  Single photons are a vital resource for optical quantum information
processing. Efficient and deterministic single photon sources do not yet exist,
however. To date, experimental demonstrations of quantum processing primitives
have been implemented using non-deterministic sources combined with heralding
and/or postselection. Unfortunately, even for eight photons, the data rates are
already so low as to make most experiments impracticable. It is well known that
quantum memories, capable of storing photons until they are needed, are a
potential solution to this `scaling catastrophe'. Here, we analyze in detail
the benefits of quantum memories for producing multiphoton states, showing how
the production rates can be enhanced by many orders of magnitude. We identify
the quantity $\eta B$ as the most important figure of merit in this connection,
where $\eta$ and $B$ are the efficiency and time-bandwidth product of the
memories, respectively.
