PIRSA:14120006

Ground state connectivity of local Hamiltonians

Sikora, J. (2014). Ground state connectivity of local Hamiltonians. Perimeter Institute. https://pirsa.org/14120006

Sikora, Jamie. Ground state connectivity of local Hamiltonians. Perimeter Institute, Dec. 01, 2014, https://pirsa.org/14120006 

          @misc{ pirsa_PIRSA:14120006,
            doi = {10.48660/14120006},
            url = {https://pirsa.org/14120006},
            author = {Sikora, Jamie},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Ground state connectivity of local Hamiltonians},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {dec},
            note = {PIRSA:14120006 see, \url{https://pirsa.org}}
          }

Jamie Sikora

Talk number
PIRSA:14120006
Collection
Talk Type
Subject
Abstract

The study of ground spaces of local Hamiltonians is a fundamental task in condensed matter physics. In terms of computational complexity theory, a common focus in this area has been to estimate a given Hamiltonian’s ground state energy. However, from a physics perspective, it is sometimes more relevant to understand the structure of the ground space itself. In this talk, we pursue the latter direction by introducing the notion of “ground state connectivity” of local Hamiltonians. In particular, we show that determining how “connected” the ground space of a local Hamiltonian is can range from QCMA-complete to NEXP-complete. (Here, QCMA is the same as QMA, but with a classical witness.) As a result, we obtain a natural QCMA-complete problem, a task which has generally proven difficult since the conception of QCMA over a decade ago.