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The Quantum States of a Graph

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohd Arif Raza & Adel N. Alahmadi & Widyan Basaffar & David G. Glynn & Manish K. Gupta & James W. P. Hirschfeld & Abdul Nadim Khan & Hatoon Shoaib & Patrick Solé, 2023. "The Quantum States of a Graph," Mathematics, MDPI, vol. 11(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2310-:d:1147741
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