Optimizing Quantum Wave Functions with Automatic Differentiation: An Educational Perspective

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 the broader range of utilization for other STEM fields. The project will further highlight how automatic differentiation can be utilized to study basics of machine learning and how a multitude of STEM fields can utilize automatic differentiation as a tool for education and general computational literacy for college undergraduate students.