The yang-baxter equation, quantum computing and quantum entanglement

Abstract

We present a method to construct infinite families of entangling (and primitive) $2$-qudit gates, and amongst them entangling (and primitive) $2$-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 decomposable states which become entangled after the application of $c \boxtimes d$.