Generation and replication of continuous-variable quadripartite cluster and Greenberger-Horne-Zeilinger states in four chains of superconducting transmission line resonators

Abstract

We consider a system consisting of four independent chains of coupled single-mode superconducting transmission line resonators and a gap-tunable qubit. When the first four resonators of the chains are coupled to the qubit properly driven by multicolor fields, we show that the resonators can be prepared in continuous-variable quadripartite cluster states via the decay of the qubit to its ground state. Moreover, the resulting cluster states can be replicated in the other resonators in column via the nearest-neighbor swapping interaction of the resonators. This means that one can generate a set of cluster states, each of which involves the four resonators from the different chains. By a similar protocol, we show that the generation and replication of continuous-variable quadripartite Greenberger-Horne-Zeilinger states in the chains of the resonators can be achieved. The numerical simulation shows that the present scheme is realizable in current accessible on-chip quantum circuit experiments. The present result may have a potential application for the realization of a large-scale one-way quantum computation.