Classical cellular automata are a very versatile tool for simulating complex distributed systems. Their quantum analogue has come into focus more recently, because this architecture is especially suited to allow quantum computation by a lattice system of many equal constituents, which are, perhaps, not easily addressed individually. Such systems are now getting realized, so there is a direct need to assess the potential of distributed lattice systems.

In contrast to the classical case, however, the general form of a quantum cellular automaton is not so easy to describe, especially when both reversible and irreversible evolutions are admitted. In this project quantum cellular automata will be studied both in a bottom-up approach of investigating detailed properties of simple automata such as quantum walks, and a top-down approach, in which the structure of general automata is analyzed from first principles.