Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid
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Quantum Physics arXiv:2606.19482 (quant-ph) [Submitted on 17 Jun 2026] Title:Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid Authors:Boren Gu, Tamas Noszko, Vincent Steffan, Jens Niklas Eberhardt, Joschka Roffe, Jens Eisert, Stergios Koutsioumpas View a PDF of the paper titled Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid, by Boren Gu and 6 other authors View PDF HTML (experimental) Abstract:High-performance quantum low-density parity-check codes promise substantial reductions in the overhead of fault-tolerant quantum computation, but most constructions require long-range connectivity or qubit shuttling, both of which are difficult to realise in superconducting architectures. Here we introduce a family of quantum low-density parity-check codes that, for the first time, combines planar open-boundary layouts, finite-size advantages over surface codes, and syndrome extraction using only nearest-neighbour gates on a square grid of qubits. The key idea is to generate check-data connectivity dynamically: nearest-neighbour iSWAP walks both define the stabiliser supports and implement their measurement, avoiding the need for a long-range hardware graph. The resulting circuits achieve optimal constant-depth stabiliser measurement, independent of code size, and naturally remove leakage from the system by exchanging the role of check and data qubits at each syndrome extraction round. We find finite-size instances such as a [[323,14,15]] code, whose code-efficiency ratio is nearly an order of magnitude larger than that of rotated surface-code patches. At around 30 circuit qubits per logical qubit, the best directional tile-code layouts reduce the per-logical per-round logical error rate by up to a factor of 1000 relative to rotated surface-code memories. These results show that the advantages of quantum low-density parity-check codes can survive compilation into strictly planar nearest-neighbour circuits, bringing low-overhead fault-tolerant memories closer to near-term hardware. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.19482 [quant-ph] (or arXiv:2606.19482v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.19482 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jens Eisert [view email] [v1] Wed, 17 Jun 2026 18:14:23 UTC (5,316 KB) Full-text links: Access Paper: View a PDF of the paper titled Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid, by Boren Gu and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)