  The use of multilevel quantum information carriers, also known as qudits,
attracts a significant deal of interest as a way for further scalability of
quantum computing devices. However, a nontrivial task is to experimentally
achieve a gain in the efficiency of realizing quantum algorithms with qudits
since higher qudit levels typically have relatively short coherence times
compared to qubit states. Here we propose and experimentally demonstrate two
approaches for the realization of continuous dynamical decoupling of
magnetic-sensitive states with $m_F=\pm1$ for qudits encoded in optical
transition of trapped $^{171}$Yb$^{+}$ ions. We achieve improvement in qudit
levels coherence time by the order of magnitude (more than 9 ms) without any
magnetic shielding, which reveals the potential advantage of the symmetry of
the $^{171}$Yb$^{+}$ ion energy structure for counteracting the magnetic field
noise. Our results are a step towards the realization of qudit-based algorithms
using trapped ions.
