Principles of Quantum Optimization for Constrained Problems

Quantum Physics arXiv:2607.14227 (quant-ph) [Submitted on 15 Jul 2026] Title:Principles of Quantum Optimization for Constrained Problems Authors:Einar Gabbassov, Gurpahul Singh, Achim Kempf View a PDF of the paper titled Principles of Quantum Optimization for Constrained Problems, by Einar Gabbassov and 2 other authors View PDF HTML (experimental) Abstract:Constrained combinatorial optimization underlies many industrial and technological decision problems. We develop a spectral theory that unifies many quantum optimization algorithms. We show that computational slowdown is driven by entanglement restructuring: the creation, redistribution, and destruction of entanglement during system evolution. The severity of the slowdown depends on how much entanglement must be changed. We show that algebraic properties of constraints induce such restructuring, and that constraint-aware dynamics reduce the associated slowdown by avoiding unnecessary restructuring. This framework explains why constraint-aware quantum methods can outperform generic penalty-based approaches. The theory connects constrained optimization, computational complexity, entanglement dynamics, and Hamiltonian spectral structure across continuous-time and circuit-based quantum optimization paradigms. Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Cite as: arXiv:2607.14227 [quant-ph] (or arXiv:2607.14227v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.14227 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Einar Gabbassov [view email] [v1] Wed, 15 Jul 2026 18:00:31 UTC (2,959 KB) Full-text links: Access Paper: View a PDF of the paper titled Principles of Quantum Optimization for Constrained Problems, by Einar Gabbassov and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: math math.OC 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?)