Generalized SWAP and iSWAP and Solutions to the Yang-Baxter Equation in All Dimensions (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 $i$SWAP 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.
Keywords: Qudits; Universal Quantum logic gates; Yang–-Baxter equation; Entangling gates