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Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions

Authors: Gilles Barthe, Minbo Gao, Jam Kabeer Ali Khan, Matthijs Muis, Ivan Renison, Keiya Sakabe, Michael Walter, Yingte Xu, Tianshi Yu, and Li Zhou

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)


Abstract
We present sound and complete relational program logics for infinite-dimensional quantum and classical-quantum programs. The logics model assertions as self-adjoint unbounded linear relations, which simultaneously support quantitative and qualitative reasoning. Our main theoretical results include new convergence theorems and infinite-dimensional duality theorems for infinite-dimensional quantum states, which we use to establish completeness.

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Gilles Barthe, Minbo Gao, Jam Kabeer Ali Khan, Matthijs Muis, Ivan Renison, Keiya Sakabe, Michael Walter, Yingte Xu, Tianshi Yu, and Li Zhou. Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 15:1-15:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{barthe_et_al:LIPIcs.LICS.2026.15,
  author =	{Barthe, Gilles and Gao, Minbo and Khan, Jam Kabeer Ali and Muis, Matthijs and Renison, Ivan and Sakabe, Keiya and Walter, Michael and Xu, Yingte and Yu, Tianshi and Zhou, Li},
  title =	{{Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{15:1--15:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.15},
  URN =		{urn:nbn:de:0030-drops-268020},
  doi =		{10.4230/LIPIcs.LICS.2026.15},
  annote =	{Keywords: relational program logics, infinite-dimensional quantum programs, classical-quantum programs, linear relations, quantum optimal transport}
}
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