  In this paper, we explore topological quantum computation augmented by
subphases and phase transitions. We commence by investigating the anyon
tunneling map, denoted as $\varphi$, between subphases of the quantum double
model $\mathcal{D}(G)$ for any arbitrary finite group $G$. Subsequently, we
delve into the relationship between $\varphi$ and the Floquet code, and extend
the Abelian Floquet code to encompass non-abelian cases. We conclude by
demonstrating how phase transitions in both the temporal and spatial directions
can enhance the diversity of topological gates for general topological orders
described by modular tensor categories.
