{"paper":{"title":"Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study","license":"","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"H. Bombin, M.A. Martin-Delgado","submitted_at":"2007-03-29T13:47:17Z","abstract_excerpt":"We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer codes. We compute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color codes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and $C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For planar codes, a typical value is $C_s=2$, while we find th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0703272","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0703272/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}