{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"731e27b7ba16ef3589a5e44368b30e87956df8011bc92396a4ed56c91d45b566","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","83eee09d9c1695b9e7ca17cc4adae820fb0e56631d118528edcbb4eb3c9a4cc7"],"salt":"c7c024968c5c4d0d2db0f50c23136eb62cd6e2e3d33f17c5bb1c6f48582f0c55","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.self-correcting-memory.translation-invariant-3d","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"83eee09d9c1695b9e7ca17cc4adae820fb0e56631d118528edcbb4eb3c9a4cc7","relation":"special_case"}],"plain":"The known three-dimensional candidates either fail eventually at large sizes or give up the regular, repeating structure of a crystal. Whether a perfectly periodic three-dimensional system can be a true passive quantum memory is open.","posed_since":"2011","precise":"Does a translation-invariant local commuting Pauli stabilizer Hamiltonian on a 3D cubic lattice exist whose memory time at fixed $T > 0$ grows without bound in system size $L$? Haah's cubic code has an energy barrier $\\sim \\log L$, giving memory time growing with $L$ only up to $L \\sim \\exp(c/T)$; Yoshida (2011) excludes stabilizer codes with both translation and scale symmetry.","problem_ref":null,"references":"","settled_by":"An explicit translation-invariant 3D stabilizer code with a proof of unbounded memory time at fixed T, or a no-go theorem for this class.","status_note":"Layer codes (2023-2025) and cored product codes (2026) give partial self-correction; the 2026 full construction breaks translation symmetry.","title":"Translation-invariant self-correcting stabilizer memory in three dimensions","topic_ref":"0ac91b5262bc7d232a08682ee033f23c99f87d6c0e1021af156138bac07de11f"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5733937023b42841ef4a84d3f61ad76c184debc00667efbc944d6d5365fb43f8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"53809bfbfd2b0407a5b98daadb6c83e87501ca73610b16e286b5ee0388662a89","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"jlQRPWVB4qD-mTcXkcMDvu8qX50W0qKt4F6Obft-T9gJdxg9WBjYI0X44PhSJBP6YC4uJMNDM5JRo0F7yakxDQ"},"schema":"pubphys.envelope/1"},"record_hash":"5733937023b42841ef4a84d3f61ad76c184debc00667efbc944d6d5365fb43f8","leaf_index":2051}