  The purpose of this paper is to present simple and general algebraic methods
for describing series connections in quantum networks. These methods build on
and generalize existing methods for series (or cascade) connections by allowing
for more general interfaces, and by introducing an efficient algebraic tool,
the series product. We also introduce another product, which we call the
concatenation product, that is useful for assembling and representing systems
without necessarily having connections. We show how the concatenation and
series products can be used to describe feedforward and feedback networks. A
selection of examples from the quantum control literature are analyzed to
illustrate the utility of our network modeling methodology.
