Treating the Independent Set Problem by 2D Ising Interactions with Adiabatic Quantum Computing

We construct a nearest-neighbor interaction whose ground states encode the solutions to the NP-complete problem independent set for cubic planar graphs. The important difference to previously used Hamiltonians in adiabatic quantum computing is that our Hamiltonian is spatially local. Due to its special structure our Hamiltonian can be easily simulated by Ising interactions between adjacent particles on a 2D rectangular lattice. We describe the required pulse sequences. Our methods could help to implement adiabatic quantum computing by physically reasonable Hamiltonians like short-range interactions. Therefore, this universal resource Hamiltonian can be used for different graphs by applying suitable control operations. This is in contrast to a previous proposal where the Hamiltonians have to be wired in hardware for each graph. PACS: 03.67.Lx