First Step Towards High-Dimensional Qudit Quantum Computing With Trapped Ions*

¹³⁷Ba⁺ is an attractive candidate for high-level qudit encoding due to the availability of its many stable and meta-stable states. Utilizing the ground 6S_1/2 and the meta-stable 5D_5/2 levels, a maximum qudit encoding of up to 25 distinguishable states is possible with our protocol in principle. State preparation and measurement (SPAM) is a necessary first step for quantum computation. We demonstrate a 13-level encoding with ¹³⁷Ba⁺ and the experimental SPAM fidelity achieved in our work.