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Adiabatic quantum optimization with qudits

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.