Non-Abelian braiding of multiple high-order photonic modes in silicon waveguides.

Non-Abelian braiding plays a vital role in fault-tolerant quantum computing because of its global feature. It has recently been introduced to photonic systems, but the operational modes are confined to the fundamental mode, limiting potential mode-multiplexed applications in parallel optical computing. Here, we propose an architecture for a CMOS-compatible silicon-on-insulator photonic platform that supports non-Abelian braiding of multiple high-order modes. Numerical simulations demonstrate that higher-order modes in this structure exhibit braiding evolution behavior consistent with the fundamental mode, revealing the feasibility of achieving mode-multiplexed non-Abelian braiding. We also demonstrate that the multi-mode non-Abelian braiding works in broadband. Our work extends the effective dimensionality of non-Abelian braiding from the fundamental-mode system to a multi-mode system, opening new avenues for multiplexing applications in non-Abelian integrated photonics.