Neural Minimum Weight Perfect Matching for Quantum Error Codes
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Quantum Physics arXiv:2601.00242 (quant-ph) [Submitted on 1 Jan 2026] Title:Neural Minimum Weight Perfect Matching for Quantum Error Codes Authors:Yotam Peled, David Zenati, Eliya Nachmani View a PDF of the paper titled Neural Minimum Weight Perfect Matching for Quantum Error Codes, by Yotam Peled and 2 other authors View PDF HTML (experimental) Abstract:Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings demonstrate significant performance reduction in the Logical Error Rate (LER) over standard baselines, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching. Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Machine Learning (cs.LG) Cite as: arXiv:2601.00242 [quant-ph] (or arXiv:2601.00242v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.00242 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eliya Nachmani [view email] [v1] Thu, 1 Jan 2026 07:25:51 UTC (355 KB) Full-text links: Access Paper: View a PDF of the paper titled Neural Minimum Weight Perfect Matching for Quantum Error Codes, by Yotam Peled and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.AI cs.IT cs.LG math math.IT 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?)