The complexity of quantum spin systems on a two-dimensional square lattice
Roberto I. Oliveira, Barbara M. Terhal · CERN Document Server (European Organization for Nuclear Research) · 2008
The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are restricted to a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate 2-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation.