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Quantum Information Processing

Quantum computing based on complex Clifford algebras

  • 01-09-2022
Published in:
Authors
Jaroslav Hrdina
Aleš Návrat
Petr Vašík
Published in
Quantum Information Processing | Issue 9/2022

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Abstract

The article introduces quantum computing based on complex Clifford algebras, highlighting its advantages over traditional matrix representations. It begins with an overview of real geometric (Clifford) algebras and their applications in various fields. The main focus is on using complex Clifford algebras to represent qubits and quantum gates, providing explicit forms for elementary gates and discussing the case of multi-gates. The article also compares this approach with the known description based on the isomorphism of unitary and spin groups. Additionally, it explores the representation of qubits and quantum gates in real Clifford algebras, offering two distinct approaches: quaternionic qubits and real complex qubits. The article concludes by emphasizing the elegance and efficiency of the complex Clifford algebra approach for quantum computing.
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previous article A lightweight three-user secure quantum summation protocol without a third party based on single-particle states
next article Experimental realization of quantum anonymous veto protocols using IBM quantum computer
Title
Quantum computing based on complex Clifford algebras
Authors
Jaroslav Hrdina
Aleš Návrat
Petr Vašík
Publication date
01-09-2022
Publisher
Springer US
Published in
Quantum Information Processing / Issue 9/2022
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-022-03648-w
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