{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3d4cde0236620825000a64ee272452d07657df601058619b2791cc80a474a013","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["3b3d6503046b814e7a36e366bdbb73c08d57731e7d09311982ede96ded1b7d47","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"a933de64644390226445df9e36b862e9ac2f43c4a5b1e958ed8883e3e2aec877","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":["ai:gpt-5.5"],"external_id":"qi.hamiltonian-complexity.commuting-hamiltonian-np","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"When all energy terms of a quantum system commute, deciding whether it has zero ground energy looks closer to a classical problem. It is proven to have short classical proofs in several special cases but not in general.","posed_since":"2003","precise":"Given $H = \\sum_i h_i$ with pairwise commuting k-local projectors $h_i$ on qudits of dimension $q$, decide whether the ground energy is 0 or at least $1/\\operatorname{poly}(n)$. Is this in NP for all constant k and q? Known in NP: 2-local (Bravyi and Vyalyi 2003), some 3-local cases (Aharonov and Eldar 2011), $2\\mathrm{D}$ qubits (Schuch 2011), $2\\mathrm{D}$ qutrits and factorized terms of any dimension (Irani and Jiang, arXiv:2309.04910).","problem_ref":"3b3d6503046b814e7a36e366bdbb73c08d57731e7d09311982ede96ded1b7d47","references":"","settled_by":"A classical witness and verifier for all constant k and q, or QMA-hardness (or hardness for a class not believed in NP) for some fixed k and q.","status_note":"","title":"Is the commuting local Hamiltonian problem in 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