Realizable Hamiltonians for universal adiabatic quantum computers

It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse ${\ensuremath{\sigma}}^{x}{\ensuremath{\sigma}}^{x}$ coupling. We also show the universality and QMA-completeness of spin models with only one-local ${\ensuremath{\sigma}}^{z}$ and ${\ensuremath{\sigma}}^{x}$ fields and two-local ${\ensuremath{\sigma}}^{z}{\ensuremath{\sigma}}^{x}$ interactions.