  Adapting techniques from the field of information geometry, we show that open
quantum system models of Frenkel exciton transport, a prevalent process in
photosynthetic networks, belong to a class of mathematical models known as
'sloppy'. Performing a Fisher-information-based multi-parameter sensitivity
analysis to investigate the full dynamical evolution of the system and reveal
this sloppiness, we establish which features of a transport network lie at the
heart of efficient performance. We find that fine tuning the excitation
energies in the network is generally far more important than optimizing the
network geometry and that these conclusions hold for different measures of
efficiency and when model parameters are subject to disorder within parameter
regimes typical of molecular complexes involved in photosynthesis. Our approach
and insights are equally applicable to other physical implementations of
quantum transport.
