Transferred QAOA Parameters Remember the Penalty Scale: A $\lambda$-Resonance Law for Constrained Quantum Optimization

Quantum Physics arXiv:2607.09927 (quant-ph) [Submitted on 10 Jul 2026] Title:Transferred QAOA Parameters Remember the Penalty Scale: A $λ$-Resonance Law for Constrained Quantum Optimization Authors:Krit Grover View a PDF of the paper titled Transferred QAOA Parameters Remember the Penalty Scale: A $\lambda$-Resonance Law for Constrained Quantum Optimization, by Krit Grover View PDF HTML (experimental) Abstract:Training the variational angles of the Quantum Approximate Optimization Algorithm once on a small instance and reusing them on larger ones, known as parameter transfer, is the standard route past the exact-simulation wall. Existing literature explains its success almost entirely through structural similarity. We identify a new, independent axis that governs transfer whenever constraints are encoded as penalties: the trained angles memorize the penalty weight $\lambda$ of their training instance. For any scalarized cost function with an integer-valued violation count, we prove that at arbitrary fixed QAOA angles $(\beta,\gamma)$ of depth $p$, the probability mass $F(\lambda)$ on the feasible subspace is a finite real trigonometric polynomial in $\lambda$ whose angular frequencies lie on an integer lattice generated by the trained $\gamma$'s. Three consequences follow immediately: transfer feasibility is a resonance peaked where the deployment penalty matches the training penalty; the resonance width scales as $1/(v_{max}\sum_k|\gamma_k|)$, so low-$|\gamma|$ angle sets are systematically more transferable; and the curve exhibits revival peaks at spacings $2\pi/\gamma_k$. We confirm all three predictions by exact statevector experiments on a 20-qubit multi-user resource-allocation QUBO. The theorem is independent of how the angles were obtained and applies to any integer-penalty QUBO, recasting a widely reported failure mode of penalty-based QAOA as deterministic, predictable phase interference rather than an energetic tuning problem. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.09927 [quant-ph] (or arXiv:2607.09927v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.09927 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Krit Grover [view email] [v1] Fri, 10 Jul 2026 19:23:41 UTC (242 KB) Full-text links: Access Paper: View a PDF of the paper titled Transferred QAOA Parameters Remember the Penalty Scale: A $\lambda$-Resonance Law for Constrained Quantum Optimization, by Krit GroverView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)