  The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin
liquids, in which fractional quasiparticles would provide applications in
decoherence-free topological quantum computing. The key ingredient is the
bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which
require strong entanglement between spin and orbital degrees of freedom. This
study investigates the identification and design of rare-earth materials
displaying robust Kitaev interactions. We scrutinize all possible $4f$ electron
configurations, which require up to $6+$ million intermediate states in the
perturbation processes, by developing a parallel computational program designed
for massive scale calculations. Our analysis reveals a predominant interplay
between the isotropic Heisenberg $J$ and anisotropic Kitaev $K$ interactions
across all realizations of the Kramers doublets. Remarkably, instances
featuring $4f^3$ and $4f^{11}$ configurations showcase the prevalence of $K$
over $J$, presenting unexpected prospects for exploring the Kitaev QSLs in
compounds including Nd$^{3+}$ and Er$^{3+}$, respectively. Beyond the Kitaev
model, our computational program also proves adaptable to a wide range of
$4f$-electron magnets.
