Continuous dynamical decoupling of optical $^{171}$Yb$^{+}$ qudits with radiofrequency fields

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.