Continuous-Time Quantum Walk on Integer Lattices and Homogeneous Trees

被引：0
|
作者：
Vladislav Kargin
机构：
[1] Stanford University,Department of Mathematics
来源：
Journal of Statistical Physics | 2010年 / 140卷
关键词：
Quantum walk; Tree; Limit theorem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with the continuous-time quantum walk on ℤ, ℤd, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on ℤ, and for nearest-neighbor walks on ℤd and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.
引用
收藏
页码：393 / 408
页数：15
相关论文
共 50 条
  • [41] Spatial search by continuous-time quantum walk with multiple marked vertices
    Thomas G. Wong
    Quantum Information Processing, 2016, 15 : 1411 - 1443
  • [42] Investigation of continuous-time quantum walk on root lattice An and honeycomb lattice
    Jafarizadeh, M. A.
    Sufiani, R.
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 381 : 116 - 142
  • [43] Continuous-time quantum walks on planar lattices and the role of the magnetic field
    Razzoli, Luca
    Paris, Matteo G. A.
    Bordone, Paolo
    PHYSICAL REVIEW A, 2020, 101 (03)
  • [44] Ergodic Theorems for Continuous-Time Quantum Walks on Crystal Lattices and the Torus
    de Monvel, Anne Boutet
    Sabri, Mostafa
    ANNALES HENRI POINCARE, 2024,
  • [45] Quantum transport on small-world networks:: A continuous-time quantum walk approach
    Muelken, Oliver
    Pernice, Volker
    Blumen, Alexander
    PHYSICAL REVIEW E, 2007, 76 (05):
  • [46] Simulating continuous-time Hamiltonian dynamics by way of a discrete-time quantum walk
    Schmitz, A. T.
    Schwalm, W. A.
    PHYSICS LETTERS A, 2016, 380 (11-12) : 1125 - 1134
  • [47] An enhanced classical approach to graph isomorphism using continuous-time quantum walk
    Qiang, Xiaogang
    Yang, Xuejun
    Wu, Junjie
    Zhu, Xuan
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (04)
  • [48] Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
    Salimi, S.
    Jafarizadeh, M. A.
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 51 (06) : 1003 - 1009
  • [49] The continuous-time magnetic quantum walk and its probability invariance on a class of graphs
    Cao, Jiaqi
    Wang, Caishi
    Zhao, Jijun
    Yang, Zheng
    INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2024, 22 (08)
  • [50] Ito formula for one-dimensional continuous-time quantum random walk
    Kang, Yuanbao
    Wang, Caishi
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2014, 414 : 154 - 162
12345