A research team led by Professors Su Yikai and Guo Xuhan from the School of Integrated Circuits at Shanghai Jiao Tong University has achieved significant advancements in the study of high-dimensional non-Abelian geometric phases within the realm of integrated optics. For the first time, the collaborative team successfully generated arbitrary high-dimensional special orthogonal group (SO(m)) non-Abelian geometric phases on a dual-layer silicon nitride platform. By harnessing the ultra-compact nature of the integrated platform and the inherent robustness of geometric phases, the research has culminated in the development of unitary matrix transformation devices that exhibit broadband (≥100 nm) capabilities, support high-order transformations (≥6th order), and maintain high fidelity (>0.95). Moreover, the team conducted both classical and quantum optical experiments, affirming the potential of non-Abelian geometric phases in both classical and quantum optical computing domains.