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 show that reaching the Heisenberg limit requires techniques that are fundamentally different from previous ones. In the Heisenberg-limited protocols, quantum control, conservation laws, and thermalization all play important roles, and all of these features are system-specific. In particular, I will discuss how to perform Heisenberg-limited Hamiltonian learning for a certain class of continous-variable systems. I will also discuss open problems that are crucial to the practical implementation of these algorithms.

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