  The generation and control of optical frequency combs in integrated photonic
systems enables complex, high-controllable, and large-scale devices. In
parallel, harnessing topological physics in multipartite systems has allowed
them with compelling features such as robustness against fabrication
imperfections. Here we experimentally demonstrate on-chip topological transport
for optical frequency combs at telecommunication wavelengths, both in classical
and nonclassical domains. We access both the quantum frequency combs and
dissipative Kerr soliton combs with a micro-resonator. The quantum frequency
comb, that is, a coherent superposition of multiple frequency modes, is proven
to be a frequency-entangled qudit state. We also show that dissipative Kerr
soliton combs are highly coherent and mode-locked due to the collective
coherence or self-organization of solitons. Moreover, the valley kink states
allow both quantum frequency combs and dissipative Kerr soliton combs with
robustness against sharp bends. Our topologically protected optical frequency
combs could enable the inherent robustness in integrated complex photonic
systems.
