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

Scalable quantum information processing will rely on fault-tolerant quantum error correction, where one typically encodes a logical qubit in many physical qubits. However, the large physical-to-logical qubit ratio is challenging to realize on near-term devices. Alternatively, one can encode a logical qubit in a single physical system, such as the mechanical oscillation of a trapped ion. To this end, one requires high-fidelity protocols to prepare logical qubits in bosonic modes. However, current protocols lack robustness and may be experimentally challenging to implement. Here, we demonstrate the robust, high-fidelity and measurement-free preparation of arbitrary targeted bosonic states in a trapped ion. We numerically optimise the modulation of the control field that drives the qubit-oscillator interaction. Dynamical error suppression is engineered in the control to make the pulses robust to leading sources of error. With this, we demonstrate the robust preparation of a binomial state with up to 4.8x error suppression. We also prepare a square Gottesman-Kitaev-Preskill code with 94.0(8)% logical fidelity, a distance-3 binomial code with an average fidelity of 80.7(7)%, and a 12.91(5) dB squeezed vacuum state.