A four-player potential game for barren-plateau-aware quantum ansatz design
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Quantum Physics arXiv:2604.21955 (quant-ph) [Submitted on 23 Apr 2026] Title:A four-player potential game for barren-plateau-aware quantum ansatz design Authors:Rubén Darío Guerrero View a PDF of the paper titled A four-player potential game for barren-plateau-aware quantum ansatz design, by Rub\'en Dar\'io Guerrero View PDF HTML (experimental) Abstract:We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $\delta_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $\Phi_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes. Comments: Subjects: Quantum Physics (quant-ph); Multiagent Systems (cs.MA) MSC classes: 81P68, 91A10, 90C29, ACM classes: I.2.8; G.1.6; G.1.6 Cite as: arXiv:2604.21955 [quant-ph] (or arXiv:2604.21955v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.21955 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rubén Darío Guerrero Mr. [view email] [v1] Thu, 23 Apr 2026 07:58:46 UTC (110 KB) Full-text links: Access Paper: View a PDF of the paper titled A four-player potential game for barren-plateau-aware quantum ansatz design, by Rub\'en Dar\'io GuerreroView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.MA 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?)