{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"70caa055f4057a5e9c87aac99ff06fa0441ac676bfef986a389c58e74eeef9ab","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","e3f94851392a5556e4c9003a0d53c0169c65251feced51461c6e659978835014"],"salt":"c6277017c4f8dee001e63925c8fcdf72970e074df3e8049b8a591d817c2e01c5","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":"2","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":"e3f94851392a5556e4c9003a0d53c0169c65251feced51461c6e659978835014","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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