Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA

Quantum Physics arXiv:2608.07686 (quant-ph) [Submitted on 7 Aug 2026] Title:Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA Authors:Tobias Rohe, Federico Harjes Ruiloba, Markus Baumann, Gerhard Stenzel, Leo Sünkel, Thomas Gabor, Claudia Linnhoff-Popien View a PDF of the paper titled Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA, by Tobias Rohe and 6 other authors View PDF HTML (experimental) Abstract:In the Quantum Approximate Optimization Algorithm (QAOA), the entanglement topology, where qubit pairs are connected by two-qubit gates, is conventionally set equal to the edge set of the problem graph. This coupling ties circuit design to explicit problem knowledge and may not yield the most trainable circuit under limited optimization budgets. We investigate whether a reinforcement learning (RL) agent can discover more effective entanglement topologies for QAOA-based MaxCut optimization without direct access to the problem graph. A Masked Proximal Policy Optimization agent sequentially places IsingZZ gates to construct a circuit topology, while a variational inner loop optimizes the resulting QAOA parameters and returns the approximation ratio as a sparse terminal reward. The agent's observation contains only the edges placed so far and the current approximation ratio; graph structure can only be inferred indirectly through the optimization reward. On Erdős--Rényi instances with up to $10$~qubits, the agent consistently converges to topologies that are strict subsets of the problem graph, achieving overlap ratios approaching $1.0$, despite receiving no explicit information about the graph structure in its observations. These sparse, problem-aligned topologies outperform the full graph topology and several structural baselines when the optimization budget is limited ($50$~gradient steps), but are overtaken by denser topologies given sufficient optimization budget. Our results reveal a trainability--expressibility trade-off governed by topology density and suggest that the variational optimization landscape implicitly encodes structural information about the problem Hamiltonian. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.07686 [quant-ph] (or arXiv:2608.07686v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.07686 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tobias Rohe [view email] [v1] Fri, 7 Aug 2026 18:17:08 UTC (150 KB) Full-text links: Access Paper: View a PDF of the paper titled Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA, by Tobias Rohe and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)