  Quantum reservoir computing (QRC) has been proposed as a paradigm for
performing machine learning with quantum processors where the training is
efficient in the number of required runs of the quantum processor and takes
place in the classical domain, avoiding the issue of barren plateaus in
parameterized-circuit quantum neural networks. It is natural to consider using
a quantum processor based on superconducting circuits to classify microwave
signals that are analog -- continuous in time. However, while theoretical
proposals of analog QRC exist, to date QRC has been implemented using
circuit-model quantum systems -- imposing a discretization of the incoming
signal in time, with each time point input by executing a gate operation. In
this paper we show how a quantum superconducting circuit comprising an
oscillator coupled to a qubit can be used as an analog quantum reservoir for a
variety of classification tasks, achieving high accuracy on all of them. Our
quantum system was operated without artificially discretizing the input data,
directly taking in microwave signals. Our work does not attempt to address the
question of whether QRCs could provide a quantum computational advantage in
classifying pre-recorded classical signals. However, beyond illustrating that
sophisticated tasks can be performed with a modest-size quantum system and
inexpensive training, our work opens up the possibility of achieving a
different kind of advantage than a purely computational advantage:
superconducting circuits can act as extremely sensitive detectors of microwave
photons; our work demonstrates processing of ultra-low-power microwave signals
in our superconducting circuit, and by combining sensitive detection with QRC
processing within the same system, one could achieve a quantum
sensing-computational advantage, i.e., an advantage in the overall analysis of
microwave signals comprising just a few photons.
