I will begin by reviewing a discrete version of scattering theory and its use in analyzing certain continuous time quantum walks on graphs. I will then describe how this was used to establish that a quantum walk with multiple (interacting) walkers is capable of universal quantum computation. The idea is to encode each qubit of a given quantum circuit in the location of a quantum walker on a graph, and to perform one- and two-qubit gates via one- and two-particle scattering processes.

This talk is based on joint work with Andrew Childs and Zak Webb.