Absorbing Many-Body Correlations into Core-Optimized Orbitals

The cost of simulating quantum many-body systems - on classical or quantum hardware - scales with the number of variational parameters, so progress at fixed computational budget hinges on more parameter-efficient ans\"atze. Configuration Interaction (CI) is widely dismissed as parameter-heavy; we show this verdict is an artifact of the orbital basis. Co-optimizing the orbital basis with a sparse CI wavefunction - a method we call Core-Optimized Orbitals (COO) - absorbs a large fraction of the dynamical correlation directly into the single-particle basis, cutting the determinant count by several orders of magnitude beyond the already compact TrimCI ansatz on which it builds. On [Fe$_4$S$_4$] (54e, 36o), a billion-determinant TrimCI+COO wavefunction reaches accuracy that would require $3\!\times\!10^{14}$ determinants in a localized basis. At matched accuracy, it is $8\times$ more compact than the largest unrestricted-DMRG benchmark ($25\times$ with PT2). Across the iron-sulfur series - from [Fe$_2$S$_2$] (30e,20o) to the P-cluster (114e,73o) - TrimCI+COO is $10$-$100\times$ more compact than SU(2)-adapted DMRG with entanglement-minimized orbitals at matched accuracy. A tunable Hubbard-on-graph model factorizes the advantage into an orbital-basis gain and an ansatz gain, the latter capturing multi-center entanglement that resists MPS localization. COO therefore changes the picture of CI efficiency: sparse CI with optimized orbitals can outperform state-of-the-art tensor networks on strongly correlated multi-center systems.