Quantum computing based on complex Clifford algebras

2022/01/06 by Jaroslav Hrdina, Hrdina, Jaroslav, Aleš Návrat +3 · 2 citations
Computer Science · Mathematics · #15A66 #68Q12 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2201.02246

openalex publication_date 2022/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Hermitian Geometry of Complex Multivectors, Determinants and Orientations
• The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information

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