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.

We acknowledge the Spanish State Research Agency, through the María de Maeztu project CEX2021-001164-M funded by the MCIU/AEI/10.13039/501100011033 and by ERDF, EU and through the COQUSY project PID2022-140506NB-C21 and -C22 funded by MCIU/AEI/10.13039/501100011033 and by ERDF, EU, MINECO through the QUANTUM SPAIN project, and EU through the RTRP—NextGenerationEU within the framework of the Digital Spain 2025 Agenda. JN gratefully acknowledges financial support from the Academy of Finland under Project No. 348854. GLG is funded by the Spanish Ministerio de Educación y Formación Profesional/Ministerio de Universidades and co-funded by the University of the Balearic Islands through the Beatriz Galindo program (BG20/00085).

With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001164-M).

Peer reviewed