Generation of quantum-dot cluster states with superconducting transmission line resonator

We propose an efficient method to generate cluster states in spatially separated double quantum dots with a superconducting transmission line resonator (TLR). When the detuning between the double-dot qubits transition frequency and the frequency of the full wave mode in the TLR satisfies some conditions, an Ising-like operator between arbitrary two separated qubits can be achieved. Even including the main noise sources, it's shown that the high fidelity cluster states could be generated in this solid system in just one step.