PIRSA:21010020

Video URL

https://pirsa.org/21010020

Unreasonable effectiveness of methods from theoretical computer science in quantum many-body physics

Anshu, A. (2021). Unreasonable effectiveness of methods from theoretical computer science in quantum many-body physics. Perimeter Institute for Theoretical Physics. https://pirsa.org/21010020

Anshu, Anurag. Unreasonable effectiveness of methods from theoretical computer science in quantum many-body physics. Perimeter Institute for Theoretical Physics, Jan. 28, 2021, https://pirsa.org/21010020 

          @misc{ scivideos_PIRSA:21010020,
            doi = {10.48660/21010020},
            url = {https://pirsa.org/21010020},
            author = {Anshu, Anurag},
            keywords = {Quantum Information},
            language = {en},
            title = {Unreasonable effectiveness of methods from theoretical computer science in quantum many-body physics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {jan},
            note = {PIRSA:21010020 see, \url{https://scivideos.org/index.php/pirsa/21010020}}
          }

Anurag Anshu Harvard University

Talk numberPIRSA:21010020
DOI10.48660/21010020
Source RepositoryPIRSA
Talk Type Scientific Series
Subject

Abstract

A central challenge in quantum many-body physics is a characterization of properties of `natural' quantum states, such as the ground states and Gibbs states of a local hamiltonian. The area-law conjecture, which postulates a remarkably simple structure of entanglement in gapped ground states, has resisted a resolution based on information-theoretic methods. We discuss how the right set of insights may come, quite unexpectedly, from polynomial approximations to boolean functions. Towards this, we describe a 2D sub-volume law for frustration-free locally-gapped ground states and highlight a pathway that could lead to an area law. Similar polynomial approximations have consequences for entanglement in Gibbs states and lead to the first provably linear time algorithm to simulate Gibbs states in 1D. Next, we consider the task of learning a Hamiltonian from a Gibbs state, where many-body entanglement obstructs rigorous algorithms. Here, we find that the effects of entanglement can again be controlled using tools from computer science, namely, strong convexity and sufficient statistics.