Fig. 1: Bosonic mode with drive-activated nonlinearities.

a Idealized circuit schematic. In the undriven state (open black symbol), the resonator behaves as a harmonic oscillator, characterized by its inductance L and capacitance C. Manipulation of the quantum states is achieved by driving the resonator with flux ϕ_e(t), which activates the (otherwise off-resonant) intrinsic nonlinearities. Different pulse compositions engage (closed orange symbol) a variety of interactions denoted by the switchable, purely nonlinear junction element. b Schematic of our circuit realization consisting of a SNAIL-terminated λ/4 coplanar waveguide resonator, following and adopting figure from ref. ³⁰. c Schematic of the SNAIL element with n = 3 Josephson junctions with Josephson energy E_J and asymmetry factor β. d False-colored micrograph of the full device layout. The SNAIL-resonator is equipped with a charge and a flux drive line and dispersively coupled to a transmon qubit with a readout resonator. (inset) Close-up of the SNAIL element with three large Josephson junctions on one arm and a single junction on the other arm. e SNAIL-resonator frequency tuning vs static flux. The solid line is the fitted model taking into account the relevant microscopic parameters (see Methods). f Tuning of resonator nonlinearities vs static flux; fourth order (left axis) and third order (right axis). Effective Kerr K⁽¹⁾ and \({g}_{3}^{{{{{{{{\rm{ac}}}}}}}}}\) nonlinearities are predicted by the model fitted to the frequency tuning. The bosonic mode with drive-activated nonlinearities is realized and operated at the Kerr-free point marked with a star.