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Quantum simulations provide means to probe challenging problems withincontrollable quantum systems. However, implementing or simulating deep-strongnonlinear couplings between bosonic oscillators on physical platforms remains achallenge. We present a deterministic simulation technique that efficiently andaccurately models nonlinear bosonic dynamics. This technique alternates betweentunable Rabi and SNAP gates, both of which are available on experimentalplatforms such as trapped ions and superconducting circuits. Our proposedsimulation method facilitates high-fidelity modeling of phenomena that emergefrom higher-order bosonic interactions, with an exponential reduction inresource usage compared to other techniques. We demonstrate the potential ofour technique by accurately reproducing key phenomena and other distinctivecharacteristics of ideal nonlinear optomechanical systems. Our technique servesas a valuable tool for simulating complex quantum interactions, simultaneouslypaving the way for new capabilities in quantum computing through the use ofhybrid qubit-oscillator systems.

Efficient quantum simulation of nonlinear interactions using SNAP and Rabi gates