Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power
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Quantum Physics arXiv:2602.07201 (quant-ph) [Submitted on 6 Feb 2026] Title:Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power Authors:Wenhan Guo, Mikhail Litvinov, Tzu-Chieh Wei, Abid Khan, Kevin C. Smith View a PDF of the paper titled Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power, by Wenhan Guo and 4 other authors View PDF HTML (experimental) Abstract:We investigate a constant-time, fusion measurement-based scheme to create AKLT states beyond one dimension. We show that it is possible to prepare such states on a given graph up to random spin-1 `decorations', each corresponding to a probabilistic insertion of a vertex along an edge. In investigating their utility in measurement-based quantum computation, we demonstrate that any such randomly decorated AKLT state possesses at least the same computational power as non-random ones, such as those on trivalent planar lattices. For AKLT states on Bethe lattices and their decorated versions we show that there exists a deterministic, constant-time scheme for their preparation. In addition to randomly decorated AKLT states, we also consider random-bond AKLT states, whose construction involves any of the canonical Bell states in the bond degrees of freedom instead of just the singlet in the original construction. Such states naturally emerge upon measuring all the decorative spin-1 sites in the randomly decorated AKLT states. We show that those random-bond AKLT states on trivalent lattices can be converted to encoded random graph states after acting with the same POVM on all sites. We also argue that these random-bond AKLT states possess similar quantum computational power as the original singlet-bond AKLT states via the percolation perspective. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.07201 [quant-ph] (or arXiv:2602.07201v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.07201 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tzu-Chieh Wei [view email] [v1] Fri, 6 Feb 2026 21:22:35 UTC (3,071 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power, by Wenhan Guo and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)