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

Quantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input 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 fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states. Most attempts to delineate quantum machine-learning-related computing capabilities of continuous variables states have relied on non-Gaussian resources. Here, the authors show that linear systems with continuous-variable Gaussian states are a promising platform for the implementation of quantum reservoir computers with universal approximation capabilities