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DOI: 10.4230/LIPIcs.FSCD.2026.12

Resource-Aware Quantum Programming with General Recursion and Quantum Control

Authors: Kostia Chardonnet, Emmanuel Hainry, Romain Péchoux, and Thomas Vinet

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract

This paper introduces the hybrid quantum language with general recursion {{Hyrql}}, driven towards resource-analysis. By design, {{Hyrql}} does not require the specification of an initial set of quantum gates. Hence, it is well amenable towards a generic cost analysis, unlike languages that use different sets of quantum gates, which yield quantum circuits of distinct complexity. Regarding resource-analysis, we show how to relate the runtime of an expressive fragment of {{Hyrql}} programs with the size of the corresponding quantum circuits. We also manage to capture the class of functions computable in quantum polynomial time, which, by Yao’s Theorem, corresponds to families of circuits of polynomial size. Consequently, this result paves the way for the use of termination and runtime-analysis techniques designed for classical programs to guarantee bounds on the size of quantum circuits.

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Kostia Chardonnet, Emmanuel Hainry, Romain Péchoux, and Thomas Vinet. Resource-Aware Quantum Programming with General Recursion and Quantum Control. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chardonnet_et_al:LIPIcs.FSCD.2026.12,
  author =	{Chardonnet, Kostia and Hainry, Emmanuel and P\'{e}choux, Romain and Vinet, Thomas},
  title =	{{Resource-Aware Quantum Programming with General Recursion and Quantum Control}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.12},
  URN =		{urn:nbn:de:0030-drops-263626},
  doi =		{10.4230/LIPIcs.FSCD.2026.12},
  annote =	{Keywords: Hybrid Quantum Programs, Resource Analysis}
}

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Resource-Aware Quantum Programming with General Recursion and Quantum Control

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