Scheme of preparing cluster states with cat qubits

Cluster states are essential quantum resources for one-way quantum computations and quantum networks. The reliable generation of cluster states in specific quantum systems is crucial for initializing complex quantum operations. In this paper, we introduce an efficient scheme for the deterministic preparation of a cluster state via circuit quantum electrodynamics (QED). Our scheme involves four individual microwave resonators, each of which is coupled to a superconducting transmon qutrit. We demonstrated that a four-cqubit cluster state can be achieved using three controlled-phase gate operations. The cluster state is prepared deterministically, eliminating the need for measurement-based feedback. Throughout these operations, the qutrit remains in its ground state, effectively minimizing decoherence from the qutrit. Numerical simulations suggest that our scheme can generate high-fidelity cluster states using current-circuit QED technology. We believe that our model will facilitate exploration of future large-scale continuous-variable quantum information processing systems.