**A spatial search with quantum cellular automata**

Quantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The salient feature of QCA is
that evolution is described by global operations that can be decomposed into local 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 implementation. However it is possible to create QCA that, while not corresponding to a fully programmable quantum computer, can nevertheless perform useful 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 spin system that may be more readily translated to a physical implementation.