  As they can travel long distances, free space optical quantum states are good
candidates for carrying information in quantum information technology
protocols. These states, however, are often complex to produce and require
protocols whose success probability drops quickly with an increase of the mean
photon number. Here we propose a new protocol for the generation and growth of
arbitrary states, based on one by one coherent adjunctions of the simple state
superposition $\alpha | 0 > +\beta | 1 >$. Due to the nature of the protocol,
that allows for the use of quantum memories, it can outperform existing
protocols.
