Peter W. Shor, John A. Smolin, et al.
Physical Review Letters
The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA [1]. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on 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 k-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. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian. © Rinton Press.
Peter W. Shor, John A. Smolin, et al.
Physical Review Letters
David P. DiVincenzo, Patrick Hayden, et al.
Foundations of Physics
Barbara M. Terhal, Karl Gerd H. MacDonald
Physical Review Letters
Barbara M. Terhal, Micha Horodecki, et al.
Journal of Mathematical Physics