Use case study: benchmarking quantum breadth-first search for maximum flow problems
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Quantum Physics arXiv:2604.24962 (quant-ph) [Submitted on 27 Apr 2026] Title:Use case study: benchmarking quantum breadth-first search for maximum flow problems Authors:Andreea-Iulia Lefterovici, Lara Lelakowski, Michael Perk View a PDF of the paper titled Use case study: benchmarking quantum breadth-first search for maximum flow problems, by Andreea-Iulia Lefterovici and 2 other authors View PDF HTML (experimental) Abstract:The maximum flow problem asks to find the largest possible flow from a source to a sink in a capacitated network. It arises frequently in scheduling, project selection, and as a core subroutine in broader optimisation tasks. Classically, it can be efficiently solved using Dinic's algorithm, which repeatedly performs breadth-first search (BFS) and blocking flow computations on the graph. As a potential candidate for quantum speedups, these BFS subroutines can be naturally replaced with quantum BFS (qBFS), an instantiation of Grover's search algorithm. In this paper, we evaluate the expected performance of qBFS on standard classical datasets. These instances are too large to be solved directly on current quantum hardware, so we adopt a hybrid benchmarking approach: (i) we run a classical implementation of Dinic's algorithm and isolate the runtime of its BFS subroutines; (ii) we analytically estimate the minimum number of quantum cycles required to implement qBFS, where we use the classically logged data. Our results indicate that achieving a practical quantum advantage for realistic problem sizes would translate to quantum gate operation times surpassing physical limitations. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.24962 [quant-ph] (or arXiv:2604.24962v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.24962 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andreea-Iulia Lefterovici [view email] [v1] Mon, 27 Apr 2026 20:03:55 UTC (782 KB) Full-text links: Access Paper: View a PDF of the paper titled Use case study: benchmarking quantum breadth-first search for maximum flow problems, by Andreea-Iulia Lefterovici and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)