Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus
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Quantum Physics arXiv:2603.06764 (quant-ph) [Submitted on 6 Mar 2026] Title:Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus Authors:Fedor Kuyanov, Aleks Kissinger View a PDF of the paper titled Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus, by Fedor Kuyanov and Aleks Kissinger View PDF HTML (experimental) Abstract:In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of width $R$, our method simulates a graph-like ZX-diagram in $Õ(4^R)$ time. Applied to classical simulation of quantum circuits, it is no slower than either naive state vector simulation or stabiliser decompositions with $\alpha = 0.5$, and in practice can be significantly faster for suitably chosen rank-decompositions. Since finding optimal rank-decompositions is NP-hard, we introduce heuristics that produce good decompositions in practice. We benchmark our simulation routine against Quimb, a popular tensor contraction library, and observe substantial reductions in floating-point operations (often by several orders of magnitude) for random and structured non-Clifford circuits as well as random ZX-diagrams. Comments: Subjects: Quantum Physics (quant-ph) MSC classes: 81P68 (Primary) 68Q12 (Secondary) Cite as: arXiv:2603.06764 [quant-ph] (or arXiv:2603.06764v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.06764 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Fedor Kuyanov [view email] [v1] Fri, 6 Mar 2026 15:00:04 UTC (2,854 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Classical Simulation of Low-Rank-Width Quantum Circuits Using ZX-Calculus, by Fedor Kuyanov and Aleks KissingerView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)