  We present an efficient method for the characterization of two coupled
discrete quantum systems, one of which can be controlled and measured. For two
systems with transition frequencies $\omega_q$, $\omega_r$, and coupling
strength $g$ we show how to obtain estimates of $g$ and $\omega_r$ whose error
decreases exponentially in the number of measurement shots rather than as a
power law expected in simple approaches. Our algorithm can thereby identify $g$
and $\omega_r$ simultaneously with high precision in a few hundred measurement
shots. This is achieved by adapting measurement settings upon data as it is
collected. We also introduce a method to eliminate erroneous estimates with
small overhead. Our algorithm is robust against the presence of relaxation and
typical noise. Our results are applicable to many candidate technologies for
quantum computation, in particular, for the characterization of spurious
two-level systems in superconducting qubits or stripline resonators.
