  To realize one desired nonadiabatic holonomic gate, various equivalent
evolution paths can be chosen. However, in the presence of errors, these paths
become inequivalent. In this paper, we investigate the difference of these
evolution paths in the presence of systematic Rabi frequency errors and aim to
find paths with optimal robustness to realize one-qubit nonadiabatic holonomic
gates. We focus on three types of evolution paths in the $\Lambda$ system:
paths belonging to the original two-loop scheme [New J. Phys. {\bf 14}, 103035
(2012)], the single-loop multiple-pulse scheme [Phys. Rev. A {\bf 94}, 052310
(2016)], and the off-resonant single-shot scheme [Phys. Rev. A {\bf 92}, 052302
(2015); Phys. Lett. A {\bf 380}, 65 (2016)]. Whereas both the single-loop
multiple-pulse and single-shot schemes aim to improve the robustness of the
original two-loop scheme by shortening the exposure to decoherence, we here
find that the two-loop scheme is more robust to systematic errors in the Rabi
frequencies. More importantly, we derive conditions under which the resilience
to this kind of error can be optimized, thereby strengthening the robustness of
nonadiabatic holonomic gates.
