Learning many-body Hamiltonians with Heisenberg-limited scaling

Estimating parameters in many-body Hamiltonians from dynamics is a fundamental problem in physics. Unlike classical parameter estimation problems where N samples can only guarantee a precision of order N^{-1/2}, quantum enhanced protocols can achieve a precision scaling of N^{-1}, which is known as the Heisenberg limit. However, these protocols are difficult to scale up to large system size, especially when the quantum system is not efficiently simulable on a classical computer. In this talk, I will introduce the first efficiently scalable algorithm to learn a many-body Hamiltonian with Heisenberg-limited scaling. This algorithm also has many features that are friendly to experimental implementation, and is provably asymptotically optimal. I will also talk about the ideas from quantum simulation algorithms that inspired this work.