Speed-up and suppression effect of side chain in quantum searching on a graph

Searching efficiency, which biologists and roboticists are ever concerned about, has become important in physics and information science nowadays. In classical probability-based searching problems, as stigmergy, the increase in graph complexity will decrease the searching efficiency. Here we study the searching efficiency based on the first-passage probability and find a counterintuitive phenomenon in quantum walk on a graph with floating vertices. Connecting one vertex in the floating layer to that in the base layer will speed up the searching rapidity, but such a speed-up effect will be suppressed at once if one more vertex is connected to the already connected vertex in the floating layer. This is a counterintuitive phenomenon in comparison to its classical counterpart, where additional vertices at the side chain will retard the searching rapidity. We also propose an ancillary model that bridges the measurement of the probability and the first-passage probability, which is expected to provide new ideas for quantum simulation by means of qubit chips.