Imagine a game where two players go back and forth making moves and at the end of a fixed number of moves the position is either a win or a loss for the first player. In this case, if both players play optimally (as well as possible), it is determined at the first move who wins or loses. To figure out who will be the winner, you need not look at all of the final positions but only at N^.753, where N is the numberof final positions. I will show that with a quantum computer the exponent can be reduced to 1/2. The technique involves quantum scattering theory.