{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"39af337d57164e4d180c55848f8484061e921933798d9f475cdcb18e0b39f378","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d0afd7fb6dafd34ec17b6d814c7c1e214e6c5ada0df240ef8fadaddcfb8d2f8e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.self-correcting-memory.two-dimensional-no-go","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Simple two-dimensional quantum codes are proven unable to protect a qubit passively against heat. Whether every two-dimensional system, including more complicated ones, must also fail is not proven.","posed_since":"2009","precise":"For any 2D local Hamiltonian on finite-dimensional spins (commuting or not, stabilizer or not) coupled weakly to a thermal bath at $T > 0$, prove that the memory time of every encoded qubit is bounded by a function of $T$ alone, independent of system size, or give a counterexample. No-go theorems cover 2D commuting Pauli stabilizer codes (Bravyi and Terhal 2009) and commuting-projector models with local topological order (Landon-Cardinal and Poulin 2013).","problem_ref":null,"references":"","settled_by":"A general no-go proof for $2\\mathrm{D}$ local Hamiltonians, or an explicit $2\\mathrm{D}$ model with memory time growing with size at fixed $T > 0$.","status_note":"","title":"Is self-correction impossible for every two-dimensional local 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