Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree
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Quantum Physics arXiv:2603.23892 (quant-ph) [Submitted on 25 Mar 2026] Title:Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree Authors:Nicholas Connolly, Shin Nishio, Dan E. Browne, Willian John Munro, Kae Nemoto View a PDF of the paper titled Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree, by Nicholas Connolly and 4 other authors View PDF HTML (experimental) Abstract:Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to single-qubit Clifford gates; one may reduce entangling resources by preparing a favorable LC-equivalent representative. However, exhaustive optimization over the LC orbit is not scalable. We address this problem using the split decomposition and its quotient-augmented strong split tree (QASST). For several families of distance-hereditary (DH) graphs, we use the QASST to characterize LC orbits and identify representatives with reduced controlled-Z count or preparation circuit depth. We also introduce a split-fuse construction for arbitrary DH graph states, achieving linear scaling with respect to entangling gates, time steps, and auxiliary qubits. Beyond the DH setting, we discuss a generalized divide-and-conquer split-fuse strategy and a simple greedy heuristic for generic graphs based on triangle enumeration. Together, these methods outperform direct implementations on sufficiently large graphs, providing a scalable alternative to brute-force optimization. Comments: Subjects: Quantum Physics (quant-ph); Discrete Mathematics (cs.DM); Combinatorics (math.CO) MSC classes: 05C76(Primary) 05C30, 05C83, 05C90 (Secondary) ACM classes: G.2.1; G.2.2; F.2.1 Cite as: arXiv:2603.23892 [quant-ph] (or arXiv:2603.23892v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.23892 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nicholas Connolly [view email] [v1] Wed, 25 Mar 2026 03:30:57 UTC (551 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree, by Nicholas Connolly and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.DM math math.CO 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)