Trigonometric Continuous-Variable Quantum Gates: Realization with Trapped Ions and Nonperturbative Wigner Negativity
Abstract
We experimentally realize trigonometric continuous-variable gates on a trapped-ion processor, for which a motional mode acquires a phase proportional to the cosine of its position quadrature, and, for the first time, implement the two-mode generalization, coupling two modes through a single nonlinear phase. Such gates provide an experimentally accessible, nonpolynomial primitive for periodic interactions acting on both compact and noncompact degrees of freedom, including rotor models, sine-Gordon-type systems, and lattice gauge theories. Scanning gate strength, spatial frequency, and circuit depth, we resolve via blue-sideband spectroscopy the parity selection rule that fingerprints the exact cosine evolution, and find that an open-system model incorporating residual thermal occupation and motional dephasing reproduces the data. We then derive the asymptotics of the Wigner negativity generated by these gates and find three scaling regimes. The negativity is beyond all algebraic orders in the gate strength while the negative regions sit in far phase-space tails, becomes linear once they reach the bulk, where it saturates a first-order bound we establish, and logarithmic at strong gate strength. These results expose a general mechanism, first identified here through the cosine gate, by which every finite-order perturbative estimate of a non-Gaussian resource can vanish even though the resource itself remains nonzero. Together, our results establish trigonometric gates as controllable, experimentally realizable building blocks for bosonic quantum simulation, expanding the class of nonlinear dynamics accessible to continuous-variable quantum processors.
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BibTeX
@misc{rainaldi2026trigonometric,
title = {{Trigonometric Continuous-Variable Quantum Gates: Realization with Trapped Ions and Nonperturbative Wigner Negativity}},
author = {Tommaso Rainaldi and Jake Montgomery and Christopher G. Yale and Brian K. McFarland and Melissa C. Revelle and Daniel Lobser and Edward C. Tortorici and Susan M. Clark and George Siopsis and Matt Grau and Felix Ringer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.14085},
eprint = {2607.14085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14085},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Trigonometric Continuous-Variable Quantum Gates: Realization with Trapped Ions and Nonperturbative Wigner Negativity
AU - Tommaso Rainaldi
AU - Jake Montgomery
AU - Christopher G. Yale
AU - Brian K. McFarland
AU - Melissa C. Revelle
AU - Daniel Lobser
AU - Edward C. Tortorici
AU - Susan M. Clark
AU - George Siopsis
AU - Matt Grau
AU - Felix Ringer
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2607.14085
UR - https://arxiv.org/abs/2607.14085
AB - We experimentally realize trigonometric continuous-variable gates on a trapped-ion processor, for which a motional mode acquires a phase proportional to the cosine of its position quadrature, and, for the first time, implement the two-mode generalization, coupling two modes through a single nonlinear phase. Such gates provide an experimentally accessible, nonpolynomial primitive for periodic interactions acting on both compact and noncompact degrees of freedom, including rotor models, sine-Gordon-type systems, and lattice gauge theories. Scanning gate strength, spatial frequency, and circuit depth, we resolve via blue-sideband spectroscopy the parity selection rule that fingerprints the exact cosine evolution, and find that an open-system model incorporating residual thermal occupation and motional dephasing reproduces the data. We then derive the asymptotics of the Wigner negativity generated by these gates and find three scaling regimes. The negativity is beyond all algebraic orders in the gate strength while the negative regions sit in far phase-space tails, becomes linear once they reach the bulk, where it saturates a first-order bound we establish, and logarithmic at strong gate strength. These results expose a general mechanism, first identified here through the cosine gate, by which every finite-order perturbative estimate of a non-Gaussian resource can vanish even though the resource itself remains nonzero. Together, our results establish trigonometric gates as controllable, experimentally realizable building blocks for bosonic quantum simulation, expanding the class of nonlinear dynamics accessible to continuous-variable quantum processors.
ER -