  Reservoir computing is a versatile paradigm in computational neuroscience and
machine learning, that exploits the non-linear dynamics of a dynamical system -
the reservoir - to efficiently process time-dependent information. Since its
introduction, it has exhibited remarkable capabilities in various applications.
As widely known, classes of reservoir computers serve as universal
approximators of functionals with fading memory. The construction of such
universal classes often appears context-specific, but in fact, they follow the
same principles. Here we present a unified theoretical framework and we propose
a ready-made setting to secure universality. We test the result in the arising
context of quantum reservoir computing.The analysis sheds light on a unified
view of classical and quantum reservoir computing.
