Future scalable photonic quantum information processing relies on the ability of integrating multiple interacting quantum emitters into a single chip. Quantum dots provide ideal on-chip quantum light sources. However, achieving quantum interaction between multiple quantum dots on-a-chip is a challenging task due to the randomness in their frequency and position, requiring local tuning technique and long-range quantum interaction. Here, we demonstrate quantum interactions between separated two quantum dots on a nanophotomc waveguide. We achieve a photon-mediated long-range interaction by integrating the quantum dots to the same optical mode of a nanophotomc waveguide and overcome spectral mismatch by incorporating on-chip thermal tuners. We observe their quantum interactions of the form of super-radiant emission, where the two dots collectively emit faster than each dot individually. Creating super-radiant emission from integrated quantum emitters could enable compact chip-integrated photonic structures that exhibit long-range quantum interactions. Therefore, these results represent a major step toward establishing photonic quantum information processors composed of multiple interacting quantum emitters on a semiconductor chip.