Publication detail

Quantum Register Algebra: The Basic Concepts

HRDINA, J. VAŠÍK, P. NÁVRAT, A. ERYGANOV, I. ALVES, R. HILDENBRAND, D. STEINMETZ, C. LAVOR, C.

Original Title

Type

conference paper

Language

English

Original Abstract

We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebra Algorithms Optimizer) implementation of our approach. Using the QRA basis vectors definitions given in Sect. 4 and the framework based on the de Witt basis presented in Sect. 5, we are able to fully describe and compute with QRA in GAALOP using the geometric product. We illustrate the intuitiveness of this computation by presenting the QRA form for the well known SWAP operation on a two qubit register.

Keywords

quantum computing; geometric algebra; quantum register algebra

Authors

HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; ERYGANOV, I.; ALVES, R.; HILDENBRAND, D.; STEINMETZ, C.; LAVOR, C.

Released

8. 5. 2024

Publisher

SPRINGER INTERNATIONAL PUBLISHING AG

Location

CHAM

ISBN

978-3-031-34030-7

Book

Advanced Computational Applications of Geometric Algebra

Pages from

112

Pages to

122

Pages count

BibTex

@inproceedings{BUT188578,
  author="Jaroslav {Hrdina} and Petr {Vašík} and Aleš {Návrat} and Ivan {Eryganov} and Rafael {Alves} and Dietmar {Hildenbrand} and Christian {Steinmetz} and Carlile C. {Lavor}",
  title="Quantum Register Algebra: The Basic Concepts",
  booktitle="Advanced Computational Applications of Geometric Algebra",
  year="2024",
  volume="13771",
  pages="112--122",
  publisher="SPRINGER INTERNATIONAL PUBLISHING AG",
  address="CHAM",
  doi="10.1007/978-3-031-34031-4\{_}10",
  isbn="978-3-031-34030-7"
}