One-dimensional lazy quantum walks and occupancy rate
Li, Dan Gettrick, Michael Mc Zhang, Wei-Wei Zhang, Ke-Jia
Li, Dan
Gettrick, Michael Mc
Zhang, Wei-Wei
Zhang, Ke-Jia
Publication Date
2015-04-30
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Article
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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.
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IOP Publishing
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Attribution-NonCommercial-NoDerivs 3.0 Ireland