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Lecture notes in computer science

Node Centrality for Continuous-Time Quantum Walks

Luca Rossi, Andrea Torsello A, Edwin R. Hancock

Published Jan 1, 2014• 15 citations
Publisher
DOI
10.1007/978-3-662-44415-3_11

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Xin Wang, Yi Zhang, Kai Lü +2 more

The source detection problem is the reverse of information diffusion. It is identifying information sources of the diffusion process. However, most existing algorithms have limited performance due to various reasons, therefore the application is limited. We propose an approach, namely Quantum Walk based Source Detection (QWSD), to identify the source nodes based on the continuous-time quantum walk (CTQW). The continuous-time quantum walk can be utilized to simulate the diffusion process. Therefore, we utilize the reversed quantum walk to reverse the diffusion, thus revealing the probability for a node to be a source node. It is the first time that the continuous-time quantum walk is applied to the source detection problem. Extensive experiments demonstrate that our algorithm outperforms other source detection algorithms on both synthetic datasets and real-world datasets.

International Conference on Systems and Informatics (ICSAI)•Nov 1, 2018•1 citation
In this paper, we consider continuous-time quantum walks (CTQWs) on a one-dimensional ring lattice of N nodes in which every node is connected to its 2m nearest neighbors ( m on either side). In the framework of the Bloch function ansatz, we calculate the space-time transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walks (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter m for both CTQWs and CTRWs. For fixed parameter m , the transport of CTRWs gets slower with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long-time limit, depending on the network size N and connectivity parameter m , the limiting probability distributions of CTQWs show various patterns. When the network size N is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter m .
We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.
The source detection problem is the reverse of information diffusion. It is identifying information sources of the diffusion process. However, most existing algorithms have limited performance due to various reasons, therefore the application is limited. We propose an approach, namely Quantum Walk based Source Detection (QWSD), to identify the source nodes based on the continuous-time quantum walk (CTQW). The continuous-time quantum walk can be utilized to simulate the diffusion process. Therefore, we utilize the reversed quantum walk to reverse the diffusion, thus revealing the probability for a node to be a source node. It is the first time that the continuous-time quantum walk is applied to the source detection problem. Extensive experiments demonstrate that our algorithm outperforms other source detection algorithms on both synthetic datasets and real-world datasets.