Neural Quantum States for Strongly Correlated Matter

Neural-network quantum states (NQS) offer a versatile variational framework for tackling quantum many-body problems in regimes where strong correlations challenge conventional approaches. Recent progress in neural architectures, symmetry enforcement, and optimization has enabled NQS to represent continuous-space wave functions with impressive accuracy and scalability. In this talk, I will present advances in graph-based architectures and Pfaffian pairing ansätze that capture the essential fermionic sign structure. These methods successfully describe ultracold Fermi gases near unitarity, the emergence of Wigner-crystal order in electron gases, and nuclei and neutron-rich matter relevant for neutron-star physics. I will also discuss hybrid NQS–diffusion Monte Carlo approaches that provide controlled routes to improving accuracy and evaluating the nodal surfaces learned by the networks.