We will discuss recent progress in the learnability of various classes of important quantum many-body states, such as Gibbs states, shallow quantum circuits and matrix product states. Our primary focus will be provably efficient algorithms, which often reveal new structures in the quantum states. Locality play a key role in these results, requiring measurements that only act on a few qubits in an entangling way. We will also highlight key challenges in further progress, in particular the search for optimal algorithms.

Speaker Biography：Anurag Anshu is an Assistant Professor of Computer Science at Harvard University. He received his PhD from National University of Singapore, focusing on quantum information theory. His research interests include quantum Hamiltonian complexity, quantum fault tolerance and quantum learning theory.