{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"cdf8cf6bbbda49c4a83c788b07b2ebe396da3b7b771b3849769b5cc15b486263","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9a12582b253095057bd7e38514b09a17d67c87e85b3125a1090f28941fa2ad41","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.quantum-chemistry-algorithms.hubbard-resource-estimate","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The two-dimensional Hubbard model, a simple model of electrons hopping on a grid and repelling each other, is a likely first case where a quantum computer could outdo classical methods. How many error-corrected qubits and operations that would take is not pinned down.","posed_since":"","precise":"For the 2D Fermi-Hubbard model at $U/t = 8$ and hole doping near $1/8$ on L x L lattices, determine the minimum logical qubit count and Toffoli count for phase estimation to give the energy per site to accuracy $10^{-3} t$ at a size L beyond reliable classical extrapolation, including state-preparation cost. Published estimates (e.g. Kivlichan et al., Quantum 2020) give roughly 10^6-10^8 Toffoli gates for lattices of about $10 x 10 \\text{ to } 20 x 20$ sites, without full overlap costs (figures approximate).","problem_ref":null,"references":"","settled_by":"An end-to-end resource estimate including state preparation, paired with the best classical error bars at the same L.","status_note":"","title":"Fault-tolerant cost to beat classical methods on the 2D Hubbard model","topic_ref":"7a5b2e4d74deb25e82b2175151e253081cb18bcfd07a0463c8d69af524e27dcb"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"561018b85d0fe7b3684ea396f1b1026020ca6fa8c1dcb46f6881824171560403","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"18c682dc12a2dd192b50840d74d4f65d335893e94aaa6c54e259ec711762ebe3","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"I3SDaHAvDp_zwgfmCcH4eSplFNtF7jZl-mShv9GSlThHdYg7sCvBqAkvA9-IIlncnv57vunr-0gO6LRfyCNSDQ"},"schema":"pubphys.envelope/1"},"record_hash":"561018b85d0fe7b3684ea396f1b1026020ca6fa8c1dcb46f6881824171560403","leaf_index":2028}