One reason why one might expect quantum computers to be more powerful than classical computers has to do with the fact that the probability of a given output is the absolute square of the sum of the amplitudes associated with each of the “computational paths” (sequences of computational states, which are themselves strings of ones and zeros), and these amplitudes are complex numbers.

One reason why one might expect quantum computers to be more powerful than classical computers has to do with the fact that the probability of a given output is the absolute square of the sum of the amplitudes associated with each of the “computational paths” (sequences of computational states, which are themselves strings of ones and zeros), and these amplitudes are complex numbers. This

http://complementaryslackness.wordpress.com/2009/08/05/path-integrals-and-quantum-computation/