Software based compensation of AC-line perturbations and randomized benchmarking on a Barium-137 quDit

Qudits provide a hardware-efficient path to scaling trapped-ion quantum processors by encoding more computational space per ion. 

Building on our recent demonstration of coherent control, high-fidelity SPAM, and algorithmic operation in a single 25-level 137Ba+ qudit encoded in the S1/2 and D5/2 manifolds (1), 

we report software-based AC-line signal compensation that suppresses mains-synchronous detuning drifts and phase accumulation. 

Left uncorrected, these deterministic perturbations accumulate across pulse/experiment sequence, producing coherent over-rotation and frame-tracking errors that grow with sequence depth and, in high-dimensional protocols, with the number of addressed transitions.

We implement a calibration-and-feedforward workflow in which we first characterize the deterministic AC-line-induced signal using a Ramsey-based technique, and then pre-compute pulse-by-pulse detuning and phase corrections for the full experimental sequence. These corrections are applied in software by updating the programmed drive frequency and phase of each transition, effectively pre-compensating the control and stabilizing the accumulated phase across long sequences.

We use randomized benchmarking in the multi-dimensional manifold to quantify the improvement in average gate fidelity with and without AC-line compensation in software. Our results provide a framework for translating qudit-level hardware complexity into stable, software-defined quantum control.