Impact of global and local interaction on quantum spatial search on chimera graph

Abstract

In the paper, we investigated the influence of local and global interaction on the efficiency of continuous-time quantum spatial search. To do so, we analyzed numerically chimera graph, which is defined as 2D grid with each node replaced by complete bipartite graph. Our investigation provides a numerical evidence that with a large number of local interactions the quantum spatial search is optimal, contrary to the case with limited number of such interactions. The result suggests that relatively large number of local interactions with the marked vertex is necessary for optimal search, which in turn would imply that poorly connected vertices are hard to be found.