Quantum computing based on complex Clifford algebras

DOI10.1007/S11128-022-03648-WarXiv2201.02246WikidataQ114223636 ScholiaQ114223636MaRDI QIDQ6387674

Jaroslav Hrdina, Petr Vašík, Aleš Návrat

Publication date: 6 January 2022

Abstract: We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in straightforward way. We demonstrate its functionality by performing quantum computations with several well known examples of quantum gates. We also compare our approach with representations that use real geometric algebras.

Mathematics Subject Classification ID

Quantum computation (81P68) Quantum algorithms and complexity in the theory of computing (68Q12) Quantum gates (81P65) Applications of Clifford algebras to physics, etc. (15A67)

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