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Encoding logical qubits in bosonic modes provides a potentiallyhardware-efficient implementation of fault-tolerant quantum informationprocessing. Recent advancements in trapped ions and superconducting microwavecavities have led to experimental realizations of high-quality bosonic statesand demonstrations of error-corrected logical qubits encoded in bosonic modes.However, current protocols for preparing bosonic code words lack robustness tocommon noise sources and can be experimentally challenging to implement,limiting the quality and breadth of codes that have been realized to date.Here, we combine concepts of error suppression via robust control with quantumerror correction encoding and experimentally demonstrate high-fidelity,deterministic preparation of highly non-classical target bosonic states in themechanical motion of a trapped ion. Our approach implements numericallyoptimized dynamical modulation of laser-driven spin-motion interactions togenerate the target state in a single step. The optimized control pulses aretailored towards experimental constraints and are designed to be robust againstthe dominant source of error. Using these protocols, we demonstrate logicalfidelities for the Gottesman-Kitaev-Preskill (GKP) state as high as$\bar{\mathcal{F}}=0.940(8)$, achieve the first realization of a distance-3binomial logical state with an average fidelity of $\mathcal{F}=0.807(7)$, anddemonstrate a 12.91(5) dB squeezed vacuum state.

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