One-dimensional lazy quantum walks and occupancy rate

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 transfor...

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Bibliographic Details
Published inChinese physics B Vol. 24; no. 5; pp. 223 - 230
Main Author 李丹 Michael Mc Gettrick 张伟伟 张可佳
Format Journal Article
LanguageEnglish
Published 01.05.2015
Subjects
Coins
DFT
Fourier transforms
Intervals
Operators
Position measurement
Probability distribution
一维
占用
概率分布
田纳西州
离散傅里叶变换
运营商
量子
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Summary: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.
Bibliography: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.
11-5639/O4
lazy quantum walk, occupancy number, occupancy rate
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/24/5/050305