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September 10, 2025Open Access

Generalized SWAP and iSWAP and Solutions to the Yang-Baxter Equation in All Dimensions

Key Points

The study introduces universal quantum logic gates that generalize conventional SWAP and iSWAP gates.
These $eta SWAP$ gates provide nonzero entries in the form $e^{eta_i}$, ensuring solutions to the Yang-Baxter equation.
The findings extend known quantum logic applications to all dimensions, expanding the functionality of quantum circuits.
Unitary solutions demonstrating the versatility of permutation matrices are established for quantum computing advancements.

Abstract

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.

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Arash Pourkia (Fri,) studied this question.

synapsesocial.com/papers/68c1a77a54b1d3bfb60e0bcb https://doi.org/https://doi.org/10.29020/nybg.ejpam.v18i3.6344