  Efficiently characterising quantum systems, verifying operations of quantum
devices and validating underpinning physical models, are central challenges for
the development of quantum technologies and for our continued understanding of
foundational physics. Machine-learning enhanced by quantum simulators has been
proposed as a route to improve the computational cost of performing these
studies. Here we interface two different quantum systems through a classical
channel - a silicon-photonics quantum simulator and an electron spin in a
diamond nitrogen-vacancy centre - and use the former to learn the latter's
Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter
with an uncertainty of approximately $10^{-5}$. Furthermore, an observed
saturation in the learning algorithm suggests deficiencies in the underlying
Hamiltonian model, which we exploit to further improve the model itself. We go
on to implement an interactive version of the protocol and experimentally show
its ability to characterise the operation of the quantum photonic device. This
work demonstrates powerful new quantum-enhanced techniques for investigating
foundational physical models and characterising quantum technologies.
