Towards Efficient Synthesis of Quantum Graph States by Fusing Graph Motifs
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Quantum Physics arXiv:2606.02880 (quant-ph) [Submitted on 1 Jun 2026] Title:Towards Efficient Synthesis of Quantum Graph States by Fusing Graph Motifs Authors:Tingxiang Ji, Hansika Weerasena, Demitry Farfurnik, Jianqing Liu View a PDF of the paper titled Towards Efficient Synthesis of Quantum Graph States by Fusing Graph Motifs, by Tingxiang Ji and Hansika Weerasena and Demitry Farfurnik and Jianqing Liu View PDF HTML (experimental) Abstract:Photonic graph states with advanced topologies can enable measurement-based quantum computing, distributed quantum sensing, and quantum interconnects. However, the efficient generation of photonic graph states is limited by the probabilistic nature of photonic entangling operations and the exponential dependence of generation rate on resource cost. In this work, we study photonic graph state synthesis as a cost-aware decomposition problem, exploiting local Clifford (LC) equivalence to identify more synthesis-friendly representations of the target graph state before decomposition. Specifically, we propose Cost-aware Fusion-based Decomposition (CFD), a three-stage heuristic framework that decomposes a target graph state into ring, star, and linear motifs, and assembles them via Type-I fusion operations to minimize fusion overhead and physical-qubit consumption. We further show that selecting the LC-equivalent graph state with the minimum number of edges provides a highly effective proxy for near-optimal synthesis: in many cases it matches the best generation rate observed within the LC equivalence class under CFD, and in most remaining cases it remains close to it. Numerical evaluations on graph state orbit data and 2D and 3D lattice graph states demonstrate that CFD achieves up to 84.6\% reduction in resource overhead compared to baseline constructions, and yields improvements in photonic generation rate spanning multiple orders of magnitude. These results suggest that combining structure-aware motif decomposition with LC equivalence is a practical and scalable strategy for photonic graph state synthesis. Subjects: Quantum Physics (quant-ph); Computational Geometry (cs.CG); Systems and Control (eess.SY) Cite as: arXiv:2606.02880 [quant-ph] (or arXiv:2606.02880v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.02880 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jianqing Liu [view email] [v1] Mon, 1 Jun 2026 20:51:29 UTC (2,149 KB) Full-text links: Access Paper: View a PDF of the paper titled Towards Efficient Synthesis of Quantum Graph States by Fusing Graph Motifs, by Tingxiang Ji and Hansika Weerasena and Demitry Farfurnik and Jianqing LiuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.CG cs.SY eess eess.SY 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?)