  In this paper, we study the subset-sum problem by using a quantum heuristic
approach similar to the verification circuit of quantum Arthur-Merlin games.
Under described certain assumptions, we show that the exact solution of the
subset sum problem my be obtained in polynomial time and the exponential
speed-up over the classical algorithms may be possible. We give a numerical
example and discuss the complexity of the approach and its further application
to the knapsack problem.
