The Quantum States of a Graph

Mohd Arif Raza (), Adel N. Alahmadi, Widyan Basaffar, David G. Glynn, Manish K. Gupta, James W. P. Hirschfeld, Abdul Nadim Khan, Hatoon Shoaib and Patrick Solé ()
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Mohd Arif Raza: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia
Adel N. Alahmadi: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Widyan Basaffar: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
David G. Glynn: College of Science and Engineering, Flinders University, Adelaide, SA 5001, Australia
Manish K. Gupta: Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar 382007, Gujarat, India
James W. P. Hirschfeld: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abdul Nadim Khan: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia
Hatoon Shoaib: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Patrick Solé: I2M, (CNRS, Aix-Marseille University, Centrale Marseille), 163 Avenue de Luminy, 13009 Marseilles, France

Mathematics, 2023, vol. 11, issue 10, 1-13

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.

Keywords: quantum state; graph; self-dual quantum code; Eulerian graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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