Denser Planar Color Codes

Quantum Physics arXiv:2609.21376 (quant-ph) [Submitted on 18 Sep 2026] Title:Denser Planar Color Codes Authors:Noah Shutty View a PDF of the paper titled Denser Planar Color Codes, by Noah Shutty View PDF HTML (experimental) Abstract:We consider the 4.8.8 color code in a brickwork layout on the square lattice with nearest-neighbor gates. We identify periodic superdense circuits with twelve CNOT layers that appear to preserve the full distance of these codes. Including ancillas, the family uses $q=(2d^2+5d-5)/2$ physical qubits for distance $d$: asymptotically $2/3$ as many as the triangular 6.6.6 color code and $1/2$ as many as the rotated surface code at the same code distance. Circuit-level simulations targeting superconducting architectures demonstrate favorable scaling of 4.8.8 color codes at plausible physical noise rates, including both for planar codes and their toroidal cousins under periodic boundary conditions. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.21376 [quant-ph] (or arXiv:2609.21376v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.21376 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Noah Shutty [view email] [v1] Fri, 18 Sep 2026 06:41:47 UTC (1,829 KB) Full-text links: Access Paper: View a PDF of the paper titled Denser Planar Color Codes, by Noah ShuttyView 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?)