Towards Categorical Quantum Concurrency Theory (Invited Talk)

Heunen, Chris

doi:10.4230/LIPIcs.CONCUR.2025.2

Towards Categorical Quantum Concurrency Theory

Chris Heunen

University of Edinburgh, UK

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.

Keywords and phrases:

Quantum computing, causality, monoidal categories, tensor topology

Category:

Invited Talk

Copyright and License:

2012 ACM Subject Classification:

Theory of computation

\rightarrow

Quantum computation theory ; Theory of computation

\rightarrow

Categorical semantics ; Theory of computation

\rightarrow

Concurrency

DOI:

10.4230/LIPIcs.CONCUR.2025.2

Event:

36th International Conference on Concurrency Theory (CONCUR 2025)

Editors:

Patricia Bouyer and Jaco van de Pol

Series and Publisher:

Leibniz International Proceedings in Informatics, Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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. doi: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. doi: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. doi: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.
[5] C. Heunen and N. van der Schaaf. Ordered locales. Journal of Pure and Applied Algebra, 228(7):107654, 2024. doi:10.1016/j.jpaa.2024.107654.
[6] C. Heunen and J. Vicary. Categories for Quantum Theory. Oxford University Press, 2019. doi:10.1093/oso/9780198739623.001.0001.
[7] R. Soares Barbosa and C. Heunen. Sheaf representation of monoidal categories. Advances in Mathematics, 416:108900, 2023. doi:10.1016/j.aim.2023.108900.

[bib.bib1] [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. doi:10.4230/LIPIcs.CSL.2022.15.

[bib.bib2] [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. doi:10.4204/EPTCS.266.25.

[bib.bib3] [3] P. Enrique Moliner, C. Heunen, and S. Tull. Tensor topology. Journal of Pure and Applied Algebra, 224(10):106378, 2020. doi:10.1016/j.jpaa.2020.106378.

[bib.bib4] [4] C. Heunen and J. S. Pacaud Lemay. Tensor-restriction categories. Theory and Applications of Categories, 37(21):635–670, 2021.

[bib.bib5] [5] C. Heunen and N. van der Schaaf. Ordered locales. Journal of Pure and Applied Algebra, 228(7):107654, 2024. doi:10.1016/j.jpaa.2024.107654.

[bib.bib6] [6] C. Heunen and J. Vicary. Categories for Quantum Theory. Oxford University Press, 2019. doi:10.1093/oso/9780198739623.001.0001.

[bib.bib7] [7] R. Soares Barbosa and C. Heunen. Sheaf representation of monoidal categories. Advances in Mathematics, 416:108900, 2023. doi:10.1016/j.aim.2023.108900.