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DOI: 10.4230/LIPIcs.FSTTCS.2021.51
Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

Authors: Dongho Lee, Valentin Perrelle, Benoît Valiron, and Zhaowei Xu

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data - qubits - into classical data - booleans -. We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.
Cite as

Dongho Lee, Valentin Perrelle, Benoît Valiron, and Zhaowei Xu. Concrete Categorical Model of a Quantum Circuit Description Language with Measurement. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 51:1-51:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lee_et_al:LIPIcs.FSTTCS.2021.51,
  author =	{Lee, Dongho and Perrelle, Valentin and Valiron, Beno\^{i}t and Xu, Zhaowei},
  title =	{{Concrete Categorical Model of a Quantum Circuit Description Language with Measurement}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{51:1--51:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.51},
  URN =		{urn:nbn:de:0030-drops-155627},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.51},
  annote =	{Keywords: Categorical semantics, Operational semantics, Quantum circuit description language}
}
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