  Most realistic solid state devices considered as qubits are not true
two-state systems but multi-level systems. They can approximately be considered
as qubits only if the energy separation of the upper energy levels from the
lowest two is very large. If this condition is not met, the upper states may
affect the evolution and therefore cannot be neglected. Here, we consider
devices with double-well potential as basic logical elements, and study the
effect of higher energy levels, beyond the lowest two, on adiabatic quantum
optimization. We show that the extra levels can be modeled by adding additional
(ancilla) qubits coupled to the original (logical) qubits. The presence of
these levels is shown to have no effect on the final ground state. We also
study their influence on the minimum gap for a set of 8-qubit spin glass
instances.
