Optimizing Quantum Wave Functions with Automatic Differentiation

One of the prominent challenges in quantum many-body physics is finding accurate approximations to ground-state wave functions, a task that becomes increasingly complex as the number of particles increases. In this project, we explore how techniques from artificial intelligence, specifically automatic differentiation, can be utilized to tackle this optimization problem in simple model systems from condensed matter and atomic physics. We will introduce the basic principles of automatic differentiation, demonstrate how it can be applied to optimize quantum wave functions by minimizing energy, and discuss how this approach could consolidate with established methods such as quantum Monte Carlo. This work intends to provide both practical computational experience and further insight into how modern AI tools can advance the study of complex quantum systems.