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Causality in Pure Quantum Computation with Quantum Control

Authors Kengo Hirata , Takeshi Tsukada

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LIPIcs.LICS.2026.57.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Type theory
  • Theory of computation → Linear logic
  • Theory of computation → Categorical semantics
Keywords
  • Quantum computing
  • supermap
  • categorical model
  • linear logic
  • BV logic
  • programming language
  • type system

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Abstract

Indefinite causal order is a characteristic phenomenon in quantum computation, with examples including the quantum SWITCH and the OCB process. Not all such processes are believed to be physically realizable: while some implementations of the quantum SWITCH have been proposed, the OCB process is suspected to be unrealizable. This difference in realizability is commonly attributed to constraints imposed by physical causality.
This paper studies such a causality issue in a higher-order setting, proposing a typed lambda calculus with quantum control and its categorical semantics. Our calculus extends pure quantum computation with higher-order functions and quantum conditional branching, and it is equipped with a type system based on intuitionistic BV logic to enforce causality. We also present a novel model that is closely related to the Caus construction, by which we prove that some physically-unrealizable processes are not definable in our language.

Cite As Get BibTex

Kengo Hirata and Takeshi Tsukada. Causality in Pure Quantum Computation with Quantum Control. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 57:1-57:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.LICS.2026.57

Author Details

Kengo Hirata
  • University of Edinburgh, UK
  • Kyoto University, Japan
Takeshi Tsukada
  • Chiba University, Japan

Funding

This work was supported by JST CREST, Japan, Grant Number JPMJCR25I5.

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