Quantum chemistry: FeMoCo and the catalyst prize

Algorithm preset

Logical qubits

Toffoli gate count

T-depth (serial layers)

Physical error rate

Code cycle time

Error budget

Physical qubits (total)

Estimated runtime

Code distance

Surface-code rounds of redundancy

Data-block physical qubits

2 × logical × d²

T-gate count

4 T per Toffoli

Physical per logical

Error-correction overhead factor

Highlighted share: magic-state factories (conservative bound shown).

Quantum chemistry: the application that could pay for the machine

Simulating strongly correlated molecules is the canonical "useful before it's famous" quantum application. The flagship benchmark is the FeMo cofactor of nitrogenase (FeMoCo) - nature's nitrogen-fixing catalyst. Reiher, Wiebe, Svore, Steiger and Troyer (2017) showed a fault-tolerant machine could elucidate its reaction mechanism in weeks with on the order of 10⁸-10⁹ physical qubits under conservative assumptions; later qubitization and tensor-hypercontraction methods (Lee et al. 2021 and successors) cut logical gate counts by orders of magnitude.

The calculator is pre-loaded with an order-of-magnitude FeMoCo-style estimate: ~500 logical qubits and 10¹⁰ Toffoli-equivalent gates. That lands around 1-2 million physical qubits and a few days of runtime at superconducting speeds - plausible mid-2030s hardware territory.

Why it matters: fertilizer production consumes ~2% of world energy. Better catalysts, batteries, and superconductors are the promise.
Why estimates vary 100x: basis-set size, target precision, and which Hamiltonian representation you pick move T-counts enormously. Treat any single number as a scenario, not a spec.
What to watch: the gap between "logical qubits announced" and "logical error rates demonstrated" - chemistry needs both at once.

Sources: Reiher et al., PNAS 114 (2017), arXiv:1605.03590 · Lee et al., PRX Quantum 2, 030305 (2021), arXiv:2011.03494 · Fowler et al. 2012 surface-code model.