Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a reservoir we consider a quantum harmonic network modeling e.g. linear quantum optical systems. We prove that unlike universal quantum computing, universal reservoir computing can be achieved without non-Gaussian resources. We find that encoding the input time series into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical intense fields or thermal fluctuations. Our results introduce a new research paradigm for reservoir computing harnessing the dynamics of a quantum system and the engineering of Gaussian quantum states, pushing both fields into a new direction.
We acknowledge the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711) and through the QUARESCproject (PID2019-109094GB-C21 and C-22 / AEI/ 10.13039/501100011033).We also acknowledgefunding by CAIB through the QUAREC project (PRD2018/47). The work of MCS has been supportedby MICINN/AEI/FEDER and the University of the Balearic Islands through a “Ramon y Cajal” Fellowship (RYC-2015-18140). VP acknowledges financial supportfrom the European Research Council under the Consol-idator Grant COQCOoN (Grant No. 820079).