Quantum search of many vertices on the joined complete graph

The quantum search on the graph is a very important topic. In this work, we develop a theoretic method on searching of single vertex on the graph Phys. Rev. Lett. 114 110503 (2015), and systematically study the search of many vertices on one low-connectivity graph, the joined complete graph. Our results reveal that, with the optimal jumping rate obtained from the theoretical method, we can find such target vertices at the time O\left(\sqrt N \right), where N is the number of total vertices. Therefore, the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.