  Quantum simulation is one of the most promising near term applications of
quantum computing. Especially, systems with a large Hilbert space are hard to
solve for classical computers and thus ideal targets for a simulation with
quantum hardware. In this work, we study experimentally the transient dynamics
in the multistate Landau-Zener model as a function of the Landau-Zener
velocity. The underlying Hamiltonian is emulated by superconducting quantum
circuit, where a tunable transmon qubit is coupled to a bosonic mode ensemble
comprising four lumped element microwave resonators. We investigate the model
for different initial states: Due to our circuit design, we are not limited to
merely exciting the qubit, but can also pump the harmonic modes via a dedicated
drive line. Here, the nature of the transient dynamics depends on the average
photon number in the excited resonator. The greater effective coupling strength
between qubit and higher Fock states results in a quasi-adiabatic transition,
where coherent quantum oscillations are suppressed without the introduction of
additional loss channels. Our experiments pave the way for more complex
simulations with qubits coupled to an engineered bosonic mode spectrum.
