Quantum ground state optimization

A fundamental computational question in physics is to understand the equilibrium state of a system composed of many particles. In the setting of quantum mechanics, the system is described by a self-adjoint operator, so-called Hamiltonian, and the goal is to compute its minimum eigenvalue or ground energy. After describing the problem in detail, I will explain how tools from convex optimization such as semidefinite programming and sums of squares relaxation can be used to study it, and if time permits, how new entropy constraints can be used to strengthen such relaxations.