  In order to expand the astrophysical reach of gravitational wave detectors,
several interferometer topologies have been proposed to evade the thermodynamic
and quantum mechanical limits in future detectors. In this work, we make a
systematic comparison among them by considering their sensitivities and
complexities. We numerically optimize their sensitivities by introducing a cost
function that tries to maximize the broadband improvement over the sensitivity
of current detectors. We find that frequency-dependent squeezed-light injection
with a hundred-meter scale filter cavity yields a good broadband sensitivity,
with low complexity, and good robustness against optical loss. This study gives
us a guideline for the near-term experimental research programs in enhancing
the performance of future gravitational-wave detectors.
