Publication

One-dimensional lazy quantum walks and occupancy rate

Li, Dan
Gettrick, Michael Mc
Zhang, Wei-Wei
Zhang, Ke-Jia
Repository DOI
Publication Date
2015-04-30
Type
Article
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Citation
Li, Dan; Gettrick, Michael Mc; Zhang, Wei-Wei; Zhang, Ke-Jia (2015). One-dimensional lazy quantum walks and occupancy rate. Chinese Physics B 24 (5),
Abstract
In this paper, we discuss the properties of lazy quantum walks. Our analysis shows that the lazy quantum walks have O(t(n)) 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.
Funder
Publisher
IOP Publishing
Publisher DOI
10.1088/1674-1056/24/5/050305
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland