Nonlinear phase gates are essential to achieve the universality of continuous-variable quantum processing and its applications. We present a deterministic protocol for generating nonlinear phase gates in trapped ion systems using simultaneous two-tone sideband drives beyond the Lamb-Dicke regime. Our approach harnesses higher-order interaction terms typically neglected or suppressed to construct nonlinear phase gates. This methodology enables high-fidelity gate engineering with a near three-fold reduction in control pulses compared to state-of-the-art theoretical proposals.
@article{arxiv.2602.15619,
title = {Nonlinear Phase Gates Beyond the Lamb-Dicke Regime},
author = {Akram Kasri and Kimin Park and Radim Filip},
journal= {arXiv preprint arXiv:2602.15619},
year = {2026}
}