PIRSA:21010020

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

APA

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

MLA

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

BibTex

          @misc{ pirsa_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},
            year = {2021},
            month = {jan},
            note = {PIRSA:21010020 see, \url{https://pirsa.org}}
          }
          

Anurag Anshu Harvard University

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.