A Denser Planar Surface Code
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Quantum Physics arXiv:2605.30455 (quant-ph) [Submitted on 28 May 2026] Title:A Denser Planar Surface Code Authors:Guang Hao Low, William J. Huggins, Dominic W. Berry, Tanuj Khattar, Alec F. White, Nicholas C. Rubin, Ryan Babbush View a PDF of the paper titled A Denser Planar Surface Code, by Guang Hao Low and William J. Huggins and Dominic W. Berry and Tanuj Khattar and Alec F. White and Nicholas C. Rubin and Ryan Babbush View PDF HTML (experimental) Abstract:We present a quantum code implementable on a regular $2$D hex grid with an estimated encoding rate up to $4.5\times$ of that of a rotated surface code patch using circuit-level noise in a one- and two-qubit $10^{-3}$ error uniform depolarizing model. Our approach is based on yoking a dense packing of surface code twist defects, enabled by new stabilizer measurement cycles with an optimal four layers of nearest-neighbor two-qubit gates, almost no distance-reducing hook errors, and efficient decoding. We demonstrate a space-efficient architecture for computing on densely packed logical qubits, including new padding-free lattice surgery protocols in an optimal bounding box of $2d^2$ data and measurement qubits per patch. Assuming a $1\mu$s surface code cycle time and a $10\mu$s reaction time, these developments enable chemically accurate ground state phase estimation of a broad class of `utility-scale' electronic structure simulation problems such as the $108$ spin-orbital FeMoco-based nitrogen fixation catalyst in under a month with $89$k noisy superconducting qubits. We elucidate a Pareto frontier of space-time trade-offs and find a minimum physical quantum volume of $1.3$ mega-qubit-hours. These correspond to a $36\times$ space and $6.6\times$ spacetime improvement, respectively, over our previous state-of-the-art minimum-Toffoli resource estimates (Phys. Rev. X 15, 041016). Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.30455 [quant-ph] (or arXiv:2605.30455v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.30455 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Guang Hao Low [view email] [v1] Thu, 28 May 2026 18:27:34 UTC (24,136 KB) Full-text links: Access Paper: View a PDF of the paper titled A Denser Planar Surface Code, by Guang Hao Low and William J. Huggins and Dominic W. Berry and Tanuj Khattar and Alec F. White and Nicholas C. Rubin and Ryan BabbushView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)