Robust and Determinisitc Preparation of Bosonic Logical States in a Trapped Ion

We demonstrate a robust, high-fidelity, and measurement-free optimal quantum control protocol to prepare arbitrary bosonic states in the mechanical motion of a trapped ion. Our protocol's versatility enables the preparation of several bosonic logical code words relevant to scaling error-corrected quantum information processing (QIP). We demonstrate the robust preparation of a binomial logical state with up to 4.8X error suppression, the creation of a Gottesman-Kitaev-Preskill code word with a logical fidelity of 0.940(8), a distance-3 binomial state with an average fidelity of 0.807(7), and a squeezed vacuum state with 12.91(5) dB of squeezing. The optimal control protocol can enact unitary gates and can be generalized to multiple bosonic modes, opening new opportunities to implement a large variety of error-robust operations for continuous variable QIP.