  Differentiable models of physical systems provide a powerful platform for
gradient-based algorithms, with particular impact on parameter estimation and
optimal control. Quantum systems present a particular challenge for such
characterisation and control, owing to their inherently stochastic nature and
sensitivity to environmental parameters. To address this challenge, we present
a versatile differentiable quantum master equation solver, and incorporate this
solver into a framework for device characterisation. Our approach utilises
gradient-based optimisation and Bayesian inference to provide estimates and
uncertainties in quantum device parameters. To showcase our approach, we
consider steady state charge transport through electrostatically defined
quantum dots. Using simulated data, we demonstrate efficient estimation of
parameters for a single quantum dot, and model selection as well as the
capability of our solver to compute time evolution for a double quantum dot
system. Our differentiable solver stands to widen the impact of physics-aware
machine learning algorithms on quantum devices for characterisation and
control.
