Quantum search by quantum cellular automata

Quantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The drawing feature of QCA is that evolution is described by global operations that can be decomposed into periodic components, instead of operations on individual data registers. While it has been demonstrated that QCA can be constructed that are equivalent to the circuit model, these constructions do not lend themselves easily to a physical system. However it is possible to create QCA that, while they do not correspond to a fully programmable quantum computer, can nevertheless implement quantum algorithms. By drawing on the connection between quantum walks and QCA, I demonstrate that it is possible to implement Grover's algorithm on a system that may be readily translated to a physical system.