Quantum Programming in Polylogarithmic Time

Fuente: arXiv
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Main Authors: Ferrari, Florent, Hainry, Emmanuel, Péchoux, Romain, Silva, Mário
Format: Preprint
Published: 2025
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author Ferrari, Florent
Hainry, Emmanuel
Péchoux, Romain
Silva, Mário
author_facet Ferrari, Florent
Hainry, Emmanuel
Péchoux, Romain
Silva, Mário
contents 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 $\subsetneq$ QNC.
format Preprint
id arxiv_https___arxiv_org_abs_2507_15415
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantum Programming in Polylogarithmic Time
Ferrari, Florent
Hainry, Emmanuel
Péchoux, Romain
Silva, Mário
Logic in Computer Science
Programming Languages
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 $\subsetneq$ QNC.
title Quantum Programming in Polylogarithmic Time
topic Logic in Computer Science
Programming Languages
url https://arxiv.org/abs/2507.15415