Convexity and Quantum Physics 

Scott Lawrence, Ph.D.; University of Colorado Boulder

Physical systems are often characterized by the minimum of some function. In quantum mechanics, this function is often convex; this is a dramatic simplification. In this talk, I describe recent results on the convex nature of various optimization problems in quantum information, quantum mechanics, and quantum field theory, and show how this perspective on quantum  mechanics, along with tools from the field of convex optimization, gives rise to valuable computational techniques (the most famous of which is the conformal bootstrap).  These methods are made particularly enticing by their applicability to regimes where lattice Monte Carlo encounters the fermion sign problem. As a demonstration, I show how convex optimization may be used to approximate the zero-temperature equation of state of the Thirring model.