  Quantifying and verifying the control level in preparing a quantum state are
central challenges in building quantum devices. The quantum state is
characterized from experimental measurements, using a procedure known as
tomography, which requires a vast number of resources. Furthermore, the
tomography for a quantum device with temporal processing, which is
fundamentally different from the standard tomography, has not been formulated.
We develop a practical and approximate tomography method using a recurrent
machine learning framework for this intriguing situation. The method is based
on repeated quantum interactions between a system called quantum reservoir with
a stream of quantum states. Measurement data from the reservoir are connected
to a linear readout to train a recurrent relation between quantum channels
applied to the input stream. We demonstrate our algorithms for quantum learning
tasks followed by the proposal of a quantum short-term memory capacity to
evaluate the temporal processing ability of near-term quantum devices.
