(untitled) (European Journal of Pure and Applied Mathematics, 2025)
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^iα_i, where the α_i are arbitrary real numbers. Moreover, we show that these gates, which we refer to as α SWAP, provide unitary solutions to the constant Yang–Baxter equation in all dimensions.