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arXiv · 1509.08252

Cyclic groups and quantum logic gates

Arash Pourkia·J. Batle·C. H. Raymond Ooi
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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.

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Arash Pourkia, J. Batle, C. H. Raymond Ooi. 2015-09-28. Cyclic groups and quantum logic gates. https://doi.org/10.1016/j.aop.2016.06.023

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