Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut

Quantum Physics arXiv:2606.23718 (quant-ph) [Submitted on 17 Jun 2026] Title:Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut Authors:Sidharth Brahmandam, Vayd Ramkumar View a PDF of the paper titled Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut, by Sidharth Brahmandam and Vayd Ramkumar View PDF HTML (experimental) Abstract:The Quantum Approximate Optimization Algorithm (QAOA) is a leading variational algorithm for combinatorial optimization on near term quantum devices. As circuit depth increases, the number of optimization parameters grows, making the search landscape increasingly nonlinear and difficult to optimize. Previous studies have shown that optimal QAOA parameters often lie on a low dimensional manifold that can be approximated using Principal Component Analysis (PCA) at shallow circuit depths. However, the effectiveness of PCA decreases at higher depths because the underlying parameter manifold becomes increasingly nonlinear. In this work, we investigate Kernel Principal Component Analysis (KPCA) with a radial basis function kernel as a nonlinear dimensionality reduction technique for QAOA parameter optimization. The model is trained using 200 graphs from each of 3 graph families, namely Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz, with graph sizes ranging from 7 to 10 nodes. Performance is evaluated on 30 test graphs containing 12 nodes at circuit depths 1, 2, 4, and 8. Experimental results demonstrate that KPCA consistently outperforms PCA at deeper circuit depths across all graph families. At depth 8, KPCA achieves approximation ratios above 0.86, while PCA declines to approximately 0.81 to 0.83. Both methods reduce the number of quantum circuit evaluations by more than 93 percent relative to unrestricted QAOA optimization. These findings suggest that nonlinear kernel methods more effectively capture the structure of the QAOA parameter manifold and provide a practical approach for scaling variational quantum optimization to deeper circuits. Comments: Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2606.23718 [quant-ph] (or arXiv:2606.23718v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.23718 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sidharth Brahmandam [view email] [v1] Wed, 17 Jun 2026 02:06:46 UTC (599 KB) Full-text links: Access Paper: View a PDF of the paper titled Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut, by Sidharth Brahmandam and Vayd RamkumarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.LG 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?)