CMSA New Technologies in Mathematics Seminar: Unreasonable effectiveness of the quantum complexity view on quantum many-body physics
Anurag Anshu - UC Berkeley Dept. of EE&CS and Harvard Dept. of Computer Science
A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit `low complexity' due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the `area law conjecture' and in the development of efficient algorithms to classically simulate quantum many-body systems.