{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"45c6f7b900cd2badfab43108035066def52feeb81cc5e5b4ce6da180ff65ef3b","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["561018b85d0fe7b3684ea396f1b1026020ca6fa8c1dcb46f6881824171560403","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"0e2cd91272838229d6ad1897111eb709190d20a0b8abd2667bfa375702e8a33f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"qi.quantum-chemistry-algorithms.hubbard-resource-estimate","kind":"well-posed","literature_status":"open","n":"2","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 $2\\mathrm{D}$ 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 $10 \\times 10 \\text{ to } 20 \\times 20$ sites, without full overlap costs (figures approximate).","problem_ref":"561018b85d0fe7b3684ea396f1b1026020ca6fa8c1dcb46f6881824171560403","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ca6e2b252d91b9b0c42d6fb812fc0da6df7b08e726bfc91ed529bfbd7ae2c3ba","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"abcc65f716aa1106576cd5b5a017b0a0aa7c3d6e2a9bba6f1354c50b02d90457","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ZLZIUmUpC52qIRkXxGxtQZCbvwA85uCqg9PZ5ILOKcNHGIEnHONAwi4AfupgXD0TUAja0ePV1yirrvflqHKRDA"},"schema":"pubphys.envelope/1"},"record_hash":"ca6e2b252d91b9b0c42d6fb812fc0da6df7b08e726bfc91ed529bfbd7ae2c3ba","leaf_index":3740}