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Clifford algebras and universal sets of quantum gates

Alexander Yu. Vlasov
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Abstract

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.

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Alexander Yu. Vlasov. 2001-04-04. Clifford algebras and universal sets of quantum gates. https://doi.org/10.1103/physreva.63.054302

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