Classical references for quantum chemistry
Quantum Chemistry
In iron–sulfur clusters the electrons interact so strongly that standard approximations struggle, which is why molecules like this are popular test cases for quantum algorithms. But to know whether a quantum method actually helps, you first need a trustworthy classical answer to compare against. This project builds that reference and checks it from several independent directions.
The checked Davidson reference
−116.605609120429 Eh
The checked full-space Davidson state reaches −116.605609120429 Eh, with residual 9.86×10⁻⁸ Eh. Block2 DMRG at M=4000 is 2.607 µEh above that state. The Davidson value is a one-sided variational upper bound; the residual target was not reached. Tested quantum proposals have not demonstrated an advantage over matched classical controls.
Comparing variational states and reported hybrid baselines in the same active space.
The energy ladder puts the gaps on a common scale. The external HCI and HI-VQE entries are reported baselines, while the Davidson state was explicitly rechecked in this work.
| State | Energy (Eh) | Gap (µEh) |
|---|---|---|
| Davidson Phase B | −116.60560912042881 | 0 |
| DMRG M=4000 | −116.60560651330825 | 2.607 |
| DMRG M=2000 | −116.60554090347244 | 68.217 |
| External HCI / QAT #187 | −116.605425 | 184.120 |
| External HI-VQE / QAT #114 | −116.6046821 | 927.020 |
Convergence & independent checks
The checked full-space Davidson state reaches −116.60560912042881 Eh with residual 9.8649×10⁻⁸ Eh.
The state spans CAS(30e,20o): 40 spin orbitals and 240,374,016 fixed-spin determinants.
Direct and reduced-density-matrix energy evaluations agree to 3.98×10⁻¹³ Eh; the checked spin expectation is approximately 5.96×10⁻¹¹.
The residual tracks eigenstate quality during the Phase B refinement. Its final value remains above the requested tolerance even though the energy changes very little.
This view resolves the small changes near the final reference energy. Use it alongside the residual rather than interpreting a flat energy trace as proof of convergence.
The quantum-proposal comparison is read against matched classical controls. The tested proposals have not established an advantage under those comparisons.
Iron–sulfur clusters contain strongly interacting electrons, making them useful tests of electronic-structure methods. Here the active space contains 30 electrons in 20 spatial orbitals. Even after fixing the spin sector, the explicit determinant space contains more than 240 million states, so both numerical correctness and computational resources matter.
A variational energy gives an upper bound, but a very small energy change does not guarantee that an eigenstate is fully converged. The residual checks how closely the explicit state satisfies the eigenvalue equation. Comparing it with norm, spin, and independently evaluated energies makes the quality of the reference easier to assess before judging a quantum proposal.
References & reproduction