Universal distributed quantum computing on superconducting qutrits with dark photons

We present a one-step scheme to construct the controlled-phase gate deterministically on remote transmon qutrits coupled to different resonators connected by a superconducting transmission line for an universal distributed quantum computing. Different from previous works on remote superconducting qubits, the present gate is implemented with coherent evolutions of the entire system in the all-resonance regime assisted by the dark photons to robust against the transmission line loss, which allows the possibility of the complex designation of a long-length transmission line to link lots of circuit QEDs. The length of the transmission line can reach the scale of several meters, which makes our scheme is suitable for the large-scale distributed quantum computing. This gate is a fast quantum entangling operation with a high fidelity of about 99%. Compare with previous works in other quantum systems for a distributed quantum computing, under the all-resonance regime, the present proposal does not require classical pulses and ancillary qubits, which relaxes the difficulty of its implementation largely.