  We study the quantum synchronization between a pair of two-level systems
inside two coupled cavities. By using a digital-analog decomposition of the
master equation that rules the system dynamics, we show that this approach
leads to quantum synchronization between both two-level systems. Moreover, we
can identify in this digital-analog block decomposition the fundamental
elements of a quantum machine learning protocol, in which the agent and the
environment (learning units) interact through a mediating system, namely, the
register. If we can additionally equip this algorithm with a classical feedback
mechanism, which consists of projective measurements in the register,
reinitialization of the register state and local conditional operations on the
agent and environment subspace, a powerful and flexible quantum machine
learning protocol emerges. Indeed, numerical simulations show that this
protocol enhances the synchronization process, even when every subsystem
experience different loss/decoherence mechanisms, and give us the flexibility
to choose the synchronization state. Finally, we propose an implementation
based on current technologies in superconducting circuits.
