中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50305-050305.doi: 10.1088/1674-1056/24/5/050305
One-dimensional lazy quantum walks and occupancy rate
李丹a b, Michael Mc Gettrickb, 张伟伟a, 张可佳a
- a State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
b The De Brun Centre for Computational Algebra, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway
One-dimensional lazy quantum walks and occupancy rate
Li Dan (李丹)a b, Michael Mc Gettrickb, Zhang Wei-Wei (张伟伟)a, Zhang Ke-Jia (张可佳)a
- a State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
b The De Brun Centre for Computational Algebra, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway
摘要：
In this paper, we discuss the properties of lazy quantum walks. Our analysis shows that the lazy quantum walks have O(tn) order of the n-th moment of the corresponding probability distribution, which is the same as that for normal quantum walks. The lazy quantum walk with a discrete Fourier transform (DFT) coin operator has a similar probability distribution concentrated interval to that of the normal Hadamard quantum walk. Most importantly, we introduce the concepts of occupancy number and occupancy rate to measure the extent to which the walk has a (relatively) high probability at every position in its range. We conclude that the lazy quantum walks have a higher occupancy rate than other walks such as normal quantum walks, classical walks, and lazy classical walks.
中图分类号: (Quantum algorithms, protocols, and simulations)
- 03.67.Ac