Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement

We present a solvable model of iterating cluster state protocols that lead to entanglement production, between contiguous blocks, of 1 ebit per iteration. This continues until the blocks are maximally entangled, at which stage an unravelling begins at the same rate until the blocks are unentangled. The model is a variant of the transverse-field Ising model and can be implemented with controlled-not and single-qubit gates. The interqubit entanglement as measured by the concurrence is shown to be zero for periodic chain realizations, while for open boundaries there are very specific instances at which these can develop. Thus we introduce a class of simply produced states with very large multipartite entanglement content of potential use in measurement-based quantum computing.