Progress Towards High-Dimensional Qudit Quantum Computing with Trapped ¹³⁷Ba⁺ Ions

The angular momentum eigenstates of the unpaired electron in trapped ¹³⁷Ba⁺ ions offer a promising pathway toward high-fidelity qudit (d > 2) encoding. Due to the non-zero nuclear spin (I = 3/2), the 6S_1/2 and 5D_5/2 manifolds contain, respectively, 8 and 24 non-degenerate levels at intermediate magnetic fields ( ∼ few Gauss).

While a maximal qudit encoding of up to 25 distinguishable states is possible in principle, we present progress towards initialising and controlling a single 137 Ba + ion in this joint-subspace. We demonstrate Rabi oscillations from the 5 initial states available in the 6S_1/2 , F = 2 level and discuss the particular challenges to working in the 5D_5/2 manifold at intermediate field. We further present an efficient scheme for calibrating the frequencies of all quadrupole-allowed transitions between the 6S_1/2 and 5D_5/2 manifolds using just 3 measured transitions.

Our work lays the ground for further advancements in high-dimensional encoding of trapped ions, which itself is a promising alternative approach to expanding the Hilbert space in trapped ion quantum computing.