Efficient bosonic nonlinear phase gates

Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.