  Implementing spatially-encoded universal linear multiport interferometers on
integrated photonic platforms with high controllability becomes increasingly
difficult as the number of modes increases. In this work, we consider an
architecture in which temporally-encoded modes are injected into a chain of
reconfigurable beamsplitters and delay loops, and provide a detailed loss
analysis for this and other comparable architectures. This analysis also yields
a straightforward and explicit description of the control sequence needed for
implementing an arbitrary temporally-encoded transformation. We consider
possible physical implementations of these architectures and compare their
performance. We conclude that implementing a chain of reconfigurable
beamsplitters and delay loops on an integrated lithum niobate platform could
outperform comparable architectures in the near future.
