Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack

Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established tools. Here, we present a general and efficient method for learning the NN representation of an arbitrary many-body complex wave function from its $N$-particle probability density and probability current density. Having reached overlaps as large as $99.9\%$, we employ our neural wave function for pre-training to effortlessly solve the fractional quantum Hall problem with Coulomb interactions and realistic Landau-level mixing for as many as $25$ particles. Our work demonstrates efficient, accurate simulation of highly-entangled quantum matter using general-purpose deep NNs enhanced with physics-informed initialization.