Universal control of a bosonic mode in a planar superconducting nonlinear resonator via native interactions

Bosonic modes, thanks to their large Hilbert space, offer a hardware-efficient alternative for quantum information processing. However, to operate linear bosonic modes, some nonlinearity is still required, which is typically realized by an ancilla qubit. We present a bosonic mode consisting of a superconducting nonlinear asymmetric inductive element (SNAIL)-terminated planar resonator, which is not controlled by an ancilla qubit but via the nonlinearities in the SNAIL element. The Kerr nonlinearity is canceled by tuning the flux through the SNAIL to realize a close to linear mode when the system is idling. The off-resonant strong third order nonlinearity can be activated by applying a flux pulse at three times the frequency of the bosonic mode. Hence, the resulting tri-squeezing interaction promotes the more easily accessible Gaussian interactions to a universal gate set. By combining these interactions, we experimentally demonstrate Wigner-negative states such as the cubic phase state. Furthermore, the operation of these native squeezing and tri-squeezing interactions can be combined with standard ancilla qubit control and thereby boost the control capabilities.