Possible implementation of adiabatic quantum algorithm with superconducting flux qubits

We show that an $LC$ parametric transducer can be effectively used to monitor an adiabatic evolution of the superconducting flux qubit. We propose a scheme to measure the qubit's state, which is a quantum nondemolition measurement. The scheme can be easily extended to a three-qubit system and allows the reading out of the qubits' states while the system remains in the ground state. An implementation of the adiabatic quantum algorithm MAXCUT for three superconducting flux qubits is discussed.