DROPS

Document

Invited Talk

DOI: 10.4230/LIPIcs.CONCUR.2025.2

Towards Categorical Quantum Concurrency Theory (Invited Talk)

Authors: Chris Heunen

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

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.

Cite as

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)

Copy BibTex To Clipboard

@InProceedings{heunen:LIPIcs.CONCUR.2025.2,
  author =	{Heunen, Chris},
  title =	{{Towards Categorical Quantum Concurrency Theory}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.2},
  URN =		{urn:nbn:de:0030-drops-239527},
  doi =		{10.4230/LIPIcs.CONCUR.2025.2},
  annote =	{Keywords: Quantum computing, causality, monoidal categories, tensor topology}
}

Document

DOI: 10.4230/LIPIcs.CSL.2022.15

Localisable Monads

Authors: Carmen Constantin, Nuiok Dicaire, and Chris Heunen

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract

Monads govern computational side-effects in programming semantics. A collection of monads can be combined together in a local-to-global way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we start with a single monad and equip it with a fine-grained structure by using techniques from tensor topology. This provides an intrinsic theory of local computational effects without needing to know how constituent effects interact beforehand. Specifically, any monoidal category decomposes as a sheaf of local categories over a base space. We identify a notion of localisable monads which characterises when a monad decomposes as a sheaf of monads. Equivalently, localisable monads are formal monads in an appropriate presheaf 2-category, whose algebras we characterise. Three extended examples demonstrate how localisable monads can interpret the base space as locations in a computer memory, as sites in a network of interacting agents acting concurrently, and as time in stochastic processes.

Cite as

Carmen Constantin, Nuiok Dicaire, and Chris Heunen. Localisable Monads. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{constantin_et_al:LIPIcs.CSL.2022.15,
  author =	{Constantin, Carmen and Dicaire, Nuiok and Heunen, Chris},
  title =	{{Localisable Monads}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.15},
  URN =		{urn:nbn:de:0030-drops-157353},
  doi =		{10.4230/LIPIcs.CSL.2022.15},
  annote =	{Keywords: Monad, Monoidal category, Presheaf, Central idempotent, Graded monad, Indexed monad, Formal monad, Strong monad, Commutative monad}
}

Search Results

Documents authored by Heunen, Chris

Towards Categorical Quantum Concurrency Theory (Invited Talk)

Abstract

Cite as

Localisable Monads

Abstract

Cite as

Thanks for your feedback!

Could not send message