{"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/analytic-and-numerical-demonstration-of","title":"Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code","arxiv_id":"1112.3252","date":"2011-12-14","proceeding":null,"authors":["Sergey Bravyi","Jeongwan Haah"],"abstract":"A big open question in the quantum information theory concerns feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction if the memory is put in contact with a cold enough thermal bath. In this paper we derive a rigorous lower bound on the memory time $T_{mem}$ of the 3D Cubic Code model which was recently conjectured to have a self-correcting behavior. Assuming that dynamics of the memory system can be described by a Markovian master equation of Davies form, we prove that $T_{mem}\\ge L^{c\\beta}$ for some constant $c>0$, where $L$ is the lattice size and $\\beta$ is the inverse temperature of the bath. However, this bound applies only if the lattice size does not exceed certain critical value $L^*\\sim e^{\\beta/3}$. We also report a numerical Monte Carlo simulation of the studied memory indicating that our analytic bounds on $T_{mem}$ are tight up to constant coefficients. In order to model the readout step we introduce a new decoding algorithm which might be of independent interest. Our decoder can be implemented efficiently for any topological stabilizer code and has a constant error threshold under random uncorrelated errors.","url_abs":"https://arxiv.org/abs/1112.3252v1","url_pdf":"https://arxiv.org/pdf/1112.3252v1.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":"analytic-and-numerical-demonstration-of","repo_url":"https://github.com/Jonsm/ClusterDecoders","is_official":0,"mentioned_in_paper":0,"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}