Discrete-time quantum walks as generators of multipartite entanglement

We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time step between the walker and the vertex qubits generates multipartite entanglement between the qubits. We demonstrate that for particular coin operators the system generates a highly entangled cluster state, of use in measurement based quantum computation.