  Machine learning techniques have achieved impressive results in recent years
and the possibility of harnessing the power of quantum physics opens new
promising avenues to speed up classical learning methods. Rather than viewing
classical and quantum approaches as exclusive alternatives, their integration
into hybrid designs has gathered increasing interest, as seen in variational
quantum algorithms, quantum circuit learning, and kernel methods. Here we
introduce deep hybrid classical-quantum reservoir computing for temporal
processing of quantum states where information about, for instance, the
entanglement or the purity of past input states can be extracted via a
single-step measurement. We find that the hybrid setup cascading two reservoirs
not only inherits the strengths of both of its constituents but is even more
than just the sum of its parts, outperforming comparable non-hybrid
alternatives. The quantum layer is within reach of state-of-the-art multimode
quantum optical platforms while the classical layer can be implemented in
silico.
