A discrete group $\Gamma$ with a length function $\ell:\Gamma\rightarrow \mathbb{N}_0$ has the property of rapid decay (RD), introduced by Haagerup and Jolissaint, if the operator norm of each element in its group algebra is not much bigger than its $\ell_2$-norm. In our work we show that the free wreath product construction of $\Gamma$ with the quantum automorphism group preserves the notion of RD in $\Gamma$. This will be an elementary talk explaining the use of Temperley-Lieb diagrams, theta-nets, and the representation theory of quantum groups in unraveling this result. Joint work with Michael Brannan and Li Gao.