where Z , X represent the Pauli matrices σ σ z , σ σ x . Such models are used for universal adiabatic quantum computation. The Hamiltonians for the QMA-complete problem can also be restricted to act on a two dimensional grid of qubits or a line of quantum particles with 12 states per particle. If such models were found to be physically realizable, they too could be used to form the building blocks of a universal adiabatic quantum computer.