arXiv:2609.03032v1 Announce Type: new 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.
Approximate cubic phase states in a trapped ion
arXiv:2609.03032v1 Announce Type: new 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...