  We have designed a tunable nonlinear resonator terminated by a SNAIL
(Superconducting Nonlinear Asymmetric Inductive eLement). Such a device
possesses a sweet spot in which the external magnetic flux allows to suppress
the Kerr interaction. We have excited photons near this Kerr-free point and
characterized the device using a transmon qubit. The excitation spectrum of the
qubit allows to observe photon-number-dependent frequency shifts about nine
times larger than the qubit linewidth. Our study demonstrates a compact
integrated platform for continuous-variable quantum processing that combines
large couplings, considerable relaxation times and excellent control over the
photon mode structure in the microwave domain.
