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SQD Recovers FeO Model Ground States from IBM Quantum Samples
A preprint reports that sample-based quantum diagonalization recovered ground-state energies for two iron-oxide molecular models using samples from IBM Quantum hardware. For FeO, the method recovered the ground-state doublet to machine prec
Quantum.world Team · Written with AI · fact-checked ·
A preprint posted to arXiv on October 26 reports that sample-based quantum diagonalization (SQD) recovered ground-state energies for two iron-oxide molecular models using samples taken on IBM Quantum hardware. The researchers used the processor to identify electronic configurations, then enlarged those sets with Hamiltonian connectivity and diagonalized the resulting subspaces classically. Their result for iron monoxide, FeO, reached machine-precision agreement with the model’s ground energy using 184 determinants. The work tests a route toward calculations of correlated iron oxides; it does not simulate bulk FeO itself.
IBM hardware samples; classical processing recovers the energies
The study, “Towards Quantum Computation of Bulk FeO,” comes from Daniel Staros, Federico Petrovich, Ammar Kirmani, Daniel N. Blaschke, M. Cerezo and Jian-Xin Zhu. The authors built low-energy models for FeO and rhombic Fe₂O₂ from density-functional-theory-informed orbital data. FeO’s model contains 12 electrons in 16 spin orbitals; Fe₂O₂ has 24 electrons in 32 spin orbitals.
They optimized one-layer Local Unitary Cluster Jastrow circuits in noiseless classical simulations, then ran the fixed circuits on IBM’s ibm_miami processor to collect occupation-number samples. The hardware did not perform the optimization, and the researchers did not update circuit parameters on the processor. Instead, they used measured bitstrings as a guide to which electronic configurations a classical calculation should examine.
“Although raw VQE does not achieve chemical accuracy for the ground state of FeO or Fe₂O₂, SQD with two connectivity shells recovers the exact ground energy for both molecules utilizing remarkably few quantum computational resources.”
Daniel Staros et al., the paper’s authors, write in “Towards Quantum Computation of Bulk FeO”
FeO reaches machine precision in 184 determinants
For FeO, the best variational quantum eigensolver (VQE) state remained 0.173 electronvolts above the model’s ground-state energy. Yet it carried 99.1% ground-space weight, concentrating samples on configurations useful to the next step. Adding one shell of configurations connected by nonzero Hamiltonian matrix elements sharply reduced the error; two shells recovered the ground-state doublet with machine-precision residuals in 184 determinants.
The model’s FeO ground state is a pair of oppositely polarized quintet states, consistent with the experimentally measured ground-state magnetism of gaseous FeO. Its first excitation energy is 2,167 cm⁻¹, closer to the experimental value of about 4,000 cm⁻¹ than earlier quantum-chemistry estimates of 300 cm⁻¹. That comparison is a result of the low-energy model, not a measurement made by the quantum processor.
Fe₂O₂ reveals a limit to compression
The larger Fe₂O₂ calculation also reached chemical accuracy, but its two-shell subspace was already about 85% of the relevant spin sector at the smallest sampling point. The paper cautions that the very small errors at higher sample counts therefore reflect convergence toward a full classical diagonalization, not strong compression. A one-shell expansion offers a more compact intermediate result, reaching chemical accuracy while retaining only part of the determinant sector.
The Fe₂O₂ model also predicts a nonet magnetic ground state, unlike the septet reported in earlier high-accuracy quantum-chemistry work. The authors point to the interaction parameters in their model: its Coulomb repulsion and Hund exchange values were not optimized from first principles specifically for Fe₂O₂. That mismatch makes the result a warning against treating agreement in energy as proof that the model has identified the molecule’s physical magnetic state.
Bulk FeO remains the next calculation
The study’s hardware experiment is a molecular benchmark built to inform later work on the solid. The paper reports that six 16-qubit FeO circuits ran in parallel on disjoint regions of ibm_miami, using 96 physical qubits and producing 120,000 molecular bitstrings from 20,000 executions. For Fe₂O₂, three 32-qubit circuits ran simultaneously using 96 physical qubits; the reported sampling dataset contains 2.7 million molecular samples per sampler.
Scaling the method to periodic FeO would add a substantial classical burden. The authors identify exact diagonalization of the projected Hamiltonian as the framework’s main limit, with the selected spaces growing as more hopping-allowed modes enter the model. They estimate that a bulk calculation could require SQD across hundreds to thousands of k-points, with Brillouin-zone symmetry helping reduce that workload. Their present result is narrower: IBM samples guide a compact classical recovery for FeO, while Fe₂O₂ shows how quickly that compactness can diminish.