Generalized SWAP and iSWAP and Solutions to the Yang-Baxter Equation in All Dimensions
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6344Keywords:
Qudits, Universal Quantum logic gates, Yang–-Baxter equation, Entangling gatesAbstract
We introduce an infinite family of universal quantum logic gates that includes not only higher-dimensional versions of the usual SWAP and $\mathbf{i}$SWAP gates, but also their previously known extensions. This family consists of permutation-like matrices with nonzero entries of the form $e^{\mathbf{i}\alpha_i}$, where the $\alpha_i$ are arbitrary real numbers. Moreover, we show that these gates, which we refer to as $\alpha SWAP$, provide unitary solutions to the constant Yang--Baxter equation in all dimensions.
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Copyright (c) 2025 Arash Pourkia
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