A Deterministic Framework for Neural Network Quantum States in Quantum Chemistry

We present a deterministic optimization framework for neural network quantum states (NQS) designed to bypass the sampling variance and slow mixing issues inherent in stochastic optimization. By projecting a neural backflow ansatz onto dynamically evolving configuration subspaces, our method provides a systematic route for optimizing the selected variational component of the wave function and estimating residual correlation through a posthoc second-order perturbative correction. The implementation utilizes a hybrid CPU-GPU architecture that shows empirical sublinear wall-time scaling with respect to the subspace size over the tested range, enabling the calculation of strongly correlated systems, such as the chromium dimer, within Hilbert spaces of 10 23 configurations. Benchmarks on molecular bond dissociations demonstrate that this deterministic approach yields stable convergence and accuracies comparable to selected reference methods in the tested systems.