Quantum Search Algorithm for Exceptional Vertexes in Regular Graphs and its Circuit Implementation

There are some interesting properties in quantum mechanics, such as quantum superposition and entanglement. We can use these features to solve some specific problems. Quantum computer has more advantages than classical computer in many problems. In this paper, we are interested in regular graph. A special case of graph structure destroyed is given. We present a search algorithm to find exceptional vertexes in the graph in this case. The algorithm uses the trick of amplitude amplification in quantum search algorithm. In the corresponding classical algorithm, the adjacency matrix may be used to store the information of vertex and edge of graph. It takes one time for the best and N times for the worst to find the target. Which means that N /2 times on average need to be conducted. In our quantum algorithm, nodes and vertexes are stored in quantum states, using quantum search to design algorithm. The search process can be accelerated in our quantum algorithm.