Laser-free Control and Entanglement of Trapped-Ion Qudits

Gates implemented with rf/microwaves (rather than laser-based gates, hence "laser-free") on trapped-ion platforms currently achieve the highest fidelity operations. In spite of these demonstrations of below threshold-error single- and two-qubit gates, scaling to the size necessary for quantum advantage remains a significant challenge. Currently, all large-scale quantum computing efforts encode information in qubits (two-level systems). However, recent consideration has been given to qudit encodings, where information is stored in d-level systems, as a potential path forward. Qudits offer potential advantages in hardware efficiency and algorithmic performance compared to traditional qubit-based approaches.

We demonstrate this advantage by implementing laser-free, universal control of a single trapped ¹³⁷Ba⁺ ion qudit with up to eight levels using multi-tone rf magnetic fields. We employ this control to perform Grover's search algorithm at dimensions five and eight, requiring only O(d) single-qudit gates and no entangling gates. This demonstrates an advantage over qubit-based approaches in both circuit depth and total number of ions required. We also present our ongoing work toward implementing qudit entangling gates using rf magnetic gradients.