PIRSA:14070031

Space-Time Circuit-to-Hamiltonian construction and Its Applications

Terhal, B. (2014). Space-Time Circuit-to-Hamiltonian construction and Its Applications. Perimeter Institute. https://pirsa.org/14070031

Terhal, Barbara. Space-Time Circuit-to-Hamiltonian construction and Its Applications. Perimeter Institute, Jul. 23, 2014, https://pirsa.org/14070031 

          @misc{ pirsa_PIRSA:14070031,
            doi = {10.48660/14070031},
            url = {https://pirsa.org/14070031},
            author = {Terhal, Barbara},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Space-Time Circuit-to-Hamiltonian construction and Its Applications},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {jul},
            note = {PIRSA:14070031 see, \url{https://pirsa.org}}
          }

Barbara Terhal Delft University of Technology

DOI 10.48660/14070031
Collection
Talk Type Scientific Series
Subject

Abstract

The circuit-to-Hamiltonian construction translates a dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev construction uses one global clock for all qubits while we consider a different construction in which a clock is assigned to each point in space where a qubit of the quantum circuit resides. We show how one can apply this construction to one-dimensional quantum circuits for which the circuit Hamiltonian realizes the dynamics of a vibrating string. We discuss how the construction can be used (1) in quantum complexity theory to obtain new and stronger results in QMA and (2) how one can realize, based on this construction, universal quantum adiabatic computation and a universal quantum walk using a 2D interacting particle Hamiltonian. See http://arxiv.org/abs/1311.6101