Haverford College, USA
Quantum cellular automata are of interest as models of physical phenomena and as a simple, yet universal, model of quantum computation. In the past decade attention has focused on the definition and classification of these models. Definitions of QCA that rely on local transition rules may violate the requirement of causality by allowing superluminal signalling. Characterizing all QCA that are local, unitary and causal remains an open problem. One sub-class of QCA are the quantum lattice gases (QLGA) which satisfy locality unitarity and causality and whose one-particle sectors are known to simulate both the Schroedinger and Dirac equations. We present the condition that characterizes when a QCA is a QLGA, give some examples of QCA that are not QLGA and some directions for the application of these models to quantum simulation problems.