Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette
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Quantum Physics arXiv:2603.28852 (quant-ph) [Submitted on 30 Mar 2026] Title:Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette Authors:Gilad Kishony, Austin Fowler View a PDF of the paper titled Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette, by Gilad Kishony and Austin Fowler View PDF HTML (experimental) Abstract:Syndrome extraction in the planar color code is complicated by high weight stabilizers and hook errors that can reduce the circuit-level distance. With a single auxiliary qubit per plaquette, any spatially uniform circuit halves the circuit-level distance. We propose a single-auxiliary syndrome extraction circuit with color-dependent gate schedules that avoids all malign hook errors in the bulk, thereby preserving the full circuit-level distance. The circuit has minimal depth: all stabilizers of the same Pauli type are measured in parallel in six time steps. Furthermore, this schedule can be readily applied to the XYZ color code circuit, yielding an improved temporal distance. We find that at the boundary, no single hook error alone reduces the distance; instead, only certain combinations of hook errors do, which we call fractional hook errors. We demonstrate through Monte Carlo simulations over a range of circuit-level noise models and physical error rates that our circuit outperforms the previous state of the art. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.28852 [quant-ph] (or arXiv:2603.28852v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.28852 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gilad Kishony [view email] [v1] Mon, 30 Mar 2026 18:00:01 UTC (195 KB) Full-text links: Access Paper: View a PDF of the paper titled Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette, by Gilad Kishony and Austin FowlerView 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?)