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DOI: 10.4230/LIPIcs.MFCS.2025.47

Quantum Programming in Polylogarithmic Time

Authors: Florent Ferrari, Emmanuel Hainry, Romain Péchoux, and Mário Silva

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the complexity class FBQPOLYLOG of functions approximable in polylogarithmic time with a quantum random access Turing machine. We introduce a quantum programming language with first-order recursive procedures, which provides the first programming language-based characterization of FBQPOLYLOG. Each program computes a function in FBQPOLYLOG (soundness) and, conversely, each function of this complexity class is computed by a program (completeness). We also provide a compilation strategy from programs to uniform families of quantum circuits of polylogarithmic depth and polynomial size, whose set of computed functions is known as qnc, and recover the well-known separation result FBQPOLYLOG ⊊ QNC.

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Florent Ferrari, Emmanuel Hainry, Romain Péchoux, and Mário Silva. Quantum Programming in Polylogarithmic Time. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ferrari_et_al:LIPIcs.MFCS.2025.47,
  author =	{Ferrari, Florent and Hainry, Emmanuel and P\'{e}choux, Romain and Silva, M\'{a}rio},
  title =	{{Quantum Programming in Polylogarithmic Time}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.47},
  URN =		{urn:nbn:de:0030-drops-241547},
  doi =		{10.4230/LIPIcs.MFCS.2025.47},
  annote =	{Keywords: Quantum programming languages, Polylogarithmic time, Quantum circuits, Implicit computational complexity}
}

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Quantum Programming in Polylogarithmic Time

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