Trace-distance characterization of recurrent pairwise synchronization in cavity-coupled superconducting qubits

Abstract

We theoretically investigate recurrent pairwise synchronization in three super?conducting qubits coupled to a common single-mode microwave cavity. The qubits interact indirectly through the cavity field and are driven by a coher?ent microwave field. We obtain the coherent dynamics in the dressed-state basis and quantify pairwise synchronization by the trace distance between reduced single-qubit density matrices. The trace-distance dynamics exhibit oscillatory wave-packet structures, with low-trace-distance regions identifying finite syn?chronization windows. An envelope-threshold procedure is introduced to extract the representative duration of these windows. By varying the middle-qubit coupling strength and the relative coupling ratio of the outer qubits, we con?struct a parameter-dependent map of the synchronization-window duration. The duration decreases rapidly with increasing relative outer-qubit coupling and becomes weakly dependent on the middle-qubit coupling in the stronger-coupling regime. These results provide a reduced-state-based characterization of coherent collective dynamics in multiqubit circuit-QED systems.