{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1e3d44b4ecf518fcd4e524d785a5e84c7fddef656ee6da37743b090da43b24b3","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f1cbbb9a253515c034813de9ecbc309260601407e71cd4cf5353cc7259252a53","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.hamiltonian-complexity.quantum-pcp-conjecture","kind":"well-posed","literature_status":"open","n":"1","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 $H = \\operatorname{sum}_{i=1}^m H_i$ 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":null,"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":"14e3082cf422607e299e3fd37b22598ee6075130731880be56919fb2cecab4a9"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"a3b98bfc838655c2c7a1abb8e6c9bddedeaddc2f66784b8c1121de63659e139d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"99629aaae6a00bc957052472ff069e9d64fa0308850384af64391d21599a4cfb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"tr3wJwmunHc1s3fbicJ8cx2oeBvN9cHlSO5y6sxGhAnSRz-r83UNwnDlvMeP7IGNlmuNIYX0b1DJMv15pSrTDw"},"schema":"pubphys.envelope/1"},"record_hash":"a3b98bfc838655c2c7a1abb8e6c9bddedeaddc2f66784b8c1121de63659e139d","leaf_index":2008}