Chris Heunen

Chris Heunen
Born
Christiaan Johan Marie Heunen

(1982-03-21) 21 March 1982 (age 44)
Nijmegen, Netherlands
EducationRadboud University Nijmegen (MSc, PhD)
Known forQuasi-Borel spaces
Distributed quantum circuits
AwardsBirkhoff–von Neumann Prize (2012)
Scientific career
FieldsCategory theory, quantum computing, quantum programming, programming language semantics
WorkplacesUniversity of Edinburgh
University of Oxford
Thesis Categorical Quantum Models and Logics  (2010)
Bart Jacobs [nl]
Klaas Landsman [nl]
Websitehomepages.inf.ed.ac.uk/cheunen/

Christiaan Johan Marie "Chris" Heunen is a Dutch mathematician and computer scientist. He is Professor of Quantum Programming in the School of Informatics, University of Edinburgh. His research applies category theory to the foundations of quantum theory, to quantum programming, and to the semantics of probabilistic programming. He is known for co-developing a topos-theoretic approach to quantum theory, for co-introducing quasi-Borel spaces, and for a method of distributing quantum circuits across networked quantum processors.

Early life and education

Heunen was born on 21 March 1982 in Nijmegen. He studied mathematics and computer science at Radboud University Nijmegen, receiving master's degrees in both in 2005. He completed his doctorate there with a thesis entitled Categorical Quantum Models and Logics, supervised by Bart Jacobs [nl] and Klaas Landsman [nl]. He defended it in January 2010.

Career

After his doctorate, Heunen held a Rubicon fellowship from the Netherlands Organisation for Scientific Research at the University of Oxford, during which he was also a visiting researcher at the California Institute of Technology. From 2014 he held an Engineering and Physical Sciences Research Council Early Career Fellowship, initially at Oxford. He joined the School of Informatics at the University of Edinburgh in October 2015.

In 2023 he became director of a Quantum and AI Centre of Excellence set up by the University of Edinburgh with Cisco. In 2024 he was named lead of the EPSRC Centre for Doctoral Training in Quantum Informatics, which Edinburgh runs with the University of Oxford, the University of Strathclyde, Heriot-Watt University and University College London. He chairs the steering committee of the Quantum Software Alliance, an international network of quantum software research centres launched in 2026.

Research

Topos approach to quantum theory

With Klaas Landsman and Bas Spitters, Heunen developed a topos-theoretic formulation of quantum theory. Motivated by Niels Bohr's doctrine of classical concepts, it studies a quantum system through the family of its commutative subalgebras. The philosopher Benjamin Eva discussed this "covariant" approach alongside the topos programme of Andreas Döring and Chris Isham, arguing that both face similar difficulties of interpretation.

Probabilistic programming

In 2017 Heunen, Ohad Kammar, Sam Staton and Hongseok Yang introduced quasi-Borel spaces, a mathematical setting for higher-order probabilistic programming languages that supports both continuous probability and function types. Other researchers have used quasi-Borel spaces as the basis of a verification framework for higher-order probabilistic programs and have formalised the theory in the Isabelle proof assistant.

Distributed quantum computing

With his doctoral student Pablo Andrés-Martínez, Heunen developed a method for distributing a quantum circuit across several networked quantum processors by reducing the task to hypergraph partitioning. A 2025 review of distributed quantum computing described the work as one of the most significant contributions to the field and a foundational reference for later research, while noting that it did not explore the full space of possible partitions. Other researchers used the method as a benchmark when developing new algorithms. Researchers at Quantinuum, including Andrés-Martínez, later extended it to networks of heterogeneous quantum computers, implementing it in the pytket-dqc software package.

Axioms for Hilbert spaces

With Andre Kornell, Heunen gave purely categorical axioms that characterise the category of Hilbert spaces and bounded linear maps. Stephen Lack and Shay Tobin later gave a related characterisation, following the same approach, that also covers quaternionic Hilbert spaces.

Quantum programming languages

His recent work develops equational foundations for quantum programming languages. With Jacques Carette, Robin Kaarsgaard, Neil J. Ross and Amr Sabry, he gave an axiomatisation of quantum computing built on reversible classical computing, replacing the continuous postulates of quantum theory with a small set of discrete equations.

Books

Heunen and Jamie Vicary wrote Categories for Quantum Theory: An Introduction, published by Oxford University Press in 2019 as volume 28 of the Oxford Graduate Texts in Mathematics. A reviewer for zbMATH Open praised its balance of theory and applications, and a reviewer for Mathematical Reviews found it self-contained and accessible. A Japanese translation by Haruyuki Kawabe was published by Morikita Publishing in 2021.

Heunen also co-edited Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse (Oxford University Press, 2013) with Mehrnoosh Sadrzadeh and Edward Grefenstette.

Recognition and service

Heunen received the Birkhoff–von Neumann Prize of the International Quantum Structures Association in 2012. He was one of the founding editors of the journal Quantum in 2016, and has been a member of its steering board since 2021. He was a member of the founding editorial board of the journal Compositionality in 2018. He is an associate editor of ACM Transactions on Computational Logic, and a member of the International Federation for Information Processing working group on the foundations of quantum computation.

Selected publications

References

  1. 1 2 3 Heunen, Chris (2009). Categorical Quantum Models and Logics (PDF) (PhD thesis). Radboud University Nijmegen. ISBN 978-90-8555-024-2.
  2. ↑ "Prof Chris Heunen". School of Informatics, University of Edinburgh. Retrieved 19 October 2026.
  3. ↑ Heunen, Chris. "Curriculum vitae" (PDF). Retrieved 19 October 2026.
  4. ↑ Chris Heunen at the Mathematics Genealogy Project
  5. ↑ "Chris Heunen". Simons Institute for the Theory of Computing. Retrieved 19 October 2026.
  6. ↑ "Chris Heunen". Gateway to Research. UK Research and Innovation. Retrieved 19 October 2026.
  7. ↑ "Chris Heunen". Edinburgh Research Explorer. University of Edinburgh. Retrieved 19 October 2026.
  8. ↑ "Quantum and AI centre launched with Cisco". University of Edinburgh. March 2023. Retrieved 19 October 2026.
  9. ↑ "Cisco and the University of Edinburgh launch Quantum and AI Centre of Excellence" (Press release). Cisco. 9 March 2023. Retrieved 23 October 2026.
  10. ↑ "Cisco sponsors AI and quantum centre at Edinburgh University". Capacity Media. March 2023. Retrieved 19 October 2026.
  11. ↑ "£1 billion doctoral training investment announced". UK Research and Innovation. March 2024. Retrieved 19 October 2026.
  12. ↑ "Centres train graduates to meet UK future challenges". University of Edinburgh. 2024. Retrieved 19 October 2026.
  13. ↑ "Global network puts spotlight on quantum software". Leiden University. 10 February 2026. Retrieved 23 October 2026.
  14. ↑ Quinn, Tom (12 February 2026). "Edinburgh Uni to lead global push on quantum software". DIGIT. Retrieved 23 October 2026.
  15. ↑ Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas (2009). "A topos for algebraic quantum theory". Communications in Mathematical Physics. 291 (1): 63–110. arXiv:0709.4364. doi:10.1007/s00220-009-0865-6.
  16. ↑ Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas (2012). "Bohrification of operator algebras and quantum logic". Synthese. 186 (3): 719–752. arXiv:0905.2275. doi:10.1007/s11229-011-9918-4.
  17. ↑ Eva, Benjamin (2017). "Topos theoretic quantum realism". The British Journal for the Philosophy of Science. 68 (4): 1149–1181. doi:10.1093/bjps/axv057.
  18. ↑ Heunen, Chris; Kammar, Ohad; Staton, Sam; Yang, Hongseok (2017). A convenient category for higher-order probability theory. 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). pp. 1–12. arXiv:1701.02547. doi:10.1109/LICS.2017.8005137.
  19. ↑ Sato, Tetsuya; Aguirre, Alejandro; Barthe, Gilles; Gaboardi, Marco; Garg, Deepak; Hsu, Justin (2019). "Formal verification of higher-order probabilistic programs: reasoning about approximation, convergence, Bayesian inference, and optimization". Proceedings of the ACM on Programming Languages. 3 (POPL). Article 38. arXiv:1807.06091. doi:10.1145/3290351.
  20. ↑ Hirata, Michikazu; Minamide, Yasuhiko; Sato, Tetsuya (2022). "Quasi-Borel spaces". Archive of Formal Proofs.
  21. ↑ Andrés-Martínez, Pablo; Heunen, Chris (2019). "Automated distribution of quantum circuits via hypergraph partitioning". Physical Review A. 100 (3). 032308. arXiv:1811.10972. doi:10.1103/PhysRevA.100.032308.
  22. ↑ Barral, David; et al. (2025). "Review of distributed quantum computing: from single QPU to high performance quantum computing". Computer Science Review. 57. 100747. arXiv:2404.01265. doi:10.1016/j.cosrev.2025.100747.
  23. ↑ Sundaram, Ranjani G.; Gupta, Himanshu; Ramakrishnan, C. R. (2021). "Efficient distribution of quantum circuits". 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics. Vol. 209. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. pp. 41:1–41:20. doi:10.4230/LIPIcs.DISC.2021.41.
  24. ↑ Andres-Martinez, Pablo; et al. (2024). "Distributing circuits over heterogeneous, modular quantum computing network architectures". Quantum Science and Technology. 9 (4). 045021. arXiv:2305.14148. doi:10.1088/2058-9565/ad6734.
  25. ↑ "pytket-dqc". GitHub. Quantinuum. Retrieved 19 October 2026.
  26. ↑ Heunen, Chris; Kornell, Andre (2022). "Axioms for the category of Hilbert spaces". Proceedings of the National Academy of Sciences. 119 (9). e2117024119. arXiv:2109.07418. doi:10.1073/pnas.2117024119.
  27. ↑ Lack, Stephen; Tobin, Shay (2025). "A characterisation for the category of Hilbert spaces". Applied Categorical Structures. 33 (2). 13. arXiv:2412.03776. doi:10.1007/s10485-025-09805-3.
  28. ↑ Carette, Jacques; Heunen, Chris; Kaarsgaard, Robin; Ross, Neil J.; Sabry, Amr (2026). "Free quantum computing". Proceedings of the National Academy of Sciences. 123 (8). e2510881123. arXiv:2602.16927. doi:10.1073/pnas.2510881123.
  29. ↑ Heunen, Chris; Vicary, Jamie (2019). Categories for Quantum Theory: An Introduction. Oxford Graduate Texts in Mathematics. Vol. 28. Oxford University Press. doi:10.1093/oso/9780198739623.001.0001. ISBN 978-0-19-873962-3.
  30. ↑ Nishimura, Hirokazu (2020). "Review of Categories for Quantum Theory: An Introduction". zbMATH Open. Zbl 1436.81004. Retrieved 23 October 2026.
  31. ↑ Cui, Shawn Xingshan. "Review of Categories for Quantum Theory: An Introduction". Mathematical Reviews. MR 3971584. Retrieved 23 October 2026.
  32. ↑ "圏論的量子力学" (in Japanese). Morikita Publishing. Retrieved 19 October 2026.
  33. ↑ Heunen, Chris; Sadrzadeh, Mehrnoosh; Grefenstette, Edward, eds. (2013). Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse. Oxford University Press. ISBN 978-0-19-964629-6.
  34. ↑ "Birkhoff–von Neumann Prize". International Quantum Structures Association. Retrieved 19 October 2026.
  35. ↑ "Founding editors". Quantum. 2016. Retrieved 19 October 2026.
  36. ↑ "People". Quantum. Retrieved 19 October 2026.
  37. ↑ Baez, John (18 July 2018). "Compositionality: the editorial board". The n-Category Café. Retrieved 23 October 2026.
  38. ↑ "Editorial board". ACM Transactions on Computational Logic. Retrieved 19 October 2026.
  39. ↑ "IFIP Working Group on Foundations of Quantum Computation". Karlsruhe Institute of Technology. Retrieved 19 October 2026.