I've submitted the underlying paper here twice before as a Zenodo link, but it didn't get much discussion. I wrote this new post to be more accessible to non-chemists, plus a couple of things have happened since the last time.

First, IBM merged two PRs (364 and 366) to qiskit-addon-sqd on Sept 9 after I reported the issue. The docs for the symmetrize_spin option now clarify that it "does not guarantee that the state is an eigenvector of the total spin operator S^2". That covers one of the options. IBM hasn't commented on the paper itself, which I've recently updated to v2 on ChemRxiv.

The short version of the post: IBM's released random-input control actually matches their quantum hardware on the smaller iron-sulfur cluster. Also, IBM's flagship paper, the published critique of it, and the RIKEN-IBM Fugaku follow-up all report energies without stating which spin state those energies belong to. If you rebuild the data for the largest [2Fe-2S] size they published, the lowest state has S^2 = 1.3711. They were aiming for a singlet, which should be 0.

You can verify this without relying on my code:

Hardware vs random (takes about 10 seconds in a browser, reading IBM's files directly): https://colab.research.google.com/github/PureStateLabs/sqd-s...

Spin check (takes about 35 seconds, running PySCF on IBM's public integrals): https://github.com/PureStateLabs/sqd-spin-referee/blob/main/...

The last section of the post outlines exactly what would change my mind. If you try to reproduce a number and it doesn't match, let me know here.

Paper: https://doi.org/10.26434/chemrxiv.15006382/v2 Data and code: https://doi.org/10.5281/zenodo.21359922

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