Neural Importance Resampling: A Practical Sampling Strategy for Neural Quantum States

Neural quantum states (NQS) have emerged as powerful tools for simulating many-body quantum systems, but their practical use is often hindered by limitations of current sampling techniques. Markov chain Monte Carlo (MCMC) methods suffer from slow mixing and require manual tuning, while autoregressive NQS impose restrictive architectural constraints that complicate the enforcement of symmetries and the construction of determinant-based multi-state wave functions. In this work, we introduce Neural Importance Resampling (NIR), a new sampling algorithm that combines importance resampling with a separately trained autoregressive proposal network. This approach enables efficient and unbiased sampling without constraining the NQS architecture. We demonstrate that NIR supports stable and scalable training, including for multi-state NQS, and mitigates issues faced by MCMC and autoregressive approaches. Numerical experiments on the 2D transverse-field Ising and $J_1$-$J_2$ Heisenberg models show that NIR outperforms MCMC in challenging regimes and yields results competitive with state of the art methods. Our results establish NIR as a robust alternative for sampling in variational NQS algorithms.