Publication detail
Quantum Register Algebra: The Basic Concepts
HRDINA, J. VAŠÍK, P. NÁVRAT, A. ERYGANOV, I. ALVES, R. HILDENBRAND, D. STEINMETZ, C. LAVOR, C.
English title
Quantum Register Algebra: The Basic Concepts
Type
conference paper
Language
en
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.
English 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 in English
quantum computing; geometric algebra; quantum register algebra
Released
08.05.2024
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
Location
CHAM
ISBN
978-3-031-34030-7
Book
Advanced Computational Applications of Geometric Algebra
Volume
13771
Pages from–to
112–122
Pages count
11
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",
month="May",
pages="112--122",
publisher="SPRINGER INTERNATIONAL PUBLISHING AG",
address="CHAM",
isbn="978-3-031-34030-7"
}