Quantum optimisation applied to the Quadratic Assignment Problem

Quantum Physics arXiv:2601.01104 (quant-ph) [Submitted on 3 Jan 2026] Title:Quantum optimisation applied to the Quadratic Assignment Problem Authors:Andrew Freeland, Jingbo Wang View a PDF of the paper titled Quantum optimisation applied to the Quadratic Assignment Problem, by Andrew Freeland and Jingbo Wang View PDF HTML (experimental) Abstract:This paper investigates the performance of the emerging non-variational Quantum Walk-based Optimisation Algorithm (NV-QWOA) for solving small instances of the Quadratic Assignment Problem (QAP). NV-QWOA is benchmarked against classical heuristics, the MaxMin Ant System (MMAS) and Greedy Local Search (GLS), as well as the Grover quantum search algorithm, which serves as a quantum baseline. Performance is evaluated using two metrics: the number of objective function evaluations and the number of algorithm iterations required to consistently reach optimal or near optimal solutions across QAP instances with 5 to 10 facilities. The motivation for this study stems from limitations of both classical exact methods and current quantum algorithms.

Variational Quantum Algorithms (VQAs), such as QAOA and VQE, while widely studied, suffer from costly parameter tuning and barren plateaus that hinder convergence. By adopting a non-variational approach, this work explores a potentially more efficient and scalable quantum strategy for combinatorial optimisation. The results provide a direct comparative analysis between classical and quantum frameworks, characterising the average case performance of NV-QWOA. Our findings highlight the practical utility of quantum walks for complex combinatorial problems and establish a foundation for future quantum optimisation algorithms. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.01104 [quant-ph] (or arXiv:2601.01104v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.01104 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jingbo Wang [view email] [v1] Sat, 3 Jan 2026 07:50:03 UTC (731 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum optimisation applied to the Quadratic Assignment Problem, by Andrew Freeland and Jingbo WangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)