High-Dimensional QuDit Control for Scalable Trapped Ion Quantum Computing*

High-dimensional qudits hold significant promise for scaling up current trapped-ion quantum processors. In this work, we highlight Ba137 ion, chosen for its nuclear spin of I=3/2, which yields 24 metastable states and 8 ground states under moderate (few-Gauss) magnetic fields. Leveraging this rich level structure, we encode and manipulate qudits via the quadrupole transition between the S1/2 and D5/2 manifolds. We present experimental methods and considerations for achieving state preparation and measurement (SPAM) on a D=25 dimensional basis with over 99.5% fidelity, along with coherent control of more than 10 states through Ramsey-type experiments.  

Additionally, we describe an approach for precisely calibrating 80 transition frequencies (with in 100Hz) and their associated Rabi frequencies using theoretically calculated magnetic field sensitivities and oscillator strengths. Finally, we discuss various noise sources that impact qudit coherence and show how an appropriate choice of encoded states can mitigate certain noise channels, underscoring the feasibility of high-dimensional qudit protocols in trapped-ion systems.  

This work presents a novel approach to addressing scalability challenges in trapped-ion systems by leveraging the intrinsic energy level structure of ions with nonzero nuclear spin.