  Quantum simulators, in which well controlled quantum systems are used to
reproduce the dynamics of less understood ones, have the potential to explore
physics that is inaccessible to modeling with classical computers. However,
checking the results of such simulations will also become classically
intractable as system sizes increase. In this work, we introduce and implement
a coherent imaging spectroscopic technique to validate a quantum simulation,
much as magnetic resonance imaging exposes structure in condensed matter. We
use this method to determine the energy levels and interaction strengths of a
fully-connected quantum many-body system. Additionally, we directly measure the
size of the critical energy gap near a quantum phase transition. We expect this
general technique to become an important verification tool for quantum
simulators once experiments advance beyond proof-of-principle demonstrations
and exceed the resources of conventional computers.
