Title: Variational Learning Quantum Wave Functions

Abstract: The quantum many-body problem is ubiquitous in physics, with profound implications for condensed matter, quantum chemistry, and nuclear physics. Solving it accurately presents significant challenges due to the exponential growth of the Hilbert space, limiting the applicability of numerically exact techniques to relatively small systems. In this talk, I will discuss how artificial neural networks can be employed to efficiently represent quantum many-body states. I will focus on a variational Monte Carlo method based on neural-network quantum states, which provides a systematically improvable solution to the nuclear Schrödinger equation with a polynomial cost in the number of nucleons. Beyond the nuclear many-body problem, I will also explore applications to condensed-matter systems, such as cold Fermi gases near the unitary limit. Additionally, I will offer perspectives on accessing the real-time dynamics of quantum many-body systems.