  We propose a generative quantum learning algorithm, R\'enyi-ADAPT, using the
Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in
which the loss function to be minimized is the maximal quantum R\'enyi
divergence of order two, an unbounded function that mitigates barren plateaus
which inhibit training variational circuits. We benchmark this method against
other state-of-the-art adaptive algorithms by learning random two-local thermal
states. We perform numerical experiments on systems of up to 12 qubits,
comparing our method to learning algorithms that use linear objective
functions, and show that R\'enyi-ADAPT is capable of constructing shallow
quantum circuits competitive with existing methods, while the gradients remain
favorable resulting from the maximal R\'enyi divergence loss function.
