  Superconducting qubits utilize the strong non-linearity of the Josephson
junctions. Control over the Josephson nonlinearity, either by a current bias or
by the magnetic flux, can be a valuable resource that brings tunability in the
hybrid system consisting of superconducting qubits. To enable such a control,
here we incorporate a fast-flux line for a frequency tunable transmon qubit in
3D cavity architecture. We investigate the flux-dependent dynamic range,
relaxation from unconfined states, and the bandwidth of the flux-line. Using
time-domain measurements, we probe transmon's relaxation from higher energy
levels after populating the cavity with $\approx 2.1\times10^4$ photons. For
the device used in the experiment, we find a resurgence time corresponding to
the recovery of coherence to be 4.8~$\mu$s. We use a fast-flux line to tune the
qubit frequency and demonstrate the swap of a single excitation between cavity
and qubit mode. By measuring the deviation in the transferred population from
the theoretical prediction, we estimate the bandwidth of the flux line to be
$\approx$~100~MHz, limited by the parasitic effect in the design. These results
suggest that the approach taken here to implement a fast-flux line in a 3D
cavity could be helpful for the hybrid devices based on the superconducting
qubit.
