PIRSA:21010002

Complexity phase diagrams

Deshpande, A. (2021). Complexity phase diagrams . Perimeter Institute. https://pirsa.org/21010002

Deshpande, Abinhav. Complexity phase diagrams . Perimeter Institute, Jan. 06, 2021, https://pirsa.org/21010002 

          @misc{ pirsa_PIRSA:21010002,
            doi = {10.48660/21010002},
            url = {https://pirsa.org/21010002},
            author = {Deshpande, Abinhav},
            keywords = {Quantum Information},
            language = {en},
            title = {Complexity phase diagrams },
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jan},
            note = {PIRSA:21010002 see, \url{https://pirsa.org}}
          }

Abinhav Deshpande University of Maryland, College Park

Talk numberPIRSA:21010002
DOI10.48660/21010002
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk, I argue that the question of whether a physical system can be simulated on a computer is important not just from a practical perspective but also a fundamental one. We consider the complexity of simulating Hamiltonians with respect to both dynamics and equilibrium properties. This gives us a classification and a phase diagram of the complexity.  I will cover recent results in this topic, such as a dynamical complexity phase diagram for a long-range bosonic Hamiltonian and a complexity classification of the local Hamiltonian problem in the presence of a spectral gap. I will talk about the physical implications of these results and cover some of the basic proof ideas if time permits.