{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"af5b206fe21a487fbbdc103fc54cea5f38667ff2f96b36e4dd22de4c554b9a84","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"fc8e07db9708a6a740b3a04e7a501867e1878b19a539462e94f05700dc003f8e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.hamiltonian-complexity.2d-gapped-ground-energy","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"For one-dimensional systems with an energy gap, a classical computer can provably find the ground energy quickly. Whether the same holds for two-dimensional gapped systems is unknown.","posed_since":"2015","precise":"Is there a classical algorithm that, for every $2\\mathrm{D}$ nearest-neighbour Hamiltonian on $n$ qudits with spectral gap $\\Delta = \\Omega(1)$, outputs the ground energy to additive error $1/\\operatorname{poly}(n)$ in time $\\operatorname{poly}(n)$? The $1\\mathrm{D}$ case is in $\\mathrm{P}$ (Landau, Vazirani and Vidick 2015); without the gap promise the $2\\mathrm{D}$ problem is QMA-complete.","problem_ref":null,"references":"","settled_by":"A polynomial-time algorithm with proof, or a hardness result for the gapped 2D promise problem.","status_note":"","title":"Classical efficiency of 2D gapped ground-state energy 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