{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"200c8798669c4cee71822c06018485f1e186a9f8e9298c7e98ddbd9631f5334f","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["a3b98bfc838655c2c7a1abb8e6c9bddedeaddc2f66784b8c1121de63659e139d","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"844ee28fc1b84a90385641ec19f0b8046c4e2217af0736c7f889ce8b4d7a74c2","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.quantum-pcp-conjecture","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Computing the ground energy of a quantum system exactly enough is known to be as hard as any problem a quantum computer can check. The conjecture says that even an estimate with a fixed fractional error stays that hard.","posed_since":"","precise":"Let $H = \\sum_{i=1}^m H_i$ be a $k$-local Hamiltonian on $n$ qubits with $\\mid\\mid H_i\\mid\\mid \\le 1$ and each qubit in $O(1)$ terms. Is it QMA-hard to approximate its ground energy to additive error $\\epsilon m$ for some constant $\\epsilon > 0$? An answer is a proof of QMA-hardness, or a proof that the problem lies in NP (or a smaller class).","problem_ref":"a3b98bfc838655c2c7a1abb8e6c9bddedeaddc2f66784b8c1121de63659e139d","references":"","settled_by":"A QMA-hardness reduction for constant relative precision, or a classical-witness algorithm for it.","status_note":"The weaker NLTS conjecture was proved in 2022 (Anshu, Breuckmann and Nirkhe, arXiv:2206.13228); the full conjecture is open.","title":"The quantum PCP conjecture for local Hamiltonians","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3cd01fb4a12e371cb0980f4c29a004d626bc937c447163db9628de809b58cf43","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"eb428736dd5ccbdf0c76415d6e6b1def1a7c070c595ca31467f3909d4c1bd8d7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"nbS5qNctif9cVPK_asTcB5prsB1CAbx2z8-rQhZ_lqhQbvEKWGiZYbVavo3jtqzarS7CNCuj1k61_5NlGOncDQ"},"schema":"pubphys.envelope/1"},"record_hash":"3cd01fb4a12e371cb0980f4c29a004d626bc937c447163db9628de809b58cf43","leaf_index":3722}