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 ⊠ d is also entangling and we can provide decomposable states which become entangled after the application of c ⊠ d .