Yang–Baxter equation in all dimensions and universal qudit gates

We construct solutions of the Yang–Baxter equation in any dimension $d\geqslant 2$ by directly generalizing the previously found solutions for $d=2$. We equip those solutions with unitarity and entangling properties. Being unitary, they can be turned into $2$-qudit quantum logic gates for qudit-based systems. The entangling property enables each of those solutions, together with all $1$-qudit gates, to form a universal set of quantum logic gates.