Sparse-Blossom Decoding in $o(1)$ Time

Quantum Physics arXiv:2609.12262 (quant-ph) [Submitted on 10 Sep 2026] Title:Sparse-Blossom Decoding in $o(1)$ Time Authors:Ryo Mikami, Hayata Yamasaki View a PDF of the paper titled Sparse-Blossom Decoding in $o(1)$ Time, by Ryo Mikami and 1 other authors View PDF HTML (experimental) Abstract:Matching-based decoding is widely used in quantum error correction, and accelerating it is key to enabling fast and scalable fault-tolerant quantum computation. Minimum-weight perfect matching (MWPM) decoding provides rigorous guarantees for error suppression, while sparse blossom enables its practical implementation at modest problem sizes. However, the runtime of existing sparse-blossom implementations unavoidably increases with problem size, motivating a rigorous parallelization framework that guarantees correctness and a runtime shorter than the syndrome-extraction timescale. Here, we present such a framework and prove that the resulting parallel sparse-blossom algorithm produces the same correction as the original, non-parallel sparse blossom. For the rotated surface code with code distance $d$ and physical error rates below a finite threshold, we prove that the average parallel runtime of decoding for $O(d)$ rounds of syndrome extraction is upper bounded by a quasi-polylogarithmic function of $d$. For a $d$-round decoding window, this implies that the average parallel runtime per round is $o(1)$. We also perform numerical simulation to identify conditions under which the parallel runtime per round decreases with increasing code distance. These results suggest that increasing code distance need not lead to longer parallel decoding times, providing a foundation for scalable parallel matching-based decoding. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.12262 [quant-ph] (or arXiv:2609.12262v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.12262 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ryo Mikami [view email] [v1] Thu, 10 Sep 2026 22:38:01 UTC (621 KB) Full-text links: Access Paper: View a PDF of the paper titled Sparse-Blossom Decoding in $o(1)$ Time, by Ryo Mikami and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)