An independent spin audit of IBM's flagship sample-based quantum diagonalization (SQD) results on [2Fe-2S] and [4Fe-4S] iron–sulfur clusters finds that no audited execution converges to the target singlet state (⟨S²⟩ = 0). Measured ⟨S²⟩ values range from 4.7 to 7.0 depending on system and subspace size, with convergence errors matching the spin-state ladder itself.

IBM's shipped mitigation expands the subspace 4.00x (194,481 vs 48,600 determinants) but never produces a singlet. The solver's spin_sq argument targeting the singlet is never set in the default pipeline. Running IBM's archived hardware shots — 2,457,600 on [2Fe-2S] and 3,163,742 on [4Fe-4S] — through their own pipeline shows [2Fe-2S] sits 248 mHa off reference, while [4Fe-4S] converges to a spin-pure triplet (S=1) 1,438 mHa from reference. Their uniform-random null control matches or beats hardware samples in every [2Fe-2S] comparison, and largest [4Fe-4S] runs trail classical HCI by 149 mHa.

The audit, accelerated by Claude under adversarial review, caught five defects and retracted its strongest pro-quantum finding when spin-sector artifacts were exposed. The author challenges critics to exhibit any spin-completed ground manifold with ⟨S²⟩ < 1, or show quantum-sampled subspace beating HCI at matched determinant count.