It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
