Cellular automata for quantum systems

Cellular automata for modelling quantum systems are presented. The mass at each site is updated according to rules that depend on the masses of neighbouring sites. An essential feature of these local rules is that mass and probability are conserved. In the limit of small spatial and time steps it is shown that the equation defining one class of automata reduces to the Schrodinger equation and the equation defining another class of automata reduces to the Dirac equation. Advantages of these methods are discussed.