Quantum search of many vertices on the joined complete graph

Abstract

The quantum search on the graph is a very important topic. In this work, we develop the theoretic method about the searching 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 theoretic method, we can find such target vertices at the time O√N , where N is the number of total vertices. Therefore, the search of many vertices on the joined complete graph possessing quantum advantage has achieved.