Cyclic groups and quantum logic gates

Abstract

We present a formula for an infinite number of universal quantum logic gates, which are $4$ by $4$ unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order $n$. We then show that this {\it discrete} family, parametrized by integers $n$, is in fact, a small sub-class of a larger {\it continuous} family, parametrized by real numbers $\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.

arXiv comment12 pages, no figures. Submitted to Physical Review A

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• Solutions to the constant Yang-Baxter equation in all dimensions
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• A note on "eight-vertex" universal quantum gates
• Quantum teleportation and Birman-Murakami-Wenzl algebra