{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/constructions-and-performance-of-hyperbolic","title":"Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes","arxiv_id":"2308.03750","date":"2023-08-07","proceeding":null,"authors":["Oscar Higgott","Nikolas P. Breuckmann"],"abstract":"We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. These codes have weight-two check operators, a finite encoding rate and can be decoded efficiently with minimum-weight perfect matching. We also construct semi-hyperbolic Floquet codes, which have improved distance scaling, and are obtained via a fine-graining procedure. Using a circuit-based noise model that assumes direct two-qubit measurements, we show that semi-hyperbolic Floquet codes can be $48\\times$ more efficient than planar honeycomb codes and therefore over $100\\times$ more efficient than alternative compilations of the surface code to two-qubit measurements, even at physical error rates of $0.3\\%$ to $1\\%$. We further demonstrate that semi-hyperbolic Floquet codes can have a teraquop footprint of only 32 physical qubits per logical qubit at a noise strength of $0.1\\%$. For standard circuit-level depolarising noise at $p=0.1\\%$, we find a $30\\times$ improvement over planar honeycomb codes and a $5.6\\times$ improvement over surface codes. Finally, we analyse small instances that are amenable to near-term experiments, including a Floquet code derived from the Bolza surface that encodes four logical qubits into 16 physical qubits.","url_abs":"https://arxiv.org/abs/2308.03750v2","url_pdf":"https://arxiv.org/pdf/2308.03750v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"constructions-and-performance-of-hyperbolic","repo_url":"https://github.com/oscarhiggott/hyperbolic-floquet-data","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}