  We consider the deterministic generation of entangled multi-qubit states by
the sequential coupling of an ancillary system to initially uncorrelated
qubits. We characterize all achievable states in terms of classes of matrix
product states and give a recipe for the generation on demand of any
multi-qubit state. The proposed methods are suitable for any sequential
generation-scheme, though we focus on streams of single photon time-bin qubits
emitted by an atom coupled to an optical cavity. We show, in particular, how to
generate familiar quantum information states such as W, GHZ, and cluster
states, within such a framework.
