Entanglement Scaling and Problem Structure in Quantum Approximate and Adiabatic Optimization Algorithms
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Quantum Physics arXiv:2606.19502 (quant-ph) [Submitted on 17 Jun 2026] Title:Entanglement Scaling and Problem Structure in Quantum Approximate and Adiabatic Optimization Algorithms Authors:Georgios Arapantonis, Paraj Titum, Gregory Quiroz View a PDF of the paper titled Entanglement Scaling and Problem Structure in Quantum Approximate and Adiabatic Optimization Algorithms, by Georgios Arapantonis and 2 other authors View PDF HTML (experimental) Abstract:Entanglement is widely regarded as a key resource underlying the power of quantum algorithms and their potential to achieve quantum advantage. With the emergence of variational quantum algorithms, however, questions have arisen regarding how entanglement relates to problem structure and algorithmic performance in near-term quantum applications. Here, we examine this relationship through the Quantum Approximate Optimization Algorithm (QAOA), a specific class of variational algorithms, applied to the MaxCut problem. We show that suboptimal variational parameter training can significantly modify the observed entanglement profile, obscuring its scaling behavior. By employing a high-performance optimizer, we find empirical evidence that QAOA exhibits entanglement scaling consistent with that of fermionic Gaussian states (up to a scaling factor) across a broad range of MaxCut instances. We further compare these results with adiabatic quantum computation, observing annealing-schedule-dependent entanglement profiles whose scaling behavior differs markedly from that of QAOA. Together, these findings provide new insight into how entanglement manifests in and distinguishes these two algorithmic paradigms, highlighting its connection to both computational performance and application structure. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.19502 [quant-ph] (or arXiv:2606.19502v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.19502 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Georgios Arapantonis [view email] [v1] Wed, 17 Jun 2026 18:40:43 UTC (1,222 KB) Full-text links: Access Paper: View a PDF of the paper titled Entanglement Scaling and Problem Structure in Quantum Approximate and Adiabatic Optimization Algorithms, by Georgios Arapantonis and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)