A quantum computer can determine who wins a game faster than a classical computer
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 best 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 N final positions but only at N^0.753. I will show that with a quantum computer the exponent can be reduced to 0.5. The technique involves quantum scattering theory and illustrates how ideas from physics can be used to design quantum algorithms that outperform even best possible classical algorithms.