  We present an empirical strategy to determine the Hamiltonian dynamics of a
two-qubit system using only initialization and measurement in a single fixed
basis. Signal parameters are estimated from measurement data using Bayesian
methods from which the underlying Hamiltonian is reconstructed, up to three
unobservable phase factors. We extend the method to achieve full control
Hamiltonian tomography for controllable systems via a multi-step approach. The
technique is demonstrated and evaluated by analyzing data from simulated
experiments including projection noise.
