  A typical goal of a quantum simulation is to find the energy levels and
eigenstates of a given Hamiltonian. This can be realized by adiabatically
varying the system control parameters to steer an initial eigenstate into the
eigenstate of the target Hamiltonian. Such an adiabatic quantum simulation is
demonstrated by directly implementing a controllable and smoothly varying
Hamiltonian in the rotating frame of two superconducting qubits, including
longitudinal and transverse fields and iSWAP-type two-qubit interactions. The
evolution of each eigenstate is tracked using time-resolved state tomography.
The energy gaps between instantaneous eigenstates are chosen such that
depending on the energy transition rate either diabatic or adiabatic passages
are observed in the measured energies and correlators. Errors in the obtained
energy values induced by finite $T_1$ and $T_2$ times of the qubits are
mitigated by extrapolation to short protocol times.
