  Quantum reservoir computing algorithms recently emerged as a standout
approach in the development of successful methods for the NISQ era, because of
its superb performance and compatibility with current quantum devices. By
harnessing the properties and dynamics of a quantum system, quantum reservoir
computing effectively uncovers hidden patterns in data. However, the design of
the quantum reservoir is crucial to this end, in order to ensure an optimal
performance of the algorithm. In this work, we introduce a precise quantitative
method, with strong physical foundations based on the Krylov evolution, to
assess the wanted good performance in machine learning tasks. Our results show
that the Krylov approach to complexity strongly correlates with quantum
reservoir performance, making it a powerful tool in the quest for optimally
designed quantum reservoirs, which will pave the road to the implementation of
successful quantum machine learning methods.
