Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons—candidates for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a unitary matrix that can also physically emerge as a geometric-phase matrix in classical systems. Hence it is predicted that non-Abelian braiding should have analogues in photonics, although a feasible platform and the experimental realization remain out of reach. Here we propose and experimentally realize an on-chip photonic system that achieves the non-Abelian braiding of up to five photonic modes. The braiding is realized by controlling the multi-mode geometric-phase matrix in judiciously designed photonic waveguide arrays. The quintessential effect of braiding—sequence-dependent swapping of photon dwell sites—is observed in both classical-light and single-photon experiments. Our photonic chips are a versatile and expandable platform for studying non-Abelian physics, and we expect the results to motivate next-generation non-Abelian photonic devices.

非阿贝尔编织因其在描述任意子交换行为（实现量子逻辑的候选者）中的关键作用而引起了广泛关注。非阿贝尔编织的输入和输出由一个酉矩阵连接，该矩阵也可以在物理上作为经典系统中的几何相位矩阵出现。因此，预计非阿贝尔编织在光子学中应该有类似物，尽管可行的平台和实验实现仍然遥不可及。在这里，我们提出并通过实验实现了一种片上光子系统，该系统可实现多达五个光子模式的非阿贝尔编织。编织是通过控制精心设计的光子波导阵列中的多模几何相位矩阵来实现的。在经典光和单光子实验中都观察到了编织的典型效果——光子驻留点的顺序依赖交换。我们的光子芯片是用于研究非阿贝尔物理的多功能且可扩展的平台，我们希望其结果能够激发下一代非阿贝尔光子器件的发展。