Adaptive Quantum Generative Training using an Unbounded Loss Function

We propose a generative quantum learning algorithm, Rényi-ADAPT, using the Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in which the loss function to be minimized is the maximal quantum Rényi 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 Rényi-ADAPT is capable of constructing shallow quantum circuits competitive with existing methods, while the gradients remain favorable resulting from the maximal Rénvi divergence loss function.