Topological quantum frequency comb is a burgeoning topic that combines topological phases and quantum systems, which inspires many intriguing sparks in topological quantum optics. Producing quantum frequency combs in valley photonic crystal topological resonators can introduce the robustness to quantum states in integrated photonic devices.
Recent advances in manipulating topological phases in quantum systems have promised integrated quantum devices with conspicuous functionalities, such as robustness against fabrication defects. At the same time, the introduction of quantum frequency combs enables extreme expansion of quantum resources. Here, it theoretically propose the generation of high-dimensional entangled quantum frequency combs via four-wave mixing processes in the valley-Hall topological resonators. Specifically, it demonstrates two irregular photonic crystal resonators supporting the whispering-gallery resonator modes that lead to coherent quantum frequency combs at telecommunication wavelengths. By using the Schmidt decomposition, It shows that the quantum frequency combs are frequency entangled, and it also concludes that the effective dimensions of quantum frequency combs in these two resonators are at least seven and six, respectively. Moreover, these quantum frequency combs inherit the topological protection of valley kink states, showing robustness against defects in the resonators. The topological quantum frequency combs have shown intriguing potentiality in the generation and control of topologically protected high-dimensional quantum states in integrated photonic crystal platforms.