Approximate cubic phase states in a trapped ion
Abstract
Universal quantum computation with continuous variables cannot be attained solely with a set of Gaussian operations, it requires the addition of a non-Gaussian element, at least of third order in the quadrature operators, such as the cubic phase state. In this work, we present a method to generate a quantum state in the vibrational mode of a trapped ion that exhibits characteristics compatible with the cubic phase state, such as the distinctive oscillating pattern in its Wigner function. This state emerges from the nonlinear Jaynes-Cummings interaction native to the trapped-ion model, and under the assumption of an initial coherent vibrational state with a large occupation number. Consequently, the evolved vibrational state approximates the cubic phase state with high fidelity, and we use the variance of a nonlinear combination of the quadratures to characterize it. Finally, we provide an analytical expression for its cubicity that shows the high performance of the approximate vibrational cubic phase state.
Related
- Cubic Phase Gate with a Trapped Ion Oscillator
- Exact Fock Amplitudes of the Cubic-Phase Gate on Arbitrary Pure Gaussian States
- Rapid multi-mode trapped-ion laser cooling in a phase-stable standing wave
- WKB approximation for quasi-bound states and trapped modes
- Exact Phase-Space Rotation in the Trapped Quantum Calogero Model
BibTeX
@misc{venturavelazquez2026approximate,
title = {{Approximate cubic phase states in a trapped ion}},
author = {C. Ventura-Velázquez and Juan Mauricio Torres},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03032},
eprint = {2609.03032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03032},
}
RIS
TY - UNPB
TI - Approximate cubic phase states in a trapped ion
AU - C. Ventura-Velázquez
AU - Juan Mauricio Torres
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03032
UR - https://arxiv.org/abs/2609.03032
AB - Universal quantum computation with continuous variables cannot be attained solely with a set of Gaussian operations, it requires the addition of a non-Gaussian element, at least of third order in the quadrature operators, such as the cubic phase state. In this work, we present a method to generate a quantum state in the vibrational mode of a trapped ion that exhibits characteristics compatible with the cubic phase state, such as the distinctive oscillating pattern in its Wigner function. This state emerges from the nonlinear Jaynes-Cummings interaction native to the trapped-ion model, and under the assumption of an initial coherent vibrational state with a large occupation number. Consequently, the evolved vibrational state approximates the cubic phase state with high fidelity, and we use the variance of a nonlinear combination of the quadratures to characterize it. Finally, we provide an analytical expression for its cubicity that shows the high performance of the approximate vibrational cubic phase state.
ER -