  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.
