Random Walks on Deterministic Weighted Scale-Free Small-World Networks with a Perfect Trap

Jing, Xing-Li; Ling, Xiang; Hu, Mao-Bin; Shi, Qing

doi:10.1088/0256-307x/31/8/080504

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…It is fair to say CW becomes one of the most significant models in the theories of probability and statistics. [1][2][3][4][5][6][7][8][9][10][11] Its most popular version is that a walker moves on a line in a discrete manner and that the walker flips a coin to decide the direction of the next step. In detail, if the result is the head, the walker will move its position (initially at x = 0) to the position x = 1; if the result is the tail, the walker will move its position to the position x = −1.…”

Section: Introductionmentioning

confidence: 99%

Quantum walk under coherence non-generating channels*

Chen¹,

Hu²

2021

Chinese Phys. B

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We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions, generalized classical random walk with memory can degrade into classical random walk and classical random walk with memory. Based on its various spreading speed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring the quantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walks with memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walk and classical random walk with memory by coherence non-generating channels. Also, we find that for another class of coherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of the coin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore the relationship between coherence and quantum walk.

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Section: Introductionmentioning

confidence: 99%

Quantum walk under coherence non-generating channels*

Chen¹,

Hu²

2021

Chinese Phys. B

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“…In contrast to stochastic models, deterministic models help us to understand the construction rules embedded in randomized structures and allow for rigorous computation of many graph features, e.g., clustering coefficients, diameter, betweenness, path length, and mean first-passage time. [10][11][12][13][14][15][16][17][18][19][20] The primary deterministic scale-free model was proposed by Barabasi et al [19] However, this model lacks the small-world effect that exists in most real networks, i.e., its clustering coefficient is too small while the average length path remains relatively large. To remedy this weakness, Chen et al [20] constructed a pseudo tree-like (PTL) deterministic model having both the small-world and the scale-free characteristics.…”

Section: Introductionmentioning

confidence: 99%

Stability of weighted spectral distribution in a pseudo tree-like network model

Nie

Huang

et al. 2016

Chinese Phys. B

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The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution (i.e., a spectral graph feature) as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.

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