  We develop a resource efficient method by which the ground-state of an
arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state
of a (k-1)-local optimization Hamiltonian. This result is important because
adiabatic quantum algorithms are often most easily formulated using many-body
interactions but experimentally available interactions are generally 2-body. In
this context, the efficiency of a reduction gadget is measured by the number of
ancilla qubits required as well as the amount of control precision needed to
implement the resulting Hamiltonian. First, we optimize methods of applying
these gadgets to obtain 2-local Hamiltonians using the least possible number of
ancilla qubits. Next, we show a novel reduction gadget which minimizes control
precision and a heuristic which uses this gadget to compile 3-local problems
with a significant reduction in control precision. Finally, we present numerics
which indicate a substantial decrease in the resources required to implement
randomly generated, 3-body optimization Hamiltonians when compared to other
methods in the literature.
