Challenges of Actualizing a 25-level Zeeman Trapped Ion Qudit

The abundant (meta)stable energy levels of ¹³⁷Ba⁺ makes it a natural trapped ion candidate for encoding many qudit levels, which is a venue for increasing the computational space of a quantum computer. The 6S_1/2 and 5D_5/2 energy orbitals of ¹³⁷Ba⁺ feature 32 independent electronic sublevels, and up to 25 levels can be encoded as a Zeeman qudit while preserving single-shot measurement readouts. In this poster presentation, we discuss our experimental progress with actualizing state preparation and coherent control of the internal energy states of a 25-level ¹³⁷Ba⁺ trapped ion qudit. The challenges that we have encountered, unique to high-level qudits and otherwise, are investigated in detail and presented in this poster.