One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective
For researchers in quantum many-body physics and machine learning, this work bridges reinforcement learning and NQS optimization, offering a scalable trust-region method that outperforms existing optimizers.
The authors frame variational energy minimization in neural quantum states as a policy-gradient problem and propose Proximal Wavefunction Optimization (PWO), a trust-region algorithm that clips probability ratios and phase increments. PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING on Ising and frustrated spin systems, and scales to a 1.5B-parameter model.
Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated $J_1$-$J_2$ one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a $1.5$B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.