Control and readout of a 13-level trapped ion qudit

Scaling up the computational space of a quantum system is necessary to demonstrate quantum algorithmic advantage. Currently, including more information carriers is still a physical challenge in general. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with 13 computational states in our chosen information host, ¹³⁷Ba⁺. Utilizing the additional energy states found in ¹³⁷Ba⁺ comes with non-trivial complexities which obscure the practical choices of energy states for qudit encoding. We report on tools we have developed for predicting energy states that are practical for qudit encoding, validated with good agreement with our experimental data. We also identify the major error sources for qudit control with ¹³⁷Ba⁺ as avenues for improvement to achieve high fidelity operations.