From Tensor Networks to Tractable Circuits, and back
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Quantum Physics arXiv:2605.00106 (quant-ph) [Submitted on 30 Apr 2026] Title:From Tensor Networks to Tractable Circuits, and back Authors:Arend-Jan Quist, Marc Farreras Bartra, Alexis de Colnet, John van de Wetering, Alfons Laarman View a PDF of the paper titled From Tensor Networks to Tractable Circuits, and back, by Arend-Jan Quist and 4 other authors View PDF HTML (experimental) Abstract:Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We show that some classes of tensor networks that are appealing in practice correspond to classes of circuits with specific properties that have been studied in knowledge compilation as \emph{tractable circuits}. In particular, we prove that matrix product states (tensor trains) coincide with nondeterministic edge-valued decision diagrams and that tree tensor networks exactly correspond to structured-decomposable circuits. These correspondences enable direct transfer of structural and algorithmic results; for example, canonicity and tractability guarantees known for circuits yield analogous guarantees for the associated tensor networks, and vice versa. Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Logic in Computer Science (cs.LO) Cite as: arXiv:2605.00106 [quant-ph] (or arXiv:2605.00106v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.00106 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arend-Jan Quist [view email] [v1] Thu, 30 Apr 2026 18:01:40 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled From Tensor Networks to Tractable Circuits, and back, by Arend-Jan Quist and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.DS cs.LO 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?)