PIRSA:14110131

Classifying Hamiltonians in terms of computational complexity

Terhal, B. (2014). Classifying Hamiltonians in terms of computational complexity. Perimeter Institute. https://pirsa.org/14110131

Terhal, Barbara. Classifying Hamiltonians in terms of computational complexity. Perimeter Institute, Nov. 26, 2014, https://pirsa.org/14110131 

          @misc{ pirsa_PIRSA:14110131,
            doi = {10.48660/14110131},
            url = {https://pirsa.org/14110131},
            author = {Terhal, Barbara},
            keywords = {Quantum Information},
            language = {en},
            title = {Classifying Hamiltonians in terms of computational complexity},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {nov},
            note = {PIRSA:14110131 see, \url{https://pirsa.org}}
          }

Barbara Terhal Delft University of Technology

DOI 10.48660/14110131
Collection
Talk Type Scientific Series
Subject

Abstract

Quantum many-body systems ranging from a many-electron atom to a solid material are described by effective Hamiltonians which are obtained from more accurate Hamiltonians by neglecting or treating weak interactions perturbatively. Quantum complexity theory asks about the quantum computational power of such quantum many-body models for both practical as well as fundamental purposes. Three distinct computational classes have emerged within this framework: namely (1) classical Hamiltonians such as the Ising model, (2) sign-free or stoquastic Hamiltonians such as the transverse field Ising model, and (3) fully quantum Hamiltonians such as the Heisenberg model. Each class can be characterized by certain prototype universal Hamiltonians which can encode the physics of any other Hamiltonian in that class. We will show how this encoding is established through the use of perturbation theory via perturbative gadgets. We will discuss the technical expression of this classification in terms of the complexity classes NP, Stoquastic MA and QMA and the power of these Hamiltonians for performing quantum adiabatic computation.