Data for: Simulating Floquet non-abelian topological insulator with photonic quantum walks

Floquet non-Abelian topological phases emerge in periodically driven
systems and exhibit properties that are absent from their Abelian or
static counterparts. Dubbed the Floquet non-Abelian topological insulators
(FNATIs), they are characterized by non-Abelian topological charges and
feature multifold bulk-boundary correspondence, making their experimental
observation challenging. Here we simulate the FNATI using a
higher-dimensional photonic quantum walk and develop dynamic measurement
schemes to demonstrate key signatures of the FNATI. Importantly, combining
a direct bulk-dynamic detection for the underlying quaternion topological
charge, and a spatially-resolved injection spectroscopy for the edge
states, we experimentally establish the multifold bulk-boundary
correspondence, and, in particular, identify the anomalous non-Abelian
phase in which edge states appear in all band gaps despite a trivial
topological charge. Our experiment marks the first experimental
characterization of the FNATI, providing general insight into the
non-Abelian topological phases.