Enhancing quantum-classical configuration interaction methods using a neural-network classifier

Abstract: Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a $\times 5$ reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.