Abstract
Topological boundary states exhibit distinctive properties, including unidirectional propagation and noise robustness, which hold significant potential for advancing the performance of quantum science and technology. Here, we demonstrate the implementation of non-Abelian quantum interference and entanglement generation, protected by dual symmetries (time-independent inversion and time-dependent interchain), in coupled Su-Schrieffer-Heeger chains. Specifically, in a multichain system, we first achieve tunable topological transfer of a single particle, where the destination chain is selected by the permutation sequence. We then extend this to two particles, observing a non-Abelian Hong-Ou-Mandel interference that generates spatially entangled NOON states whose properties are dictated by the permutation sequence. Our work establishes an alternative pathway for exploring non-Abelian topology applied to quantum science and technology, enabled by the unique protection of time-dependent symmetry.