Is there an efficient gate that swaps values of different superposition kets?
Let $ \alpha_i, \beta_i $ be string in $ \{0,1\}^n$. I'm wondering if there are known results about the existence of a gate which, for a given superposition, swaps only specific segment of it. Namely the following mapping: $$ \frac{1}{\sqrt{2}} (\vert{0,\alpha_1, \alpha_2}\rangle +\vert{1,\beta_1, \beta_2}\rangle) \mapsto \frac{1}{\sqrt{2}} (\vert{0,\beta_1, \alpha_2}\rangle +\vert{1,\alpha_1, \beta_2}\rangle )$$
At first glance, it seems that such map would be unitary, but I couldn't figure out how to implement such a gate. So, does this gate exist?