Even if the particles can only be in just two positions, the wavefunction for N particles requires 2 complex numbers, one for each total configuration of positions. This is exponentially many numbers in N, so simulating quantum mechanics on a computer requires exponential resources. Conversely, this suggests that it might be possible to find quantum systems of size N which physically compute the answers to problems which classically require 2 bits to solve. This is the aspiration behind quantum computing.