{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d3eab26ca1b79e797d4275e74d697ac1ad51751986e36afde839b475b53b5aef","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"bdee76567ed97be818a4e29e78f75581d514b373fbc77264a40613e200fa8d88","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.hamiltonian-complexity.commuting-hamiltonian-np","kind":"well-posed","literature_status":"open","n":"1","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 $H = \\operatorname{sum}_i h_i$ 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), 2D qubits (Schuch 2011), 2D qutrits and factorized terms of any dimension (Irani and Jiang, arXiv:2309.04910).","problem_ref":null,"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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