Nonlinearity is an important element to realize complex quantum states or dynamics

Nonlinearity is an important element to realize complex quantum states or dynamics. Due to their accessibility, magnitude, and controllability, lower order nonlinearities are often utilized to prepare quantum states in quantum optical and solid-state architectures. However, mitigating the effects of decoherence and noise is challenging for executing tasks at the quantum scale. Here, we show that higher-order Kerr nonlinearities can be a powerful resource to enhance the fidelity of quantum states of a single bosonic mode. The key aspect is that higher-order nonlinearities allow for a faster preparation of states, thus shortening the time for decoherence to accumulate by orders of magnitude. We find that the nonlinear system is fully controllable, and thus in principle every state in the Hilbert space of the bosonic mode is reachable. As an example, we focus here on the superposition of coherent states. We show that strong higher-order nonlinearities can be found in an ensemble of Rydberg atoms, a platform suitable for implementing our state preparation protocol.