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, Patrick Solé

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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.

Original languageEnglish
Article number2310
Number of pages13
Issue number10
Publication statusPublished - 16 May 2023


  • quantum state
  • graph
  • self-dual quantum code
  • Eulerian graph


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