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Quantum Programming in Polylogarithmic Time

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum programming languages
  • Polylogarithmic time
  • Quantum circuits
  • Implicit computational complexity

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.MFCS.2025.47

Author Details

Florent Ferrari
  • École Normale Supérieure de Lyon, France
Emmanuel Hainry
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Romain Péchoux
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Mário Silva
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France

Funding

This work is supported by the the Plan France 2030 through the PEPR integrated project EPiQ ANR-22-PETQ-0007 and the HQI platform ANR-22-PNCQ-0002; and by the European Union through the MSCA SE project QCOMICAL (Grant Agreement ID: 101182520), project NEASQC (Grant Agreement 951821), and project HPCQS (Grant Agreement 101018180).

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