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Synchronization has recently been explored deep in the quantum regime withelementary few-level quantum oscillators such as qudits and weakly pumpedquantum Van der Pol oscillators. To engineer more complex quantum synchronizingsystems, it is practically relevant to study composite oscillators built upfrom basic quantum units that are commonly available and offer highcontrollability. Here, we consider a minimal model for a composite oscillatorconsisting of two interacting qubits coupled to separate baths, for which wealso propose and analyze an implementation on a circuit quantum electrodynamicsplatform. We adopt a `microscopic' and `macroscopic' viewpoint and study theresponse of the constituent qubits and of the composite oscillator when one ofthe qubits is weakly driven. We find that the phase-locking of the individualqubits to the external drive is strongly modified by interference effectsarising from their mutual interaction. In particular, we discover aphase-locking blockade phenomenon at particular coupling strengths.Furthermore, we find that interactions between the qubits can strongly enhanceor suppress the extent of synchronization of the composite oscillator to theexternal drive. Our work demonstrates the potential for assembling complexquantum synchronizing systems from basic building units, which is of pragmaticimportance for advancing the field of quantum synchronization.

Exploring Quantum Synchronization with a Composite Two-Qubit Oscillator