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PIRSA:14070031

Video URL

https://pirsa.org/14070031

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

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

Barbara Terhal Delft University of Technology

Talk numberPIRSA:14070031
DOI10.48660/14070031
Source RepositoryPIRSA
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