevA.80.052327
|
14 |
Shikano Y , Katsura H . Localization and fractality in inhomogeneous quantum walks with self-duality. Physical Review E, 2010, 82 (3): 031122
doi: 10.1103/PhysRevE.82.031122
|
15 |
Rousseva J , Kovchegov Y . On alternating quantum walks. Physica A: Statistical Mechanics and its Applications, 2017, 470, 309- 320
doi: 10.1016/j.physa.2016.11.138
|
16 |
Konno N , Luczak T , Segawa E , et al. Limit measures of inhomogeneous discrete-time quantum walks in one dimension. Quantum Information Processing, 2013, 12 (1): 33- 53
doi: 10.1007/s11128-011-0353-8
|
17 |
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): 135- 144
|
|
Han Q , Guo T , Yin S D , Chen Z H . The stationary measure of a space-inhomogeneous three-state quantum walk on the line. Acta Math Sci, 2019, 39 (1): 135- 144
|
18 |
Machida T . Limit distribution for a time-inhomogeneous 2-state quantum walk. Journal of Computational and Theoretical Nanoscience, 2013, 10 (7): 1571- 1578
doi: 10.1166/jctn.2013.3090
|
19 |
Konno N . A note on Itô's formula for discrete-time quantum walk. Journal of Computational and Theoretical Nanoscience, 2013, 10 (7): 1579- 1582
doi: 10.1166/jctn.2013.3091
|
20 |
Kang Y , Wang C . Itô formula for one-dimensional continuous-time quantum random walk. Physica A: Statistical Mechanics and its Applications, 2014, 414, 154- 162
doi: 10.1016/j.physa.2014.06.086
|
21 |
康元宝. 多维连续时间量子随机游动的Itô公式. 数学物理学报, 2016, 36A (4): 771- 782
|
|
Kang Y B . Itô's formula for multidimensional continuous-time quantum random walk. Acta Math Sci, 2016, 36A (4): 771- 782
|