Spin audit of SQD/QSCI quantum-chemistry benchmarks on iron–sulfur clusters

Author here. Background, for anyone who hasn't followed this fight: IBM's iron–sulfur SQD results (Sci. Adv. 2025) are one of the flagship "quantum computers are useful for chemistry now" claims, and a published critique (arXiv:2501.07231) argues the quantum samples never beat classical selected-CI at matched cost. That argument is still live. Both sides have been arguing about energies. Neither measured which electronic state these calculations actually converge to. So I measured it. ⟨S²⟩ comes out between 4.7 and 7.0 depending on the system and the subspace size, where the target these papers name is a singlet at ⟨S²⟩ = 0. Every starting guess I tried lands in the same place, and the error at convergence is about the size of the spin-state ladder itself, which is the physics under dispute. IBM ships a mitigation for this. Run exactly as shipped, using their driver, their recovery loop and their own spin_square() diagnostic, it moves the ground energy by under a nanohartree while making the subspace 4.00x bigger: 194,481 determinants against 48,600. It makes a singlet representable. It never produces one. Their solver also takes a spin_sq argument that would target the singlet directly, and the default pipeline never sets it. I filed that narrow part on their tracker yesterday, before posting this: https://github.com/Qiskit/qiskit-addon-sqd/issues/337 . A maintainer answered and closed it the same day, and his answer is the useful part. The flag, in his words, augments the sampled subspace by using alpha CI strings as beta strings and vice versa. That is a statement about which determinants span the space, not about what spin the returned state comes out in, which is exactly what the measurement says. He did not contest the numbers. The second question, whether the default path is meant to reach spin_sq at all, is still unanswered. The obvious objection is that this is all my own reimplementation, so here's the part that isn't. IBM's data-availability archive for t