Where classical methods stop for FeMoco-class iron-sulfur clusters
In plain words
The iron-molybdenum cluster in nitrogenase, the enzyme that turns nitrogen from air into ammonia, was long the flagship target for quantum chemistry on quantum computers. A 2026 classical calculation reached the target accuracy for the standard model, so it is open which larger or harder version still needs a quantum computer.
Precise statement
Zhai et al. (arXiv:2601.04621, 2026) report the ground energy of the standard 76-orbital, 113-electron FeMoco model to chemical accuracy ($1.6\,\mathrm{mHa}$), with several spin isomers degenerate within that accuracy, using unrestricted coupled cluster and DMRG at roughly $10^{5}$-$10^{6}$ CPU core hours, while fault-tolerant estimates for the same model need of order 2000 logical qubits and $10^{9}$-$10^{10}$ Toffoli gates (approximate). Identify a chemically meaningful extension (larger active space, catalytic intermediates, relative energies of the near-degenerate spin isomers) where the classical cost to $1.6\,\mathrm{mHa}$ exceeds the quantum cost, with both costs computed explicitly.
What would settle it
A side-by-side classical calculation and fault-tolerant resource estimate for a specified Hamiltonian showing the crossover.
Status in the literature
Unverified note
Classical chemical accuracy for the standard model was reported in January 2026; 2025 algorithm improvements reduced quantum Toffoli counts further.