  Quantum cellular automata consist in arrays of identical finite-dimensional
quantum systems, evolving in discrete-time steps by iterating a unitary
operator G. Moreover the global evolution G is required to be causal (it
propagates information at a bounded speed) and translation-invariant (it acts
everywhere the same). Quantum cellular automata provide a model/architecture
for distributed quantum computation. More generally, they encompass most of
discrete-space discrete-time quantum theory. We give an overview of their
theory, with particular focus on structure results; computability and
universality results; and quantum simulation results.
