  We demonstrate a novel approach to reservoir computer measurements using
random matrices. We do so to motivate how atomic-scale devices might be used
for real-world computing applications. Our approach uses random matrices to
construct reservoir measurements, introducing a simple, scalable means for
producing state descriptions. In our studies, two reservoirs, a five-atom
Heisenberg spin chain, and a five-qubit quantum circuit, perform time series
prediction and data interpolation. The performance of the measurement technique
and current limitations are discussed in detail alongside an exploration of the
diversity of measurements yielded by the random matrices. Additionally, we
explore the role of the parameters of the reservoirs, adjusting coupling
strength and the measurement dimension, yielding insights into how these
learning machines might be automatically tuned for different problems. This
research highlights using random matrices to measure simple quantum reservoirs
for natural learning devices and outlines a path forward for improving their
performance and experimental realization.
