Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders

Neural Quantum States (NQS) are a remarkably expressive class of variational ansätze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.