The Yang-Baxter equation, Quantum computing and Quantum entanglement

We present a method to construct infinite families of entangling $2$-qudit gates, and amongst them entangling $2$-qudit gates which satisfy the Yang-Baxter equation. We show that, given $2$-qudit gates $c$ and $d$, if $c$ or $d$ is entangling, then their Tracy-Singh product $c⊠d$ is also entangling and we can provide non-entangled states which become entangled after the application of $c⊠d$.