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Lecture notes in computer science

Application of Continuous Time Quantum Walks to Image Segmentation

Michał Krok, Katarzyna Rycerz, Marian Bubak

Published Jan 1, 2019• 4 citations
Publisher
DOI
10.1007/978-3-030-22741-8_2

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We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.
To further improve the performance of image retrieval, we propose an image two-classification algorithm based on continuous-time quantum walk (CTQW) model. First, a weighted undirected complete graph is constructed based on a new weighted edge method, that is, the images in the image set are used to represent the nodes on the weighted complete graph, and every two images are connected to represent the edge on the weighted complete image, the weighted value of which represents the similarity between adjacent images. Then, the CTQW is executed to realize the image two-classification based on the quantum walk model of the weighted complete graph, that is, the CTQW is performed from two types of unrelated images, and the two-classification of images is realized that the relevant and unrelated labels are assigned to each image according to the obtained probability distribution two-classification. Finally, the experimental results show that the proposed two-classification algorithm based on CTQW has a good classification effect from the visual effect, and the evaluation indexes of image classification, such as the average precision rate, the recall rate, and the accuracy rate, are all higher than 0.85. In addition, the proposed image two-classification algorithm based on CTQW can be extended to image multiclassification if the quantum walk is performed using multiple irrelevant pictures as the starting point. Similarly, the extended image multiclassification method also has a better classification effect through the experiments and the evaluation indexes of image classification.
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.