{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"065f35bfd3e7b057cbb931e3e25ca5baa5df8c5a948379b26a990f346868d8a2","created":"2026-10-03T07:17:54Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0c9cf21c49b7e235519f87e5face4126d30206af22167022cec45ecf4d743388","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"amo.simulator-verification.hard-gibbs-observable","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Hot quantum systems turn out to be easy for classical computers. The question is whether any cooled simulator can reach a regime that is both hard for classical methods and accessible to the hardware.","posed_since":"","precise":"Identify a family of local Hamiltonians and a temperature $T$ for which estimating a local observable in the Gibbs state is classically hard (under standard complexity assumptions), while an analog simulator with realistic cooling can prepare that Gibbs state to accuracy $\\epsilon$. Answer: an explicit family with a hardness proof and a preparation scheme.","problem_ref":null,"references":"","settled_by":"A complexity-theoretic hardness proof for a specific Hamiltonian family plus a cooling scheme with proven or measured accuracy.","status_note":"2024 results showed Gibbs states above a constant temperature are efficiently preparable classically (Bakshi, Liu, Moitra, Tang), so any advantage must be at low T.","title":"A classically hard equilibrium observable an analog simulator can reach","topic_ref":"e8947e412d1aec3755e18a4e515f79785deae1599261032ed3cb02aac34a80b5"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d66fbb5b3ddbde9fe503d7cbb3b94a93dced78c031bd22b3bd61ecdde0e9c8e4","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"af886b2bb66a6d9b52dd7ec85bc38689f2c10d8ff87bfaa8445bc5c7b5b75a4f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"bRUWdurVW6JgOyHL3l2-7O2ZibVcwYpSz3d2DB0FoY-fUi0LOXkKwKuDYqgymiwi7LZplXm5GfduVQ80xFxWCA"},"schema":"pubphys.envelope/1"},"record_hash":"d66fbb5b3ddbde9fe503d7cbb3b94a93dced78c031bd22b3bd61ecdde0e9c8e4","leaf_index":460}