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DOI: 10.4230/LIPIcs.ICALP.2025.157

Bayesian Inference in Quantum Programs

Authors: Christina Gehnen, Dominique Unruh, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also known as Bayesian inference. This paper equips a quantum while-language with conditioning, defines its denotational and operational semantics over infinite-dimensional Hilbert spaces, and shows their equivalence. We provide sufficient conditions for the existence of weakest (liberal) precondition-transformers and derive inductive characterizations of these transformers. It is shown how w(l)p-transformers can be used to assess the effect of Bayesian inference on (possibly diverging) quantum programs.

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Christina Gehnen, Dominique Unruh, and Joost-Pieter Katoen. Bayesian Inference in Quantum Programs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 157:1-157:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gehnen_et_al:LIPIcs.ICALP.2025.157,
  author =	{Gehnen, Christina and Unruh, Dominique and Katoen, Joost-Pieter},
  title =	{{Bayesian Inference in Quantum Programs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{157:1--157:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.157},
  URN =		{urn:nbn:de:0030-drops-235345},
  doi =		{10.4230/LIPIcs.ICALP.2025.157},
  annote =	{Keywords: Quantum Program Logics, Weakest Preconditions, Bayesian Inference, Program Semantics}
}

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Bayesian Inference in Quantum Programs

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