Reversible cellular automata, systems that resemble Conway's Game of Life in that their state changes are determined by a simple rule, but in which there's also another rule for running them backwards.

The part about quantum CA is the shortest, partly because it's the part I understand the least about myself, but I think it's also the most closely related to a lot of current research in mainstream theoretical computer science. For more in that direction, see quantum cellular automata (an article I can't take any credit for, because my only edit to it was over a minor point of grammar).