In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, global and local walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a single step. After that we construct the corresponding continuous-time quantum walks and discuss its spectral structures. Then we define multi-dimensional continuous-time quantum walks by taking a marginal distribution respect to the global walker.
Akahori et al. (Fri,) studied this question.