  The identification of parameters in the Hamiltonian that describes complex
many-body quantum systems is generally a very hard task. Recent attention has
focused on such problems of Hamiltonian tomography for networks constructed
with two-level systems. For open quantum systems, the fact that injected
signals are likely to decay before they accumulate sufficient information for
parameter estimation poses additional challenges. In this paper, we consider
use of the gateway approach to Hamiltonian tomography
\cite{Burgarth2009,Burgarth2009a} to complex quantum systems with a limited set
of state preparation and measurement probes. We classify graph properties of
networks for which the Hamiltonian may be estimated under equivalent conditions
on state preparation and measurement. We then examine the extent to which the
gateway approach may be applied to estimation of Hamiltonian parameters for
network graphs with non-trivial topologies mimicking biomolecular systems.
