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Lecture notes in computer science

CTQW-GraphSAGE: Trainabel Continuous-Time Quantum Walk On Graph

Yangjie Xu, Hui Huang, Radu State

Published Jan 1, 2024• 3 citations
Publisher
DOI
10.1007/978-3-031-72344-5_6

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In this paper, we focus on discrete-time random walks (DTRWs) on the path graph with reflecting walls. Also we consider the corresponding continuous-time random walks (CTRWs), discrete-time quantum walks (DTQWs) and continuous-time quantum walks (CTQWs). We give formulas for the return probabilities of these four walks (DTRWs, CTRWs, DTQWs, CTQWs) at the boundary point of the path graph and discuss their relationships. Furthermore, by considering the Ehrenfest model, we derive the scaling limit theorems for the return probabilities of both the CTRW and the CTQW.