QWalkVec: Node Embedding by Quantum Walk

TL;DR

QWalkVec introduces a quantum walk-based node embedding method that balances depth-first and breadth-first search processes, improving node classification performance on small datasets.

Contribution

It formulates novel coin operators for quantum walks, enabling better integration of DFS and BFS in node embedding, which was not addressed in prior work.

Findings

QWalkVec outperforms existing methods on several small datasets.

Quantum walk with tailored coin operators enhances node embedding quality.

Balanced DFS and BFS processes improve node classification accuracy.

Abstract

In this paper, we propose QWalkVec, a quantum walk-based node embedding method. A quantum walk is a quantum version of a random walk that demonstrates a faster propagation than a random walk on a graph. We focus on the fact that the effect of the depth-first search process is dominant when a quantum walk with a superposition state is applied to graphs. Simply using a quantum walk with its superposition state leads to insufficient performance since balancing the depth-first and breadth-first search processes is essential in node classification tasks. To overcome this disadvantage, we formulate novel coin operators that determine the movement of a quantum walker to its neighboring nodes. They enable QWalkVec to integrate the depth-first search and breadth-first search processes by prioritizing node sampling. We evaluate the effectiveness of QWalkVec in node classification tasks conducted on four small-sized real datasets. As a result, we demonstrate that the performance of QWalkVec is superior to that of the existing methods on several datasets. Our code will be available at \url{https://github.com/ReiSato18/QWalkVec}.