One-step generation of cluster states in multiple flux qubits coupled with a nanomechanical resonator

We propose a scheme to efficiently produce large cluster states by using many superconducting Josephson junction flux qubits coupling to the quantized nanomechanical resonator (NAMR). This coupling is independently controlled by an external coupling magnetic field. Through controlling the parameter of system, the cluster states are generated by this scheme. Also, our approach is convenient for implementing one way quantum computing.