We introduce an infinite family of universal quantum logic gates that includes not only higher-dimensional versions of the usual SWAP and iSWAP gates, but also their previously known extensions. This family consists of permutation-like matrices with nonzero entries of the form e^iᵢ, where the ᵢ are arbitrary real numbers. Moreover, we show that these gates, which we refer to as SWAP, provide unitary solutions to the constant Yang--Baxter equation in all dimensions.
Arash Pourkia (Fri,) studied this question.