  An algebraic method has been developed which allows one to engineer several
energy levels including the low-energy subspace of interacting spin systems. By
introducing ancillary qubits, this approach allows k-body interactions to be
captured exactly using 2-body Hamiltonians. Our method works when all terms in
the Hamiltonian share the same basis and has no dependence on perturbation
theory or the associated large spectral gap. Our methods allow problem instance
solutions to be embedded into the ground energy state of Ising spin systems.
Adiabatic evolution might then be used to place a computational system into
it's ground state.
