Recent advances in neural quantum states application to condensed-matter systems are reviewed, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics.
Abstract
Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.
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