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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 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