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Towards Categorical Quantum Concurrency Theory (Invited Talk)

Author Chris Heunen

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Categorical semantics
  • Theory of computation → Concurrency
Keywords
  • Quantum computing
  • causality
  • monoidal categories
  • tensor topology

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Abstract

Quantum computing inherently has concurrent aspects. Even with only local operations, qubits can influence each other. This ability leads to genuinely new quantum communication protocols, but also raises even thornier questions of causality than in classical concurrent computing. Monoidal categories and their string diagrams form a convenient and popular language for quantum computing. After an introduction to quantum concurrency, I will discuss the framework of tensor topology, which aims to analyse the interaction of several agents in monoidal categories, using notions from sheaf theory and ordered locales.

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Chris Heunen. Towards Categorical Quantum Concurrency Theory (Invited Talk). In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CONCUR.2025.2

Author Details

Chris Heunen
  • University of Edinburgh, UK

References

  1. C. Constantin, N. Dicaire, and C. Heunen. Localisable monads. In Computer Science Logic, volume 15 of Leibniz International Proceedings in Informatics, pages 1-17, 2022. URL: https://doi.org/10.4230/LIPIcs.CSL.2022.15.
  2. P. Enrique Moliner, C. Heunen, and S. Tull. Space in monoidal categories. In Quantum Physics and Logic, volume 266 of Electronic Proceedings in Theoretical Computer Science, pages 399-410, 2017. URL: https://doi.org/10.4204/EPTCS.266.25.
  3. P. Enrique Moliner, C. Heunen, and S. Tull. Tensor topology. Journal of Pure and Applied Algebra, 224(10):106378, 2020. URL: https://doi.org/10.1016/j.jpaa.2020.106378.
  4. C. Heunen and J. S. Pacaud Lemay. Tensor-restriction categories. Theory and Applications of Categories, 37(21):635-670, 2021. Google Scholar
  5. C. Heunen and N. van der Schaaf. Ordered locales. Journal of Pure and Applied Algebra, 228(7):107654, 2024. URL: https://doi.org/10.1016/j.jpaa.2024.107654.
  6. C. Heunen and J. Vicary. Categories for Quantum Theory. Oxford University Press, 2019. URL: https://doi.org/10.1093/oso/9780198739623.001.0001.
  7. R. Soares Barbosa and C. Heunen. Sheaf representation of monoidal categories. Advances in Mathematics, 416:108900, 2023. URL: https://doi.org/10.1016/j.aim.2023.108900.
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