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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61272057 and 61170270)the Higher Education Young Elite Teacher Project of Beijing,China(Grant No.YETP0475 and YETP0477)+1 种基金the BUPT Excellent Ph.D.Students Foundation(Grant Nos.CX201325 and CX201326)the China Scholarship Council(Grant No.201306470046)
文摘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.
