Recent progress in Hamiltonian learning
In the last few years, a number of works have proposed and improved provably efficient algorithms for learning the Hamiltonian from real-time dynamics. In this talk, I will first provide an overview of these developments, and then discuss how the Heisenberg limit, the fundamental precision limit imposed by quantum mechanics, can be reached for this task. I will demonstrate that reaching the Heisenberg limit requires techniques that are fundamentally different from previous ones, and the important roles played by quantum control, conservation laws, and thermalization. I will also discuss open problems that are crucial to the practical implementation of these algorithms.