Which state are you converging? A spin audit of sample-based quantum diagonalization benchmarks on iron–sulfur clusters
- 1Pure State Labs
Abstract
Sample-based quantum diagonalization (SQD/QSCI) diagonalizes the Hamiltonian classically in determinant subspaces selected from quantum-circuit samples. Its iron–sulfur demonstrations underpin claims of utility-scale quantum chemistry, and a recent critique disputes them at matched subspace dimension. Both sides compare energies; neither reports which spin state was computed. Our spin audit uses the exact determinant-space ⟨S²⟩, the invariant spectrum of the S² block over quasi-degenerate manifolds, and higher moments (⟨S⁴⟩ to ⟨S⁸⟩) bounding the spin-sector weights. We apply it to the public [2Fe-2S] and [4Fe-4S] benchmarks, IBM's released qiskit-addon-sqd pipeline and published hardware data. No audited execution returned the named singlet at competitive energy; for published states unavailable to direct audit, the energy-only records do not establish singlet identity. Under the audited HCI protocols, selected-CI growth approaches a spin-contaminated state (⟨S²⟩ ≈ 4.7 on [2Fe-2S]) whose samples keep the contamination. Spin-inversion completion leaves the energy and ⟨S²⟩ of these states unchanged. The released [2Fe-2S] hardware samples give no energy advantage over the released uniform-random control. A scalar mean does not identify these states: two audited arms share ⟨S²⟩ ≈ 2.00, but one is a triplet eigenstate (Var(S²) = 3×10⁻⁶) and the other a 2:1 singlet–quintet mixture whose third moment bounds its triplet weight below 10⁻⁴. At the largest published dimension (5.625×10⁷ determinants, reconstructed here from the released support), the lowest root, 170 mHa below the published energy, has ⟨S²⟩ = 1.3711, unchanged under an 18.6-fold residual tightening to 1.1% of the 0.285 mHa gap. Its first two moments, with Var(S²) = 6.9, exclude any decomposition confined to S ≤ 2. Near-singlet character appears only as a non-stationary superposition, because determinant selection does not commute with S². Energy-only benchmarks therefore do not establish convergence to the named state. We recommend reporting spin moments with every energy and controlling spin during selection.
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BibTeX
@misc{vitale2026which,
title = {{Which state are you converging? A spin audit of sample-based quantum diagonalization benchmarks on iron–sulfur clusters}},
author = {Tyler Vitale},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15006382/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006382/v2},
note = {CC BY},
}
RIS
TY - UNPB
TI - Which state are you converging? A spin audit of sample-based quantum diagonalization benchmarks on iron–sulfur clusters
AU - Tyler Vitale
PY - 2026
DA - 2026/09/15
PB - ChemRxiv
DO - 10.26434/chemrxiv.15006382/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006382/v2
AB - Sample-based quantum diagonalization (SQD/QSCI) diagonalizes the Hamiltonian classically in determinant subspaces selected from quantum-circuit samples. Its iron–sulfur demonstrations underpin claims of utility-scale quantum chemistry, and a recent critique disputes them at matched subspace dimension. Both sides compare energies; neither reports which spin state was computed. Our spin audit uses the exact determinant-space ⟨S²⟩, the invariant spectrum of the S² block over quasi-degenerate manifolds, and higher moments (⟨S⁴⟩ to ⟨S⁸⟩) bounding the spin-sector weights. We apply it to the public [2Fe-2S] and [4Fe-4S] benchmarks, IBM's released qiskit-addon-sqd pipeline and published hardware data. No audited execution returned the named singlet at competitive energy; for published states unavailable to direct audit, the energy-only records do not establish singlet identity. Under the audited HCI protocols, selected-CI growth approaches a spin-contaminated state (⟨S²⟩ ≈ 4.7 on [2Fe-2S]) whose samples keep the contamination. Spin-inversion completion leaves the energy and ⟨S²⟩ of these states unchanged. The released [2Fe-2S] hardware samples give no energy advantage over the released uniform-random control. A scalar mean does not identify these states: two audited arms share ⟨S²⟩ ≈ 2.00, but one is a triplet eigenstate (Var(S²) = 3×10⁻⁶) and the other a 2:1 singlet–quintet mixture whose third moment bounds its triplet weight below 10⁻⁴. At the largest published dimension (5.625×10⁷ determinants, reconstructed here from the released support), the lowest root, 170 mHa below the published energy, has ⟨S²⟩ = 1.3711, unchanged under an 18.6-fold residual tightening to 1.1% of the 0.285 mHa gap. Its first two moments, with Var(S²) = 6.9, exclude any decomposition confined to S ≤ 2. Near-singlet character appears only as a non-stationary superposition, because determinant selection does not commute with S². Energy-only benchmarks therefore do not establish convergence to the named state. We recommend reporting spin moments with every energy and controlling spin during selection.
ER -