Abstract
In this study, we combine the quantum search algorithm and the quantum counting algorithm to perform a quantum optimization algorithm. We propose a method which applies the quantum counting algorithm to obtain the order of an element in a N-element set. Observing that the order information enable us to recognize the optimization solution, we employ the quantum search algorithm with order estimation algorithm to solve the optimization problem. Since the order estimation suffers a non-ideal effect that will affect the performance of quantum optimization algorithm, a performance analysis of quantum optimization algorithm is also provided. Finally, a numerical example is given to illustrate the proposed quantum optimization algorithm.