In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice gas automata--and show how to implement them efficiently on standard quantum computers.

13 pages, plain TeX, 10 PostScript figures included with epsf.tex; for related work see http://math.ucsd.edu/~dmeyer/research.html