Scalable Neural Quantum States with Modern Language Modeling

Scaling neural representations to increasingly large quantum many-body systems remains a central challenge in quantum physics. Despite the success of Neural Quantum States (NQS), their dependence on costly Monte Carlo sampling and second-order optimizations fundamentally limits their scalability to large systems. Here, we introduce FastNQS, a transformer-based variational framework that combines autoregressive Born sampling, FlashAttention-accelerated wavefunction evaluation, and Muon optimization. Across benchmarks on the transverse-field Ising model, two-dimensional $J_1$, $J_1\text{-}{J}_2$, and random-bond Heisenberg models, FastNQS achieves competitive accuracy against Parallel RNN or ViT-based NQS baselines, while being significantly faster: an approximately $23.6\times$ speedup over ViT-based NQS in end-to-end runtime per step. The results highlight modern language modeling as a practical route toward scalable neural quantum states.