Applications of quantum walk algorithms

Tomoki Yamagami, Etsuo Segawa, Takatomo Mihana +3 more

Quantum walks (QWs) have a property that classical random walks (RWs) do not possess-the coexistence of linear spreading and localization-and this property is utilized to implement various kinds of applications. This paper proposes RW- and QW-based algorithms for multi-armed-bandit (MAB) problems. We show that, under some settings, the QW-based model realizes higher performance than the corresponding RW-based one by associating the two operations that make MAB problems difficult-exploration and exploitation-with these two behaviors of QWs.

Renato Portugal

Miklós Sántha

Fei Yan, Liang Wen, Fangyan Dong

This chapter outlines the applications of quantum walks in network representation learning, comprising node similarity estimation algorithms and role embedding algorithms based on quantum walks. It further examines the applications of quantum walks in graph neural networks, highlighting quantum walk neural networks with feature-dependent coins and R-convolution kernels based on fast quantum walks.

Kendon

Fei Yan, Liang Wen, Fangyan Dong

This chapter explores the applications of discrete-time quantum walks in node mining, covering algorithms such as the quantum PageRank, the parameterized coin quantum walk, and the three-degree decay Grover walk. It also examines the applications of continuous-time quantum walks in this domain, including adaptations of the Google PageRank algorithm for open quantum systems, the quantum Jensen-Shannon divergence algorithm, and an information propagation model based on quantum walks.