{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8083aae2f43fcf54ced791951210158030f6dd47dc7c187d7c7d06ace7128030","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"28e5bc7a2f7f47f1788972ad3d272d6f2be64ae5c16dd63aea9d16826c39a415","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.hamiltonian-complexity.nlss-conjecture","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Some quantum systems are now known to have no simple low-energy states that a shallow circuit can make. A stronger claim, that no low-energy state can even be sampled by a classical computer, is unproved.","posed_since":"2022","precise":"Does there exist a family of $O(1)$-local Hamiltonians on $n$ qubits and a constant $\\epsilon > 0$ such that every state with energy below $E_{0} + \\epsilon m$ fails to be classically sampleable in the sense of Gharibian and Le Gall (2022), i.e. no $\\operatorname{poly}(n)$ classical algorithm samples its computational-basis distribution with the required query access?","problem_ref":null,"references":"","settled_by":"An explicit Hamiltonian family with a proof that no low-energy state is classically sampleable.","status_note":"2025 work excluded restricted classes (Clifford, near-Clifford and fermionic Gaussian low-energy states, e.g. arXiv:2502.15368).","title":"No low-energy sampleable states 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