Stabilizing MinSR for RNN Neural Quantum states

Finding the ground state of a quantum many-body system in two- or three- spatial dimensions remains a major computational challenge. Neural Quantum States (NQS) provide a powerful neural network–based variational framework for representing many-body wavefunctions and solving for the ground-state wavefunctions. Recurrent Neural Networks (RNNs) are particularly promising, as they can efficiently sample wavefunctions without costly Monte Carlo procedures. Recently, RNNs have been considered unstable under curvature-based optimizers such as the minimum-step stochastic reconfiguration (minSR) method, limiting their applicability to large-scale simulation. We show that minSR can be stabilized through various regularization techniques, enabling robust training of RNN-based NQS. Our approach surpasses the Adam optimizer on the one-dimensional transverse-field Ising model and the two-dimensional Heisenberg model and achieves energies that are competitive with state-of-the-art algorithms.