Explicitly correlated wavefunctions as classical seeds and property references for sample-based quantum diagonalization beyond the Born–Oppenheimer approximation

This work evaluates how well hybrid classical–quantum simulation methods capture notonly the energy of small atomic and molecular systems, but also their other properties: contactdensities, molecular structure, and state identity — the spin sector a computed state actuallylives in. It employs explicitly correlated Gaussian (ECG) wavefunctions both as references forevaluating these properties and as classical seeds for sample-based quantum diagonalization(SQD), on the simulator and on IBM quantum hardware. Our testbeds — positronium hydride,the muonic heliumlike ions, the HD+ molecular ion, and the positronium anion and molecule —realize three typical failure regimes: boxes that lack the property no matter how configurationsare selected, boxes that hold it exactly with no selection needed, and the middle regime where theselection itself decides. In every regime the property error dwarfs the energy error: a subspacecan converge the energy to microhartrees while misstating an annihilation rate, a bond length,or the spin by whole percent. Property fidelity, not energy, is the discriminating test of amulticomponent simulation.