# Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

- Authors
- Type
- Published Article
- Publication Date
- Apr 14, 2009
- Submission Date
- Apr 14, 2009
- Identifiers
- DOI: 10.1088/0253-6102/51/6/08
- Source
- arXiv
- License
- Yellow
- External links

## Abstract

In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs (complete cycle, complete $K_n$, charter and $n$-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as $t\longrightarrow \infty$ but for quantum state is not always satisfy.