  An on-demand single-photon source is a key requirement for scaling many
optical quantum technologies. A promising approach to realize an on-demand
single-photon source is to multiplex an array of heralded single-photon sources
using an active optical switching network. However, the performance of
multiplexed sources is degraded by photon loss in the optical components and
the non-unit detection efficiency of the heralding detectors. We provide a
theoretical description of a general multiplexed single-photon source with
lossy components and derive expressions for the output probabilities of
single-photon emission and multi-photon contamination. We apply these
expressions to three specific multiplexing source architectures and consider
their tradeoffs in design and performance. To assess the effect of lossy
components on near- and long-term experimental goals, we simulate the
multiplexed sources when used for many-photon state generation under various
amounts of component loss. We find that with a multiplexed source composed of
switches with ~0.2-0.4 dB loss and high efficiency number-resolving detectors,
a single-photon source capable of efficiently producing 20-40 photon states
with low multi-photon contamination is possible, offering the possibility of
unlocking new classes of experiments and technologies.
