Quantum Algorithm for Finding a Maximum Clique in an Undirected Graph

The maximum clique in an undirected graph is the largest subset of a set of graph's vertices where each pair of elements in the subset is connected. The problem of finding maximum clique in an arbitrary graph is NP-Hard problem with many applications in practice and it is very important to try to develop a new and a potentially faster algorithms that solve it. In this paper I would like to propose a new algorithm for quantum computers that finds the maximum clique in an arbitrary undirected graph which is based on a version of Grover's quantum algorithm for finding an element in an unsorted list in which there can be an unknown number of solutions. A new algorithm has 0 (vertical bar V vertical bar root 2(vertical bar v vertical bar)) worst case time complexity and 0 (root 2(vertical bar v vertical bar)) best case time complexity. Algorithm's space complexity for each case is 0 (vertical bar V vertical bar).