  Multi-level qudit systems are increasingly being explored as alternatives to
traditional qubit systems due to their denser information storage and
processing potential. However, qudits are more susceptible to decoherence than
qubits due to increased loss channels, noise sensitivity, and crosstalk. To
address these challenges, we develop protocols for dynamical decoupling (DD) of
qudit systems based on the Heisenberg-Weyl group. We implement and
experimentally verify these DD protocols on a superconducting transmon
processor that supports qudit operation based on qutrits $(d=3)$ and ququarts
$(d=4)$. Specifically, we demonstrate single-qudit DD sequences to decouple
qutrits and ququarts from system-bath-induced decoherence. We also introduce
two-qudit DD sequences designed to suppress the detrimental cross-Kerr
couplings between coupled qudits. This allows us to demonstrate a significant
improvement in the fidelity of time-evolved qutrit Bell states. Our results
highlight the utility of leveraging DD to enable scalable qudit-based quantum
computing.
