  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 $c \boxtimes d$ is also
entangling and we can provide non-entangled states which become entangled after
the application of $c \boxtimes d$.
