  Reservoir computing is a powerful machine learning paradigm for online time
series processing. It has reached state-of-the-art performance in tasks such as
chaotic time series prediction and continuous speech recognition thanks to its
unique combination of high computational power and low training cost which sets
it aside from alternatives such as traditionally trained recurrent neural
networks, and furthermore is amenable to implementations in dedicated hardware,
potentially leading to extremely compact and efficient reservoir computers.
Recently the use of random quantum systems has been proposed, leveraging the
complexity of quantum dynamics for classical time series processing. Extracting
the output from a quantum system without disturbing its state too much is
problematic however, and can be expected to become a bottleneck in such
approaches. Here we propose a reservoir computing inspired approach to online
processing of time series consisting of quantum information, sidestepping the
measurement problem. We illustrate its power by generalizing two paradigmatic
benchmark tasks from classical reservoir computing to quantum information and
introducing a task without a classical analogue where a random system is
trained to both create and distribute entanglement between systems that never
directly interact. Finally, we discuss partial generalizations where only the
input or only the output time series is quantum.
