Adiabatic quantum optimization with qudits

Most realistic solid state devices considered as qubits are not true two-state systems. If the energy separation of the upper energy levels from the lowest two levels is not large, then these upper states may affect the evolution of the ground state over time and therefore cannot be neglected. In this work, we study the effect of energy levels beyond the lowest two energy levels on adiabatic quantum optimization in a device with a double-well potential as the basic logical element. We show that the extra levels can be modeled by adding additional ancilla qubits coupled to the original logical qubits, and that the presence of upper levels has no effect on the final ground state. We also study the influence of upper energy levels on the minimum gap for a set of 8-qubit spin glass instances.