The Quantum States of a Graph-Reference-Cited by-同舟云学术

The Quantum States of a Graph

Published:2023-05-16 Issue:10 Volume:11 Page:2310
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Raza Mohd Arif¹^ORCID,Alahmadi Adel N.²,Basaffar Widyan²,Glynn David G.³^ORCID,Gupta Manish K.⁴^ORCID,Hirschfeld James W. P.²,Khan Abdul Nadim¹,Shoaib Hatoon²^ORCID,Solé Patrick⁵

Affiliation:

1. Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia

2. Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

3. College of Science and Engineering, Flinders University, Adelaide, SA 5001, Australia

4. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar 382007, Gujarat, India

5. I2M, (CNRS, Aix-Marseille University, Centrale Marseille), 163 Avenue de Luminy, 13009 Marseilles, France

Abstract

Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role.

Funder

the Institutional Fund Projects of Saudi Arabia

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/10/2310/pdf

Reference10 articles.

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2. Lomonaco, S.J. (2002). Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, American Mathematical Society. Proceedings of Symposia in Applied Mathematics.

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4. stabiliser codes can be realized as graph codes;Schlingemann;Quantum Inf. Comput.,2002

5. Danielsen, L.E. (2005). On Self-Dual Quantum Codes, Graphs, and Boolean Functions. [Master’s Thesis, Department Informatics, University Bergen].